For a rational agent with goals that don’t include “being averse to risk”, risk aversion is a bias. The correct decision theory acts on expected utility, with utility of outcomes and probability of outcomes factored apart and calculated separately. Risk aversion does not factor them.
“Risk Aversion,” as a technical term, means that the utility function is concave with respect to its input, like in thelittledoctor’s example. I think you’re thinking of something else, like the certainty effect. But I don’t know of anyone who considers the certainty effect to be a terminal goal rather than an instrumental one (woo, I don’t have to compute probabilities!).
A proper utilitarian would feel approximately the same desire to do something about each
And we should be proper utilitarians… why?
what if we discover, for example, that some murders are not calculated defections, but failures of self control caused by a bad upbringing and lack of education.
Then we have evidence they will strike again.
What if we then further discover that there is a two-month training course that has a high success rate of turning murderers into productive members of society.
Does that exist? My impression is that violent criminals often have suffered head injuries, not just poor upbringings.
Even if it does exist, and we have a way to restore people to normalcy, are there strong game theoretic reasons to? There could still be calculated defections, which we should attempt to deter by punishing violent crime. The rehab program also seems far more useful before crimes happen, rather than after.
“Risk Aversion,” as a technical term, means that the utility function is concave with respect to its input, like in thelittledoctor’s example. I think you’re thinking of something else, like the certainty effect. But I don’t know of anyone who considers the certainty effect to be a terminal goal rather than an instrumental one (woo, I don’t have to compute probabilities!).
Oh, ok. I mean the affect where people make their utility functions “risk averse” to avoid bad possibilities, or just go ahead and avoid bad possibilities, and I have seen people on LW take “risk aversion” (whatever that means to them) as terminal.
And we should be proper utilitarians… why?
Because it works better for achieving values that don’t include “non-utilitarianism”? Why should we be Bayesians either?
Does that exist? My impression is that violent criminals often have suffered head injuries, not just poor upbringings.
Even if it does exist, and we have a way to restore people to normalcy, are there strong game theoretic reasons to? There could still be calculated defections, which we should attempt to deter by punishing violent crime. The rehab program also seems far more useful before crimes happen, rather than after.
Did you see the disclaimer about how this is fictional? I put that there to avoid this...
The fictional psychologists assure us that Dan is curable.
It would be nice to avoid murders by putting people through the course preemptively, but it’s no good to give up on the course afterwards.
“Risk Aversion,” as a technical term, means that the utility function is concave with respect to its inpu [...]
Oh, ok. I mean the affect where people make their utility functions “risk averse” to avoid bad possibilities, or just go
ahead and avoid bad possibilities, and I have seen people on LW take “risk aversion” (whatever that means to them)
as terminal.
You don’t “make” your utility function anything; it is what it is. “Risk aversion” just means that the most obvious scale for measuring your utility isn’t proportional to your true utility scale. For example, one’s utility for money is generally not proportional to the amount of money, and is approximately proportional only if the amount is not large compared to your current wealth.
For larger quantities of money it’s not even close to proportional. In particular, I—and most people, for that matter—do not value $2 billion twice as much as $1 billion. The positive impact on my life of gaining $1 billion dollars at my current level of wealth is vastly greater than the additional positive impact of going from $1 billion to $2 billion. Hence if I were offered a choice between a guaranteed $1 billion dollars vs. a 90% chance of gaining $2 billion dollars, I would choose the sure thing—the expected utility of the second option is greater than 90% but less than 91% of the expected utility of the first option for me.
Likewise, suppose that my net worth is $100,000. An extra $100,000 would be great, but losing $100,000 would be disastrous; it would wipe me out. So my gain in utility from gaining $100,000 is considerably less than my loss of utility from losing $100,000… and it makes sense for me to do things like insure my home.
Both of these examples show me to be risk averse. It is not a strategy I have chosen; it is simply a statement of my personal utility function.
I know your position is dominant around here, but I intended to tackle it anyway. If you care about doing good, once you’ve handled your personal expenses, additional marginal dollars have fixed marginal utility (until you’re dealing with enough money to seriously impact the global market for marginal utility).
Money utility is linear between the amounts where you’re worrying about personal expenses, and the amounts where you’re impacting the global market for marginal utility. That’s most of the range.
This may be true, and so we might expect someone who was very wