The purpose of this experiment was to measure the effects of wording on people's behavior.
Method
Participants were randomly assigned to three groups, two experimental and one control. Participants were payed $5 to participate in this experiment and were told that it would only take five minutes of their time, and then were sent into a room with an experimenter who introduced himself and handed participants their instructions.
Participants in the first experimental condition were handed a sheet of paper that said, "Please complete as many push ups as you can without stopping."
Participants in the second experimental condition were handed a sheet of paper that said, "Please complete as many sit ups as you can without stopping."
Participants in the control condition were handed a blank sheet of paper.
Results
Participants in the first experimental condition completed on average 10.4 push ups (median 8). They completed on average 0 sit ups (median 0).
Participants in the second experimental condition completed on average 22.8 sit ups (median 24). They completed on average 0 push ups (median 0).
Participants in the control condition completed on average 0 push ups (median 0) and 0 sit ups (median 0).
Conclusion
This experiment found with high probability (p < 0.05) that people's behavior is affected by the wording of instructions they are given.
Sunday, April 26, 2015
Saturday, April 25, 2015
Do people respond to incentives?
One of the discrepancies between behavioral economics and traditional economics is that traditional economists tend to hold a much stronger belief that people respond to incentives than do behavioral economists.
I believe that the behavioral economists are right, for the purposes of describing individual behavior. In particular, I believe that the traditional model of human behavior that claims that people change in response to incentives contains unnecessary assumptions. Incentives are self-enforcing. They don't need to change people to affect the state of the system containing the incentives. Instead, they cause the people who behave in ways that align with the incentive structure to gain power within the system and people whose behavior does not align with the incentive structure of the system to lose power within. I will consider three examples below.
To clarify: I fully agree with the statement "Systems converge towards a condition that maximizes the rewarded behavior." The problem I have with the statement "Human respond to incentives" is that it is a statement about humans and not about systems. I am going to argue that the behavior of responding to incentives is a general property of systems that have sufficiently many actors affecting results and not one that has anything to do with the particulars of human nature.
I would expect to see the system-level effects observed by traditional economist combined with the individual effects observed by behavioral economists. In particular, I would expect that the sum of aggregate behavior converges towards the result you would expect by assuming that humans respond to behavior while individual behavior remains mostly unchanged by the introduction of new incentives. The aggregating function is what is actually changing not the behavior of the individual people.
I. Peer review.
One of the (many) problems with the peer review system, is that insufficient controls are in place to ensure that the people who review and approve articles actually bother to read them. If the reviewers do read the papers, they for the most part don't read them carefully enough to catch the sorts of mistakes that you could only find through careful analysis.
They have no incentive to do so. Thus we should not expect that reviewers typically do the amount of due diligence required to actually sign off on the validity of the papers they review. I'm not disputing this result. I am simply claiming that the cause of this result has to do with the effects of the incentive on the peer review system, not the absence of incentives corrupting people.
Suppose that there are some people who have a natural tendency to carefully review every article, and others who have a natural tendency to be less thorough than they should be. In the absence of an incentive to review carefully, the people who are less thorough will be able to review far more papers than the people who are more careful.
(Note: I'm not an academic. I'm using a hypothetical "I," along with a hypothetical "you" because it makes discussing ...)
The reasons are twofold. First, there is the problem of simple bandwidth. If you spend three hours and significant mental energy on the average paper you review. And I spend twenty minutes skimming through each paper I review, I can review nine papers in the time that you can review one, while exerting far less mental energy in the process. Ergo, I have the bandwidth capacity to review more papers than you.
Secondly, skimming through papers instead of carefully reading them allows me to build my personal brand in academia faster than you can, which will result in more people asking me to review papers than ask you to review papers. To carefully review a paper, you have to work-time that drains you that you could be spending on your research and devote it instead to thinking about somebody else's research. I on the other hand, never have to really push my own research out of my head as I'm glancing through other people's results just carefully enough to glean any insights that might be relevant to me. Ergo, all other things being more or less equal, I will be able to produce more research than you and/or better research than you, simply since I was able to devote more energy to that. Since our respective reputations have everything to do with the quality of the work that we publish and nothing to do with the quality of work that we expend review other people's research, my reputation grows faster than yours. When publications are looking for someone they can trust to give good reviews, they're going to look for people with a good reputation, so they'll choose me over you precisely because I didn't expend the energy on reviewing that would have distracted me from covering more ground on my own research. Incidentally, reversing their criteria so that they looked for reviewers who did not have as a good of a reputation would produce even worse results, because now they would be selecting for incompetence instead of selecting for complete devotion to one's own personal research that doesn't leave time or energy for careful peer reviewing.
The lack of an incentive might never cause you to yell "screw it" and give up on doing the high quality reviews that you feel personally or morally obliged to conduct. But it doesn't matter. Precisely because your behavior is less aligned with the incentive structure than mine is, you will have less total impact on the system than I do. And the incentive structure will cause reviews to be cursory and swift without having to cause reviewers to be less thorough in their review process than they would be if the incentives were more aligned with the desired results.
In this particular case, I would not expect monetary incentives to solve the problem because they would not adjust the way that the aggregating incentive is perverse, even though they presumably would modify human behavior if the mechanism of incentives affecting the system were for the incentives to modify human behavior. Reputation is the currency of academia, not money. Getting payed more for being able to accurately predict which studies would replicate wouldn't fix peer review unless accurately predicting which studies would replicate also resulted in an improved reputation within academia.
II. Wages.
We both run factories. I decide that it's unethical to pay your employees minimum wage, and instead pay then $20/hour because that's the most you can pay them without going into the red. You have no ethical problems with paying people minimum wage, so you pay them minimum wage.
At first things are fine for me, but you're able to take some of the money you save and reinvest it into improving your product as well as improving your factory. Pretty soon, my product is noticeably sub-par. So I go out of business.
The incentive structure didn't need to make me any more greedy. It just needed to exist. Because my behavior doesn't fit with the incentive structure, I become irrelevant, while you remain relevant because your behavior does.
III. Investing.
People realize that businesses are resource constrained and incapable of operating outside their incentive structure so long as anyone operates within the incentive structure. Some of them decide to solve the moral hazards that businesses face by improving the incentive structure through investing. They'll only buy the stock of companies that the deem to be more moral than other companies; thereby making it easier for those companies to raise capital and improve themselves.
Let's say a third of investors do this. Another third of investors throws darts at the market, thereby getting the average return. And the remaining third of investors carefully research what to buy focusing on the expected profitability of the companies rather than moral issues. They all start out with the same amount of money.
At this point, I need to explain something that a lot of people naively don't understand. The stock market is not a Ponzi scheme. Valuations are not simply determined by the will of the market. Companies make a profit. They use some of their profits to pay dividends, buy back shares, and pay off their debts. In the long term, the valuation of a stock is dictated by the profitability of the company, not by the whims of the market.
In the last section, we already discussed one way that moral behavior causes companies to underperform the market. In fact, that's the whole premise of moral investing. People know that "being greedy" causes companies to perform better, and they are trying to create a different incentive to counteract that effect. So what happens?
The moral investors underperform the market. The random investors perform at market. And the investors that research profitability outperform the market. Let's say they get 2%, 5%, and 8% annual returns respectively. These are reasonable numbers. (David Einhorn and Warren Buffet do much better than 8% on average annually. The 5% return is close to market average for the last century, and 2% is probably generous for people whose investment strategy is systematically favoring companies that are likely to get out-competed.) After thirty years, the moral investors will only control 11% of the market. The random investors will control 27% of the market, and the investors that research profitability will control the remaining 62% of the market. After 50 years (20 more than thirty not 50 more years), the respective percentages will be 4%, 19%, and 77%. The investment strategy that is aligned with the market's incentive structure converges towards controlling 100% of the market; while the one that is systematically mis-aligned with its values pretty rapidly converges towards zero.
I believe that the behavioral economists are right, for the purposes of describing individual behavior. In particular, I believe that the traditional model of human behavior that claims that people change in response to incentives contains unnecessary assumptions. Incentives are self-enforcing. They don't need to change people to affect the state of the system containing the incentives. Instead, they cause the people who behave in ways that align with the incentive structure to gain power within the system and people whose behavior does not align with the incentive structure of the system to lose power within. I will consider three examples below.
To clarify: I fully agree with the statement "Systems converge towards a condition that maximizes the rewarded behavior." The problem I have with the statement "Human respond to incentives" is that it is a statement about humans and not about systems. I am going to argue that the behavior of responding to incentives is a general property of systems that have sufficiently many actors affecting results and not one that has anything to do with the particulars of human nature.
I would expect to see the system-level effects observed by traditional economist combined with the individual effects observed by behavioral economists. In particular, I would expect that the sum of aggregate behavior converges towards the result you would expect by assuming that humans respond to behavior while individual behavior remains mostly unchanged by the introduction of new incentives. The aggregating function is what is actually changing not the behavior of the individual people.
I. Peer review.
One of the (many) problems with the peer review system, is that insufficient controls are in place to ensure that the people who review and approve articles actually bother to read them. If the reviewers do read the papers, they for the most part don't read them carefully enough to catch the sorts of mistakes that you could only find through careful analysis.
They have no incentive to do so. Thus we should not expect that reviewers typically do the amount of due diligence required to actually sign off on the validity of the papers they review. I'm not disputing this result. I am simply claiming that the cause of this result has to do with the effects of the incentive on the peer review system, not the absence of incentives corrupting people.
Suppose that there are some people who have a natural tendency to carefully review every article, and others who have a natural tendency to be less thorough than they should be. In the absence of an incentive to review carefully, the people who are less thorough will be able to review far more papers than the people who are more careful.
(Note: I'm not an academic. I'm using a hypothetical "I," along with a hypothetical "you" because it makes discussing ...)
The reasons are twofold. First, there is the problem of simple bandwidth. If you spend three hours and significant mental energy on the average paper you review. And I spend twenty minutes skimming through each paper I review, I can review nine papers in the time that you can review one, while exerting far less mental energy in the process. Ergo, I have the bandwidth capacity to review more papers than you.
Secondly, skimming through papers instead of carefully reading them allows me to build my personal brand in academia faster than you can, which will result in more people asking me to review papers than ask you to review papers. To carefully review a paper, you have to work-time that drains you that you could be spending on your research and devote it instead to thinking about somebody else's research. I on the other hand, never have to really push my own research out of my head as I'm glancing through other people's results just carefully enough to glean any insights that might be relevant to me. Ergo, all other things being more or less equal, I will be able to produce more research than you and/or better research than you, simply since I was able to devote more energy to that. Since our respective reputations have everything to do with the quality of the work that we publish and nothing to do with the quality of work that we expend review other people's research, my reputation grows faster than yours. When publications are looking for someone they can trust to give good reviews, they're going to look for people with a good reputation, so they'll choose me over you precisely because I didn't expend the energy on reviewing that would have distracted me from covering more ground on my own research. Incidentally, reversing their criteria so that they looked for reviewers who did not have as a good of a reputation would produce even worse results, because now they would be selecting for incompetence instead of selecting for complete devotion to one's own personal research that doesn't leave time or energy for careful peer reviewing.
The lack of an incentive might never cause you to yell "screw it" and give up on doing the high quality reviews that you feel personally or morally obliged to conduct. But it doesn't matter. Precisely because your behavior is less aligned with the incentive structure than mine is, you will have less total impact on the system than I do. And the incentive structure will cause reviews to be cursory and swift without having to cause reviewers to be less thorough in their review process than they would be if the incentives were more aligned with the desired results.
In this particular case, I would not expect monetary incentives to solve the problem because they would not adjust the way that the aggregating incentive is perverse, even though they presumably would modify human behavior if the mechanism of incentives affecting the system were for the incentives to modify human behavior. Reputation is the currency of academia, not money. Getting payed more for being able to accurately predict which studies would replicate wouldn't fix peer review unless accurately predicting which studies would replicate also resulted in an improved reputation within academia.
II. Wages.
We both run factories. I decide that it's unethical to pay your employees minimum wage, and instead pay then $20/hour because that's the most you can pay them without going into the red. You have no ethical problems with paying people minimum wage, so you pay them minimum wage.
At first things are fine for me, but you're able to take some of the money you save and reinvest it into improving your product as well as improving your factory. Pretty soon, my product is noticeably sub-par. So I go out of business.
The incentive structure didn't need to make me any more greedy. It just needed to exist. Because my behavior doesn't fit with the incentive structure, I become irrelevant, while you remain relevant because your behavior does.
III. Investing.
People realize that businesses are resource constrained and incapable of operating outside their incentive structure so long as anyone operates within the incentive structure. Some of them decide to solve the moral hazards that businesses face by improving the incentive structure through investing. They'll only buy the stock of companies that the deem to be more moral than other companies; thereby making it easier for those companies to raise capital and improve themselves.
Let's say a third of investors do this. Another third of investors throws darts at the market, thereby getting the average return. And the remaining third of investors carefully research what to buy focusing on the expected profitability of the companies rather than moral issues. They all start out with the same amount of money.
At this point, I need to explain something that a lot of people naively don't understand. The stock market is not a Ponzi scheme. Valuations are not simply determined by the will of the market. Companies make a profit. They use some of their profits to pay dividends, buy back shares, and pay off their debts. In the long term, the valuation of a stock is dictated by the profitability of the company, not by the whims of the market.
In the last section, we already discussed one way that moral behavior causes companies to underperform the market. In fact, that's the whole premise of moral investing. People know that "being greedy" causes companies to perform better, and they are trying to create a different incentive to counteract that effect. So what happens?
The moral investors underperform the market. The random investors perform at market. And the investors that research profitability outperform the market. Let's say they get 2%, 5%, and 8% annual returns respectively. These are reasonable numbers. (David Einhorn and Warren Buffet do much better than 8% on average annually. The 5% return is close to market average for the last century, and 2% is probably generous for people whose investment strategy is systematically favoring companies that are likely to get out-competed.) After thirty years, the moral investors will only control 11% of the market. The random investors will control 27% of the market, and the investors that research profitability will control the remaining 62% of the market. After 50 years (20 more than thirty not 50 more years), the respective percentages will be 4%, 19%, and 77%. The investment strategy that is aligned with the market's incentive structure converges towards controlling 100% of the market; while the one that is systematically mis-aligned with its values pretty rapidly converges towards zero.
Tuesday, April 21, 2015
Universal Ethics
I believe their are at least two ethical claims that any sufficiently intelligent agent would agree to. I do not believe that the standard of sufficient intelligence is so low to permit all humans to meet it, but most mathematically competent people who have been exposed to the appropriate background material are I believe sufficiently intelligent to see that these claims are accurate.
Game theory provides notation that helps describe some sorts of moral claims precisely. Of particular interest, game theory describes two particularly interesting conditions that coordination problems dealing with agents having competing desires might achieve: Nash equilibria and Pareto optima. Many Nash equilibria are not Pareto optimal, and many Pareto optima are not in a Nash equilibrium. For every Nash equilibrium that is not a Pareto optimum, there exists a Pareto optimum that is at least as good for all participants than the Nash equilibrium and better for at least some of the participants than the Pareto optimum. Moreover, the general structure of the game ensures that the Nash equilibrium is a more stable condition than the Pareto optimum, so the natural final state of this game (provided it reaches conditions sufficiently close to a non-Pareto-optimal Nash equilibrium) is strictly worse than some theoretically attainable condition that is only not attainable in practice because of the behavior of the participants in the game.
I assert that anyone who is smart enough to understand game theory as it applies to the situations they are dealing with (which, in many cases, requires somewhat more intelligence than simply understanding it well enough to push the symbols and do the math, though that is often a prerequisite) will concede that a game which has the same possible states assigned to the same players but has slightly different rules so that all achievable Nash equilibria are Pareto optimal is a better game than the game which has rules that permit the nearest Nash equilibrium to be something other than Pareto optimal. This is a very precise way of saying that, if the incentive structures can be rearranged so that some of the participants benefit, none of the participants are harmed, and you have to let the game play out to determine whether you benefit or merely do as well as you would have done without the rule change, all of the participants, no matter how risk adverse they may be will agree to the rule change unless they are simply insufficiently intelligent to see that the rule change cannot possibly harm them but can possibly benefit them.
(Side note for the truly pedantic: The way I've phrased it, the rule is slightly too weak. It is always true, but a stronger version of the rule would always be true, and also apply to a slightly wider variety of cases. The stronger version is much harder to state precisely, so I presented the weaker version instead. The strong version acknowledges that in some games, it is not possible to change the rules so that all achievable Nash equilibria are Pareto optimal, but in many of these games, some potential rulesets give Nash equilibria that are closer to being Pareto optimal than the achievable Nash equilibria produced by other rulesets. In these cases, the rulesets that come the closest to producing Pareto optimal Nash equilibria are better than the rulesets that fail to achieve as much Pareto efficiency in their equilibrium conditions. I don't know any way to phrase this rule precisely in words, without resorting to definition that includes variables, which is simply rude to do in a blog post. In any game which includes randomization, future outcomes are not predictable, so the consideration can be extended even further. People should be able to agree to rules that increase their net expected outcomes even when it is statistically possible that the rule will hurt the ultimate outcome they face. That is: If a game includes enough randomization that more than one possible equilibrium condition is possible, people ought to be able to agree that a rule change that improves several of the attainable equilibrium conditions from their perspective, even if it doesn't improve all of them, as long as it improves enough of them by a significant enough margin that the net expected outcome for each participant is an improvement... but at this point, you need to be computing each participant's risk aversion function as a separate thing from each participant's risk aversion function because the various possible Nash equilibria have different probabilities of being reached.)
(Additional side note to answer a possible objection of wannabe pedants: What if the original game under is a deterministic, solved game? You can postulate a rule change R that would be a Pareto optimum that benefits some but not all of the participants. Why should the people who know in advance that they won't benefit from R agree to R? The answer is that they shouldn't but, in the event that R exist, there is also a ruleset R` that would benefit everyone. In particular, R benefits one participant by the amount x. There are plenty of infinitely sub-dividable abstract things that can be distributed within a game some of which are no more valuable in total than x is to the player who benefits by receiving x. [For example: Add randomization into the game, and give each participant some non-zero, non-negative change of receiving x instead of the person who would have received it under R. Simpler solutions exist if x is itself sub-dividable or if x is valued in a currency that is itself infinitely sub-dividable (which any currency can be made to be)]. Add a rule that says, once the game plays out under R enough for a player to achieve x, x enters a lottery to determine who actually gets it. What I've described does not tell you which Pareto optimum the game should achieve, merely that Pareto optima are better than Nash equilibria. [For example, not everyone has to be given the same chance of getting x. The person who would receive it under R might get a 50% chance of receiving x while everyone else gets a 1/2(n-1) chance of receiving x where n is the number of players.] There is a new meta-game that describes negotiating the rule change with an infinite regression of meta-meta-games for negotiating the rules of those games. Throughout this whole infinite regression, you never lose the condition that says that everyone intelligent enough to understand what's going on recognizes that the game in which all achievable Nash equilibria are Pareto optimal is better than one in which at least one achievable Nash equilibrium is not a Pareto optimum. You just gain a whole lot of complexity... A lot of heated moral arguments are about negotiating the rule changes. People know that the current state of things permits a tragedy of the commons, but they realize that different ways to resolve the tragedy favor different parties to different extents and argue vehemently about why they are morally entitled to receive a larger share of the expected gain from negotiating the rule change than anyone else gets. The moral rule I have postulated is (mostly) agnostic about this condition. Switching the rules so that the Nash equilibrium moves to a Pareto optimum makes the game better, but switching it so that it moves to the best Pareto optimum for you, your friends, and equals does not necessarily make it a better game than switching it so that it moves to the best Pareto optimum for me, my friends, and equals. And we both have an incentive to claim that our side is right in our advocacy of a particular improvement that differs from the particular improvement another side wants.)
Innate human ethics has at least one feature that I believe can be explained as the result of evolved optimization "discovering" through trial and error this moral rule that will be naturally discovered by any sufficiently intelligent process or agent. (Natural selection, like all optimization engines, is a system that produces results consistent with the application of intelligence whether or not we would call the system itself intelligent.) The human impulse to seek justice (shared with some other animals, certainly chimpanzees, but probably most social animals) is a rule that helps constrain the game so that Nash equilibria tend to be Pareto optimal. Justice, as it is typically practiced and/or desired, is the impulse to ensure that anyone who willfully harms someone is harmed as a result even if no benefit to the original victim(s) (or anyone else) comes from [society/god/the victim/the victim's friends] harming the original perpetrator. The rule of justice is added to the game as a disincentive against committing harm, thereby causing many conditions that would otherwise have been Nash equilibria that were not Pareto optimal to cease to be Nash equilibria -- in the process causing the equilibrium to shift to something that is closer to Pareto optimal, if not necessarily optimal itself.
This rule can be erroneously extended, and misapplied in a way that causes short-term improvements in the game, without actually shift the end condition to a better state. Natural selection is a blind optimizer that finds short-term local maxima even when they caused long term problems, so it should not be surprising that the natural human sense of ethics builds on justice in non-optimal ways that would be obviously wrong to a sufficiently intelligent outside observer too. The human tendency to promote among each other the belief that an invisible supernatural being that loves justice is watching everyone even when they think they are alone is similarly likely to promote better equilibrium conditions. This application of the previous rule is more problematic than the simple promotion of justice among each other because it is easily violated. In particular it's an unenforceable rule. Once people figure out is unenforceable, the Nash equilibrium it may have prevented while people believed that Someone would enforce it, goes away again. It the mean time, people who have figured out that the rule is false can exploit it to the detriment of the people who still believe it
This consideration brings me to the second rule that all sufficiently intelligent agents ought to be able to agree upon as a moral rule.
Actions predicated upon false hypotheses are always wrong.
There are many cases in which an agent has beliefs and allows its actions to be predicated upon its beliefs. If the agent believed A, it would do X. Whereas; if it instead believed B, it would do Y instead. In these cases the agent is wrong to do A if Y is true, because the agent's actions are based on the false predicate X.
This is distinct from saying that it's wrong to hold false hypotheses. Merely that actions which would not have been conducted if it were not for the erroneous belief being held are wrong. (For whatever reason, inaction seems to be morally favored. Some theories treat a moral preference for inaction as an inconsistency and a failure of human reason -- read almost anyone's discussion of the trolley problem to see that this is something that people tend to object to on theoretical grounds, though people almost universally hold it as far as practical application goes.)
Two ancient tribes get into a territorial dispute. Both sides know that if they get into a war with each other, the war can win either in a stalemate or with one side victorious. If it ends in a stalemate, both sides will lose resources and men, and neither side will gain enough to offset their loss. Neither side would engage the other in combat if they believed that the ensuing war would end in a stalemate.
Both sides also know that if the war ends with the other side victorious, things will go badly for them. Their gods will be disgraced, their men will be slain, their women raped, and their children carried off into slavery (with the male children having been made eunuchs). Either side would rather surrender up front and simply sacrifice some of its territory and pay a tribute than face these terrible consequences.
They should never get into a war because they never would get into a war if they always correctly predicted whether the war would win in a stalemate and who would win if it wouldn't. Neither side would be the aggressor in the event that both sides knew the war would lead to a stalemate. In the event that it wouldn't, the weaker side should capitulate preemptively, averting the conflict.
Since you would only aggressively initiate a war if you expected to win it, it is wrong to initiate a war that you will not win. It is not wrong to defend yourself in the event that someone who will not defeat you if you defend yourself has initiated a war against you. These two statements fit well with most people's moral intuitions about wrong behavior... which should be true of a moral theory. Even if it's axioms seem irrefutable and/or unquestionable, a moral theory that makes repugnant claims ought to be called into question.
This brings us to the case when it is wrong to defend, something that, on its face seems odd for a moral theory to assert, but which I claim demonstrates the strength of the two ideas posited so far.
To begin with, it explains a major edge case in most that is problematic for most moral theories: what makes a power legitimate? People wince at the suggestion that "might makes right" as an explanation for why the government has legitimate authority to prescribe or proscribe various activities... but most other explanations are simply absurd. This explanation transforms that claim a little, into one that I find far less morally repugnant: which is the assertion that the governments ability to correctly ascertain that they have the power to enforce their makes them "not wrong" to do so, to the extent that they are actually correct in figuring out what they have the power to enforce. It does not necessarily mean that they are "right" to do so. Secondly, it adds the further caveat, based on exactly the same principal, that the government is wrong to make certain judgments even if they have the ability to enforce those judgments. For example, even though Nazi Germany (more or less) had the power to enforce a law prohibiting anyone from being Jewish in German-controlled territories, they were wrong to do so, because the only reason that they would do so is that they had many false beliefs about Jewish conspiracies and the effects of ethnic purity on a population. If it were not for those false beliefs, the holocaust wouldn't have happened.
But, we still have the previous case about the two ancient societies getting into a war with each other. My moral theory postulates that, in the event that one side will lose the war if a war occurs, they are wrong to fight it, and should instead surrender if surrendering gives them a better expected result than losing the war. (Game theory says it should, since the other society has an incentive to give them an incentive not to fight them.) In this case, they are wrong to fight the war because the only reason that they would fight it is because they falsely believe that things can be expected to go better for them if they fight it than if they surrender. In the modern world this sort of situation mainly deals with rebels and terrorists who erroneously believe that they can establish an independent state somewhere... and most of us have no qualms calling them "wrong" to do so. What we have qualms with is the idea of calling the ancient society that is going to be the victim of atrocities wrong to have defended itself when they wouldn't have had atrocities committed against them at all if they hadn't defended themselves. It feels too much like blaming the victim. But at the same time, it's obvious that they "shouldn't have" fought, which is really all I am saying when I say "it was wrong" of them to fight. They shouldn't have fought because they, their children, and everyone else would be better of if they didn't (including their enemies), and because they wouldn't have fought if they had been able to correctly infer the outcome, but they were some combination of too unwilling to pay the tribute and too overconfident in their abilities to realize that the course of action that they should have taken is simply to pay the tribute and surrender. These two qualities are qualities we tend to describe as "greed" (an enforceable tribute is no different from a tax) and "arrogance" both of which we would typically call "bad" so our intuitive notion is that it is wrong to have these qualities.
The real cause of our squeamishness around calling the side that erroneously defended itself wrong in this ancient conflict is not that saying this violates our general sense of morality, it's that saying this almost seems like it's saying that the side that defended itself "deserved" to have atrocities committed against them. Which is not what this moral theory says at all. It simply says that they should not have fought. Previous considerations about changing the rules of the game to improve the equilibrium conditions explain why it is wrong to commit genocide. If people were able to get together and make rules, they would want to make rules that prevent atrocities, because (with a few assumptions) everybody's expected outcome in the game is better when the consequences of warfare are less horrific. (Mostly because the game is already non-deterministic.) We come up with a rule to say that genocide is also wrong, and that all remaining countries will punish the invading country for its war crimes. Notably, this moral theory does not have the property of most modern judicial systems of ultimately taking one side or the other. It is fully capable of declaring both sides wrong. In this case, we can agree that the ancient societies should have agreed on rules to prevent what we would consider war crimes, and this is a separate consideration from saying that the side that would be harmed from fighting the war should not have fought the war.
In fact, these rules never declare anything "right" except insofar as they say that adding certain rules to a game makes the game better, which can arguably be extended to saying that including and enforcing those rules in a game is "right"... though that's more semantics than substance.
There's one more thing that I want to point out about the second moral rule: Actions predicated on false hypotheses are always wrong.
This rule resolves the is/ought question. It has reduced a question of "ought" to a question of "is." In particular, it is the observation that many actions are based on truth-propositions about the world. When someone believes that God created human life and made it sacred from the moment of conception, they believe that they ought to oppose abortion even if they wouldn't feel that way if they didn't have this belief about human life. Most people who are strongly opposed to abortion would not be strongly opposed to abortion if they did not hold the religious views that cause them to be strongly opposed to abortion. Similarly, most people who support either state-mandated abortion (as in China) or the right of women to choose to have abortions if they see fit (as in most Western countries) would not do so if they believed the proposition, "There exists a God who judges the world who is offended by abortion and will judge nations/people harshly if they tolerate abortion." Despite all of the other moral posturing that people do around this subject, it pretty readily reduces to a truth-proposition about morality. If the theistic views of pro-lifers are largely correct, they are taking the side of morality. If not, they are taking the immoral view.
In the process, it explains why a sin is worse than a error of calculation -- at least for a certain form of sin. A sin is a miscalculation that results in an action that would not have occurred without the miscalculation. Many miscalculations can be errors without causing sins. Someone can hold an erroneous belief that would cause them to take the same actions that they would have taken if they instead held a true belief. These people are still mistaken, but their actions are not "wrong" because they are still doing what they "should" do.
Another thing to point out about this moral rule is that it invalidates Pascal's wager. Pascal's wager is about computing the utility that various beliefs purport to give to their holders multiplying that utility by the likelihood of that belief system being true, and then choosing the belief that maximizes expected utility. It has many problems, not the least of which is that it is subject to Pascal's mugging. However, the moral rule I have suggested says that you are wrong to act on erroneous beliefs, which would make acting on Pascal's wager wrong whenever Pascal's wager leads you to act wrongly, which one is much more often than you would act wrongly if you didn't consider the purported rewards associated with a belief when selecting between them, since it easy to contrive a false theory with arbitrarily high purported punishment for failure to believe and comply or arbitrarily high purported reward for choosing to believe and comply. (Or both the carrot and the stick if you want both.)
(Notice, this theory does not preclude holding beliefs with humility: "What I would do if I believed I had at least a one percent chance of being wrong about beliefs I hold as strongly as I believe that evolution through the mechanism of natural selection produced life" is still a valid proposition. For reasons of elementary statistics, "what I would do if I believed the fundamentalist interpretation of the Bible had a 1% chance of being correct" is an absurd alternative to "What I would do if I believed I had at least a 1% chance of being wrong." You have infinitely many possible beliefs to choose from and have no reason to elevate any particular belief you do not hold to this sort of prominence. Though this particular idea has more to do with my rejection of the bit-complexity formulation of Occam's razor than it does with the moral theory I am presenting.)
All told from these considerations:
We have two axioms of morality, one of which has a natural formulation in game theory, and the other has a natural formulation in proposition logic. Both axioms are consistent with behavior we would expect from a fully-rational entity. They explain features of the natural human ethics, resolve the is-ought problem, show errant actions to be more erroneous than simple miscalculation, invalidate Pascal's wager, explain why the aggressor is in the wrong in a conflict that ends in a stalemate, and say why the rule of a government is usually legitimate while still explaining why the Nazis were wrong.
I would say that this list of results strongly indicates that there's something to the theory.
Most of these results come from the second axiom. So most of the support that these observation give to the moral theory come from the second axiom. That said, all of the objections I can think of to the second axiom are resolved by the first one, which (possibly because it has been more fully developed by other people before me) is also the one that seems more obvious to me, and certainly is the first of the two which I held. Without the first rule, the theory seems noticeably incomplete, in a bad way.
The theory probably doesn't satisfy most people's desire for completeness. If we hypothesize a being of infinite power and infinite malice, this theory does not explain why it would be wrong for that being to torture everyone else for all of forever. However, it does say that if no such hypothetical being exists, you would be wrong to reject a theory on the grounds that it cannot deal with the false hypothetical.
Game theory provides notation that helps describe some sorts of moral claims precisely. Of particular interest, game theory describes two particularly interesting conditions that coordination problems dealing with agents having competing desires might achieve: Nash equilibria and Pareto optima. Many Nash equilibria are not Pareto optimal, and many Pareto optima are not in a Nash equilibrium. For every Nash equilibrium that is not a Pareto optimum, there exists a Pareto optimum that is at least as good for all participants than the Nash equilibrium and better for at least some of the participants than the Pareto optimum. Moreover, the general structure of the game ensures that the Nash equilibrium is a more stable condition than the Pareto optimum, so the natural final state of this game (provided it reaches conditions sufficiently close to a non-Pareto-optimal Nash equilibrium) is strictly worse than some theoretically attainable condition that is only not attainable in practice because of the behavior of the participants in the game.
I assert that anyone who is smart enough to understand game theory as it applies to the situations they are dealing with (which, in many cases, requires somewhat more intelligence than simply understanding it well enough to push the symbols and do the math, though that is often a prerequisite) will concede that a game which has the same possible states assigned to the same players but has slightly different rules so that all achievable Nash equilibria are Pareto optimal is a better game than the game which has rules that permit the nearest Nash equilibrium to be something other than Pareto optimal. This is a very precise way of saying that, if the incentive structures can be rearranged so that some of the participants benefit, none of the participants are harmed, and you have to let the game play out to determine whether you benefit or merely do as well as you would have done without the rule change, all of the participants, no matter how risk adverse they may be will agree to the rule change unless they are simply insufficiently intelligent to see that the rule change cannot possibly harm them but can possibly benefit them.
(Side note for the truly pedantic: The way I've phrased it, the rule is slightly too weak. It is always true, but a stronger version of the rule would always be true, and also apply to a slightly wider variety of cases. The stronger version is much harder to state precisely, so I presented the weaker version instead. The strong version acknowledges that in some games, it is not possible to change the rules so that all achievable Nash equilibria are Pareto optimal, but in many of these games, some potential rulesets give Nash equilibria that are closer to being Pareto optimal than the achievable Nash equilibria produced by other rulesets. In these cases, the rulesets that come the closest to producing Pareto optimal Nash equilibria are better than the rulesets that fail to achieve as much Pareto efficiency in their equilibrium conditions. I don't know any way to phrase this rule precisely in words, without resorting to definition that includes variables, which is simply rude to do in a blog post. In any game which includes randomization, future outcomes are not predictable, so the consideration can be extended even further. People should be able to agree to rules that increase their net expected outcomes even when it is statistically possible that the rule will hurt the ultimate outcome they face. That is: If a game includes enough randomization that more than one possible equilibrium condition is possible, people ought to be able to agree that a rule change that improves several of the attainable equilibrium conditions from their perspective, even if it doesn't improve all of them, as long as it improves enough of them by a significant enough margin that the net expected outcome for each participant is an improvement... but at this point, you need to be computing each participant's risk aversion function as a separate thing from each participant's risk aversion function because the various possible Nash equilibria have different probabilities of being reached.)
(Additional side note to answer a possible objection of wannabe pedants: What if the original game under is a deterministic, solved game? You can postulate a rule change R that would be a Pareto optimum that benefits some but not all of the participants. Why should the people who know in advance that they won't benefit from R agree to R? The answer is that they shouldn't but, in the event that R exist, there is also a ruleset R` that would benefit everyone. In particular, R benefits one participant by the amount x. There are plenty of infinitely sub-dividable abstract things that can be distributed within a game some of which are no more valuable in total than x is to the player who benefits by receiving x. [For example: Add randomization into the game, and give each participant some non-zero, non-negative change of receiving x instead of the person who would have received it under R. Simpler solutions exist if x is itself sub-dividable or if x is valued in a currency that is itself infinitely sub-dividable (which any currency can be made to be)]. Add a rule that says, once the game plays out under R enough for a player to achieve x, x enters a lottery to determine who actually gets it. What I've described does not tell you which Pareto optimum the game should achieve, merely that Pareto optima are better than Nash equilibria. [For example, not everyone has to be given the same chance of getting x. The person who would receive it under R might get a 50% chance of receiving x while everyone else gets a 1/2(n-1) chance of receiving x where n is the number of players.] There is a new meta-game that describes negotiating the rule change with an infinite regression of meta-meta-games for negotiating the rules of those games. Throughout this whole infinite regression, you never lose the condition that says that everyone intelligent enough to understand what's going on recognizes that the game in which all achievable Nash equilibria are Pareto optimal is better than one in which at least one achievable Nash equilibrium is not a Pareto optimum. You just gain a whole lot of complexity... A lot of heated moral arguments are about negotiating the rule changes. People know that the current state of things permits a tragedy of the commons, but they realize that different ways to resolve the tragedy favor different parties to different extents and argue vehemently about why they are morally entitled to receive a larger share of the expected gain from negotiating the rule change than anyone else gets. The moral rule I have postulated is (mostly) agnostic about this condition. Switching the rules so that the Nash equilibrium moves to a Pareto optimum makes the game better, but switching it so that it moves to the best Pareto optimum for you, your friends, and equals does not necessarily make it a better game than switching it so that it moves to the best Pareto optimum for me, my friends, and equals. And we both have an incentive to claim that our side is right in our advocacy of a particular improvement that differs from the particular improvement another side wants.)
Innate human ethics has at least one feature that I believe can be explained as the result of evolved optimization "discovering" through trial and error this moral rule that will be naturally discovered by any sufficiently intelligent process or agent. (Natural selection, like all optimization engines, is a system that produces results consistent with the application of intelligence whether or not we would call the system itself intelligent.) The human impulse to seek justice (shared with some other animals, certainly chimpanzees, but probably most social animals) is a rule that helps constrain the game so that Nash equilibria tend to be Pareto optimal. Justice, as it is typically practiced and/or desired, is the impulse to ensure that anyone who willfully harms someone is harmed as a result even if no benefit to the original victim(s) (or anyone else) comes from [society/god/the victim/the victim's friends] harming the original perpetrator. The rule of justice is added to the game as a disincentive against committing harm, thereby causing many conditions that would otherwise have been Nash equilibria that were not Pareto optimal to cease to be Nash equilibria -- in the process causing the equilibrium to shift to something that is closer to Pareto optimal, if not necessarily optimal itself.
This rule can be erroneously extended, and misapplied in a way that causes short-term improvements in the game, without actually shift the end condition to a better state. Natural selection is a blind optimizer that finds short-term local maxima even when they caused long term problems, so it should not be surprising that the natural human sense of ethics builds on justice in non-optimal ways that would be obviously wrong to a sufficiently intelligent outside observer too. The human tendency to promote among each other the belief that an invisible supernatural being that loves justice is watching everyone even when they think they are alone is similarly likely to promote better equilibrium conditions. This application of the previous rule is more problematic than the simple promotion of justice among each other because it is easily violated. In particular it's an unenforceable rule. Once people figure out is unenforceable, the Nash equilibrium it may have prevented while people believed that Someone would enforce it, goes away again. It the mean time, people who have figured out that the rule is false can exploit it to the detriment of the people who still believe it
This consideration brings me to the second rule that all sufficiently intelligent agents ought to be able to agree upon as a moral rule.
Actions predicated upon false hypotheses are always wrong.
There are many cases in which an agent has beliefs and allows its actions to be predicated upon its beliefs. If the agent believed A, it would do X. Whereas; if it instead believed B, it would do Y instead. In these cases the agent is wrong to do A if Y is true, because the agent's actions are based on the false predicate X.
This is distinct from saying that it's wrong to hold false hypotheses. Merely that actions which would not have been conducted if it were not for the erroneous belief being held are wrong. (For whatever reason, inaction seems to be morally favored. Some theories treat a moral preference for inaction as an inconsistency and a failure of human reason -- read almost anyone's discussion of the trolley problem to see that this is something that people tend to object to on theoretical grounds, though people almost universally hold it as far as practical application goes.)
Two ancient tribes get into a territorial dispute. Both sides know that if they get into a war with each other, the war can win either in a stalemate or with one side victorious. If it ends in a stalemate, both sides will lose resources and men, and neither side will gain enough to offset their loss. Neither side would engage the other in combat if they believed that the ensuing war would end in a stalemate.
Both sides also know that if the war ends with the other side victorious, things will go badly for them. Their gods will be disgraced, their men will be slain, their women raped, and their children carried off into slavery (with the male children having been made eunuchs). Either side would rather surrender up front and simply sacrifice some of its territory and pay a tribute than face these terrible consequences.
They should never get into a war because they never would get into a war if they always correctly predicted whether the war would win in a stalemate and who would win if it wouldn't. Neither side would be the aggressor in the event that both sides knew the war would lead to a stalemate. In the event that it wouldn't, the weaker side should capitulate preemptively, averting the conflict.
Since you would only aggressively initiate a war if you expected to win it, it is wrong to initiate a war that you will not win. It is not wrong to defend yourself in the event that someone who will not defeat you if you defend yourself has initiated a war against you. These two statements fit well with most people's moral intuitions about wrong behavior... which should be true of a moral theory. Even if it's axioms seem irrefutable and/or unquestionable, a moral theory that makes repugnant claims ought to be called into question.
This brings us to the case when it is wrong to defend, something that, on its face seems odd for a moral theory to assert, but which I claim demonstrates the strength of the two ideas posited so far.
To begin with, it explains a major edge case in most that is problematic for most moral theories: what makes a power legitimate? People wince at the suggestion that "might makes right" as an explanation for why the government has legitimate authority to prescribe or proscribe various activities... but most other explanations are simply absurd. This explanation transforms that claim a little, into one that I find far less morally repugnant: which is the assertion that the governments ability to correctly ascertain that they have the power to enforce their makes them "not wrong" to do so, to the extent that they are actually correct in figuring out what they have the power to enforce. It does not necessarily mean that they are "right" to do so. Secondly, it adds the further caveat, based on exactly the same principal, that the government is wrong to make certain judgments even if they have the ability to enforce those judgments. For example, even though Nazi Germany (more or less) had the power to enforce a law prohibiting anyone from being Jewish in German-controlled territories, they were wrong to do so, because the only reason that they would do so is that they had many false beliefs about Jewish conspiracies and the effects of ethnic purity on a population. If it were not for those false beliefs, the holocaust wouldn't have happened.
But, we still have the previous case about the two ancient societies getting into a war with each other. My moral theory postulates that, in the event that one side will lose the war if a war occurs, they are wrong to fight it, and should instead surrender if surrendering gives them a better expected result than losing the war. (Game theory says it should, since the other society has an incentive to give them an incentive not to fight them.) In this case, they are wrong to fight the war because the only reason that they would fight it is because they falsely believe that things can be expected to go better for them if they fight it than if they surrender. In the modern world this sort of situation mainly deals with rebels and terrorists who erroneously believe that they can establish an independent state somewhere... and most of us have no qualms calling them "wrong" to do so. What we have qualms with is the idea of calling the ancient society that is going to be the victim of atrocities wrong to have defended itself when they wouldn't have had atrocities committed against them at all if they hadn't defended themselves. It feels too much like blaming the victim. But at the same time, it's obvious that they "shouldn't have" fought, which is really all I am saying when I say "it was wrong" of them to fight. They shouldn't have fought because they, their children, and everyone else would be better of if they didn't (including their enemies), and because they wouldn't have fought if they had been able to correctly infer the outcome, but they were some combination of too unwilling to pay the tribute and too overconfident in their abilities to realize that the course of action that they should have taken is simply to pay the tribute and surrender. These two qualities are qualities we tend to describe as "greed" (an enforceable tribute is no different from a tax) and "arrogance" both of which we would typically call "bad" so our intuitive notion is that it is wrong to have these qualities.
The real cause of our squeamishness around calling the side that erroneously defended itself wrong in this ancient conflict is not that saying this violates our general sense of morality, it's that saying this almost seems like it's saying that the side that defended itself "deserved" to have atrocities committed against them. Which is not what this moral theory says at all. It simply says that they should not have fought. Previous considerations about changing the rules of the game to improve the equilibrium conditions explain why it is wrong to commit genocide. If people were able to get together and make rules, they would want to make rules that prevent atrocities, because (with a few assumptions) everybody's expected outcome in the game is better when the consequences of warfare are less horrific. (Mostly because the game is already non-deterministic.) We come up with a rule to say that genocide is also wrong, and that all remaining countries will punish the invading country for its war crimes. Notably, this moral theory does not have the property of most modern judicial systems of ultimately taking one side or the other. It is fully capable of declaring both sides wrong. In this case, we can agree that the ancient societies should have agreed on rules to prevent what we would consider war crimes, and this is a separate consideration from saying that the side that would be harmed from fighting the war should not have fought the war.
In fact, these rules never declare anything "right" except insofar as they say that adding certain rules to a game makes the game better, which can arguably be extended to saying that including and enforcing those rules in a game is "right"... though that's more semantics than substance.
There's one more thing that I want to point out about the second moral rule: Actions predicated on false hypotheses are always wrong.
This rule resolves the is/ought question. It has reduced a question of "ought" to a question of "is." In particular, it is the observation that many actions are based on truth-propositions about the world. When someone believes that God created human life and made it sacred from the moment of conception, they believe that they ought to oppose abortion even if they wouldn't feel that way if they didn't have this belief about human life. Most people who are strongly opposed to abortion would not be strongly opposed to abortion if they did not hold the religious views that cause them to be strongly opposed to abortion. Similarly, most people who support either state-mandated abortion (as in China) or the right of women to choose to have abortions if they see fit (as in most Western countries) would not do so if they believed the proposition, "There exists a God who judges the world who is offended by abortion and will judge nations/people harshly if they tolerate abortion." Despite all of the other moral posturing that people do around this subject, it pretty readily reduces to a truth-proposition about morality. If the theistic views of pro-lifers are largely correct, they are taking the side of morality. If not, they are taking the immoral view.
In the process, it explains why a sin is worse than a error of calculation -- at least for a certain form of sin. A sin is a miscalculation that results in an action that would not have occurred without the miscalculation. Many miscalculations can be errors without causing sins. Someone can hold an erroneous belief that would cause them to take the same actions that they would have taken if they instead held a true belief. These people are still mistaken, but their actions are not "wrong" because they are still doing what they "should" do.
Another thing to point out about this moral rule is that it invalidates Pascal's wager. Pascal's wager is about computing the utility that various beliefs purport to give to their holders multiplying that utility by the likelihood of that belief system being true, and then choosing the belief that maximizes expected utility. It has many problems, not the least of which is that it is subject to Pascal's mugging. However, the moral rule I have suggested says that you are wrong to act on erroneous beliefs, which would make acting on Pascal's wager wrong whenever Pascal's wager leads you to act wrongly, which one is much more often than you would act wrongly if you didn't consider the purported rewards associated with a belief when selecting between them, since it easy to contrive a false theory with arbitrarily high purported punishment for failure to believe and comply or arbitrarily high purported reward for choosing to believe and comply. (Or both the carrot and the stick if you want both.)
(Notice, this theory does not preclude holding beliefs with humility: "What I would do if I believed I had at least a one percent chance of being wrong about beliefs I hold as strongly as I believe that evolution through the mechanism of natural selection produced life" is still a valid proposition. For reasons of elementary statistics, "what I would do if I believed the fundamentalist interpretation of the Bible had a 1% chance of being correct" is an absurd alternative to "What I would do if I believed I had at least a 1% chance of being wrong." You have infinitely many possible beliefs to choose from and have no reason to elevate any particular belief you do not hold to this sort of prominence. Though this particular idea has more to do with my rejection of the bit-complexity formulation of Occam's razor than it does with the moral theory I am presenting.)
All told from these considerations:
We have two axioms of morality, one of which has a natural formulation in game theory, and the other has a natural formulation in proposition logic. Both axioms are consistent with behavior we would expect from a fully-rational entity. They explain features of the natural human ethics, resolve the is-ought problem, show errant actions to be more erroneous than simple miscalculation, invalidate Pascal's wager, explain why the aggressor is in the wrong in a conflict that ends in a stalemate, and say why the rule of a government is usually legitimate while still explaining why the Nazis were wrong.
I would say that this list of results strongly indicates that there's something to the theory.
Most of these results come from the second axiom. So most of the support that these observation give to the moral theory come from the second axiom. That said, all of the objections I can think of to the second axiom are resolved by the first one, which (possibly because it has been more fully developed by other people before me) is also the one that seems more obvious to me, and certainly is the first of the two which I held. Without the first rule, the theory seems noticeably incomplete, in a bad way.
The theory probably doesn't satisfy most people's desire for completeness. If we hypothesize a being of infinite power and infinite malice, this theory does not explain why it would be wrong for that being to torture everyone else for all of forever. However, it does say that if no such hypothetical being exists, you would be wrong to reject a theory on the grounds that it cannot deal with the false hypothetical.
Friday, April 3, 2015
Axing Occam's Razor Part 1 (Overview of complaints)
Occam's razor as it is typically said in words is "The simplest explanation is always the best." I don't know of anyone who considers that version of Occam's razor to be sufficiently precise to be treated as a theory of epistemology. A reasonably common epistemology, notably popularized by the rationalist movement though it has predated that movement by quite a while, is the computational information-theoretic version of Occam's razor that says that theories should be assigned prior probabilities according to their minimum length as measured in bits. Typically, people don't specify anything beyond this. The minimum length in bits of any program in one programming language is after all somewhat related to its minimum length in any other programming language. You can pretty easily show that every pair of Turing complete languages can completely describe the operations of the other, and from there, the proof that for every pair of languages (P,Q) and for every integer N, there exists an integer M such that any program that can be expressed in N or fewer bits in P can be expressed in M or fewer bits in Q. This constraint doesn't puts a very week bound on the relationship between languages. You can also pretty easily prove that for every state S, there exists a programming language P(S) such that S can be expressed in only one bit in P(S). (At this point P(S) is a contrived language specifically designed to permit this hack, so I think it is only fair to reference S in the description of the language P(S).
People who are serious about providing computational information theoretic version of Occam's razor must specify (at least vaguely) what they believe the ideal programming language should be like.
I'm not a fan of Occam's razor, so the choice of language I would recommend is itself not consistent with Occam's razor. I would consider anything that wasn't specifically engineered to minimize the length of all of its most validated theories a very weak candidate. (This would have to be a language that revises itself in response to evidence, and has a system of pointers that permits frequently referenced concepts to be reused with ease; keeping track of what language you ought to be using would be computationally intractible because they are reflexive in complicated ways... but that's beyond the scope of the current conversation. I will discuss it later.) Most people pick something far more arbitrary. Actually, most people avoid picking anything at all, which is worse than picking something arbitrary.
But of the people who I have read who do put some effort into describing which programming language they would use as the basis of their version of Occam's razor, the most popular choice tends to be Binary Lambda calculus. Actually, if you are truly a proponent of Occam's razor this is pretty much the right choice, since it is probably very close to the simplest possible programming language that can possibly be devised. It autocompiles very easily (requiring few bits to describe itself), which if you truly have strong Occam priors ought to be a requirement for any self-consistent basis for your theory. Of course, anyone can devise a programming language that autocompiles with a single bit instruction, which would make them simpler in one sense. However, any of these programming languages is going to be much more challenging to implement in any other language than binary lambda calculus. Binary lambda calculus is very simple in most pair-wise language comparisons. It's very difficult to come up with other programming languages that compile each other with as little difficulty as most programming languages can compile binary lambda calculus.
One of the arguments I would make against Occam's razor is that many more complicated programming languages than binary lambda calculus are practically guaranteed to outperform binary lambda calculus as the best programming language to use for measuring length. In particular, binary lambda calculus does not have a good enough system of pointers to make the explanation for "someone carried the box" simpler than "the box teleported itself." Teleportation is practically guaranteed to be the simplest explanation for motion in this sort of system by many, many orders of magnitude. Just update the position stored for the object is always way easier than specifying that somebody or something else moved it, and the degree to which this explanation is likely to be simpler overwhelms available evidence. It is likely to be simpler by thousands of bits setting the prior odds against any alternative at 2 ** 1000 to 1 even in optimistic projections.
In short, I think there are very strong information-theoretic counterarguments to the validity of interpretations of information-theoretic formulations of Occam's razor, and I think that the theory does deserve to be refuted on these grounds, but I also think that there is an even stronger logical refutation of Occam's razor that takes that deals with "True statements are true" sort of tautologies.
In particular:
The simplest explanation is always the simplest.
Equivalent theories are always equivalent.
The most persuasive explanation is always the most persuasive.
The most probable explanation (given available data) is always the most probable explanation (given available data).
Reflexively self-consistent explanations are always reflexively self-consistent.
The most accurate explanation is always the most accurate.
The epistemology that produces the most predictive priors is the epistemology that produces the most predictive priors.
Self-improving epistemologies are self-improving; whereas static epistemologies are static.
Etc.
We can model all of these things separately and see that all of these things contain some elements of consistency with Occam's razor and some elements of inconsistency with Occam's razor -- the most damning of which are that considerations about persuasiveness and reflexive self-consistency would lead us to realize that statements like Occam's razor would be likely to be believed even if they don't have any merit.
We can even create an epistemology that (assuming the basic accuracy of statistics) is guaranteed to be asymptotically equivalent to Occam's razor if and only if no better alternative exists.
This brings me to my final note which is to say that most epistemologies that include Occam's razor and another theory are themselves inconsistent with Occam's razor. It is possible to devise a system of priors from the assumption that probability theory is more-or-less correct. In which case you have a formal system that takes only probability theory as its axioms, and this system is itself information-theoretically simpler than a system which also has axioms for weighting simplicity.
Some of these considerations may be a little abstruse, but most of them should be relatively straightforward to anyone with the mathematical background required to understand the information-theoretic formulation of Occam's razor to begin with.
People who are serious about providing computational information theoretic version of Occam's razor must specify (at least vaguely) what they believe the ideal programming language should be like.
I'm not a fan of Occam's razor, so the choice of language I would recommend is itself not consistent with Occam's razor. I would consider anything that wasn't specifically engineered to minimize the length of all of its most validated theories a very weak candidate. (This would have to be a language that revises itself in response to evidence, and has a system of pointers that permits frequently referenced concepts to be reused with ease; keeping track of what language you ought to be using would be computationally intractible because they are reflexive in complicated ways... but that's beyond the scope of the current conversation. I will discuss it later.) Most people pick something far more arbitrary. Actually, most people avoid picking anything at all, which is worse than picking something arbitrary.
But of the people who I have read who do put some effort into describing which programming language they would use as the basis of their version of Occam's razor, the most popular choice tends to be Binary Lambda calculus. Actually, if you are truly a proponent of Occam's razor this is pretty much the right choice, since it is probably very close to the simplest possible programming language that can possibly be devised. It autocompiles very easily (requiring few bits to describe itself), which if you truly have strong Occam priors ought to be a requirement for any self-consistent basis for your theory. Of course, anyone can devise a programming language that autocompiles with a single bit instruction, which would make them simpler in one sense. However, any of these programming languages is going to be much more challenging to implement in any other language than binary lambda calculus. Binary lambda calculus is very simple in most pair-wise language comparisons. It's very difficult to come up with other programming languages that compile each other with as little difficulty as most programming languages can compile binary lambda calculus.
One of the arguments I would make against Occam's razor is that many more complicated programming languages than binary lambda calculus are practically guaranteed to outperform binary lambda calculus as the best programming language to use for measuring length. In particular, binary lambda calculus does not have a good enough system of pointers to make the explanation for "someone carried the box" simpler than "the box teleported itself." Teleportation is practically guaranteed to be the simplest explanation for motion in this sort of system by many, many orders of magnitude. Just update the position stored for the object is always way easier than specifying that somebody or something else moved it, and the degree to which this explanation is likely to be simpler overwhelms available evidence. It is likely to be simpler by thousands of bits setting the prior odds against any alternative at 2 ** 1000 to 1 even in optimistic projections.
In short, I think there are very strong information-theoretic counterarguments to the validity of interpretations of information-theoretic formulations of Occam's razor, and I think that the theory does deserve to be refuted on these grounds, but I also think that there is an even stronger logical refutation of Occam's razor that takes that deals with "True statements are true" sort of tautologies.
In particular:
The simplest explanation is always the simplest.
Equivalent theories are always equivalent.
The most persuasive explanation is always the most persuasive.
The most probable explanation (given available data) is always the most probable explanation (given available data).
Reflexively self-consistent explanations are always reflexively self-consistent.
The most accurate explanation is always the most accurate.
The epistemology that produces the most predictive priors is the epistemology that produces the most predictive priors.
Self-improving epistemologies are self-improving; whereas static epistemologies are static.
Etc.
We can model all of these things separately and see that all of these things contain some elements of consistency with Occam's razor and some elements of inconsistency with Occam's razor -- the most damning of which are that considerations about persuasiveness and reflexive self-consistency would lead us to realize that statements like Occam's razor would be likely to be believed even if they don't have any merit.
We can even create an epistemology that (assuming the basic accuracy of statistics) is guaranteed to be asymptotically equivalent to Occam's razor if and only if no better alternative exists.
This brings me to my final note which is to say that most epistemologies that include Occam's razor and another theory are themselves inconsistent with Occam's razor. It is possible to devise a system of priors from the assumption that probability theory is more-or-less correct. In which case you have a formal system that takes only probability theory as its axioms, and this system is itself information-theoretically simpler than a system which also has axioms for weighting simplicity.
Some of these considerations may be a little abstruse, but most of them should be relatively straightforward to anyone with the mathematical background required to understand the information-theoretic formulation of Occam's razor to begin with.
Thursday, April 2, 2015
Where does the time go?
My mind has just been blank the last few days, much more blank than I ever recall it being. I've edited To Change the World (the book I just finished writing), done a little reading, less writing, started exercising again, saw my family, and got in contact with a few people that I've needed to contact, began a little work getting back into the swing of programming, and caught up with a few things that I was putting off while I made a final surge on my book the last few days. It doesn't sound like nearly as paltry a list as it is, when I list it out like that, but that's most of what I did over the past three days, and I don't even know what I thought about in between. My mind has just been blank, and I've had a growing sense of worry building up in the back of my head the past couple days.
I guess I've been looking at profiles for literary agents and reading about what I should do in my next steps and started thinking about my job search quite a bit. When I start to worry about something, time just evaporates. I feel tired, but I don't feel like I've been up long today. I felt exhausted yesterday, and again felt exhausted without having felt like the day had existed. I think anxiety messes with my sense of time a lot more than I used to think it did. Hopefully, I can overcome that.
I don't know what to do about my job search. I really don't know what sort of career I'd like to have. Some part of me wants to go back into developing software. It's just an easy way to do something where I know I have a lot to contribute, and would do well... especially if I can avoid becoming anxious, which I should be able to do. Another part of me remembers that I've just come from a recent experience that I don't want to go back to. I was too isolated at my last job for sure. Part of the problem was that I was working from home. Sometimes, I truly love writing code. Sometimes, I think it's one of the most fun things I've ever done. (Writing, painting, reading, and playing music are also up there with it for sure.) I pretty much quit playing computer games when I started learning to write code, because it was more enthralling in a similar way. It's puzzles to be solved and progress to be made in a highly imaginative medium, but I also burnt out really hard when I did eventually burn out.
I don't know. I'm halfway tempted to think that I should go back into programming and start taking medication if I do start to burn out again. If I can find a job in an office with interesting people, programming in a language that I like (preferably Python or Haskell) working on something that interests me (algorithms, possibly some design and UI), I think I would enjoy it a lot more than what I've been doing. It's just, I don't know where to find that.
On the other hand, if I can get a job doing consulting, spending most of my day interacting with other people, doing research, and writing up the results of my research, I think I'd have a lot of energy to spend on programming when I get home. I want to work on a project that I can keep developing for years, and I just don't think I have much hope of maintaining my enthusiasm for development if I do it at work and do it again on my own time. I'm a complete variety junky.
I suppose my real options are that I either get a job where I code by day, and then I come home and I write nights and weekends or I find a job where I write and research during the day, and then I come home and code nights and weekends.
That should solve my problem for me. I ought to be able to have a better career doing coding than I would as a consultant, and I would expect to have more success as a writer on my own than I would as a developer on my own. Either way though, I have to scrap a ton of what I want to do with my life.
That's my biggest problem. I want to do way too much.
I always feel like I'm wasting my time because I always feel as if there is something more important that I ought to be doing, if I could simply figure out how to be doing all of it.
I need to be doing things like this just to keep my sanity. If I wasn't writing through my thought process, it would keep spinning out into all sorts of irrelevant directions. I actually do accomplish far more when I let myself indulge in a few minutes worth of writing stream of consciousness each day than when I try to organize my thoughts some other way, so I need to keep doing that. I also accomplish more when I go for a run (and I'm way happier too) so long as I keep my runs pretty short, so I need to do that again. But then those things start to feel like a waste of time as soon as I have something else going that seems productive. It's a catch 22 that I just need to accustom myself to, I guess.
But then there are the projects that I really wish I could spend my whole life working on... I really wish I could divide myself into multiple copies so that I could spend a lifetime writing songs, another lifetime writing books, another lifetime painting, and another lifetime writing code. Maybe more than one on a couple of those.
I have so many thoughts in my head that I feel like are screaming to get out. Designs related to programming languages and AI, images that I really want to see, songs that are half-completed, unfinished books for which I have a chapter or two and an outline. Somethings got to give. I know I need to abandon my music... but it hurts. I probably should abandon my art, but that also hurts... I didn't bring my painting supplies home with me because I knew they would distract me from my writing if I had them, and I miss them. (I went a little while without a piano when I moved back out to Chicago, that was also really hard for me. It wasn't the hardest time I've had when I tried to give up piano, but it was close. I actually became depressed one of the times I tried to quit, and I've never even made much of an attempt to give up singing. In some ways, I want to, in others, I'd rather just die. This is just such a part of me.)
I should probably just take a day sometime to let myself cry, and face the fact that I can't keep these things in my life as much as I'd like to. I need to grow up, and growing up is... fucking stupid. Seriously, pretty much all I want in life is to have the freedom to split my time between four productive activities that I've loved. (Ok, I'd also like to spend some time researching and learning, and other time socializing and being in relationships with other people, and a little bit exercising and showering and eating.) But the chances of that happening any time soon are practically zero.
Whatever, I need to go to bed tonight, and tomorrow, I need to come to turns with what I'm doing in this world.
I guess I've been looking at profiles for literary agents and reading about what I should do in my next steps and started thinking about my job search quite a bit. When I start to worry about something, time just evaporates. I feel tired, but I don't feel like I've been up long today. I felt exhausted yesterday, and again felt exhausted without having felt like the day had existed. I think anxiety messes with my sense of time a lot more than I used to think it did. Hopefully, I can overcome that.
I don't know what to do about my job search. I really don't know what sort of career I'd like to have. Some part of me wants to go back into developing software. It's just an easy way to do something where I know I have a lot to contribute, and would do well... especially if I can avoid becoming anxious, which I should be able to do. Another part of me remembers that I've just come from a recent experience that I don't want to go back to. I was too isolated at my last job for sure. Part of the problem was that I was working from home. Sometimes, I truly love writing code. Sometimes, I think it's one of the most fun things I've ever done. (Writing, painting, reading, and playing music are also up there with it for sure.) I pretty much quit playing computer games when I started learning to write code, because it was more enthralling in a similar way. It's puzzles to be solved and progress to be made in a highly imaginative medium, but I also burnt out really hard when I did eventually burn out.
I don't know. I'm halfway tempted to think that I should go back into programming and start taking medication if I do start to burn out again. If I can find a job in an office with interesting people, programming in a language that I like (preferably Python or Haskell) working on something that interests me (algorithms, possibly some design and UI), I think I would enjoy it a lot more than what I've been doing. It's just, I don't know where to find that.
On the other hand, if I can get a job doing consulting, spending most of my day interacting with other people, doing research, and writing up the results of my research, I think I'd have a lot of energy to spend on programming when I get home. I want to work on a project that I can keep developing for years, and I just don't think I have much hope of maintaining my enthusiasm for development if I do it at work and do it again on my own time. I'm a complete variety junky.
I suppose my real options are that I either get a job where I code by day, and then I come home and I write nights and weekends or I find a job where I write and research during the day, and then I come home and code nights and weekends.
That should solve my problem for me. I ought to be able to have a better career doing coding than I would as a consultant, and I would expect to have more success as a writer on my own than I would as a developer on my own. Either way though, I have to scrap a ton of what I want to do with my life.
That's my biggest problem. I want to do way too much.
I always feel like I'm wasting my time because I always feel as if there is something more important that I ought to be doing, if I could simply figure out how to be doing all of it.
I need to be doing things like this just to keep my sanity. If I wasn't writing through my thought process, it would keep spinning out into all sorts of irrelevant directions. I actually do accomplish far more when I let myself indulge in a few minutes worth of writing stream of consciousness each day than when I try to organize my thoughts some other way, so I need to keep doing that. I also accomplish more when I go for a run (and I'm way happier too) so long as I keep my runs pretty short, so I need to do that again. But then those things start to feel like a waste of time as soon as I have something else going that seems productive. It's a catch 22 that I just need to accustom myself to, I guess.
But then there are the projects that I really wish I could spend my whole life working on... I really wish I could divide myself into multiple copies so that I could spend a lifetime writing songs, another lifetime writing books, another lifetime painting, and another lifetime writing code. Maybe more than one on a couple of those.
I have so many thoughts in my head that I feel like are screaming to get out. Designs related to programming languages and AI, images that I really want to see, songs that are half-completed, unfinished books for which I have a chapter or two and an outline. Somethings got to give. I know I need to abandon my music... but it hurts. I probably should abandon my art, but that also hurts... I didn't bring my painting supplies home with me because I knew they would distract me from my writing if I had them, and I miss them. (I went a little while without a piano when I moved back out to Chicago, that was also really hard for me. It wasn't the hardest time I've had when I tried to give up piano, but it was close. I actually became depressed one of the times I tried to quit, and I've never even made much of an attempt to give up singing. In some ways, I want to, in others, I'd rather just die. This is just such a part of me.)
I should probably just take a day sometime to let myself cry, and face the fact that I can't keep these things in my life as much as I'd like to. I need to grow up, and growing up is... fucking stupid. Seriously, pretty much all I want in life is to have the freedom to split my time between four productive activities that I've loved. (Ok, I'd also like to spend some time researching and learning, and other time socializing and being in relationships with other people, and a little bit exercising and showering and eating.) But the chances of that happening any time soon are practically zero.
Whatever, I need to go to bed tonight, and tomorrow, I need to come to turns with what I'm doing in this world.
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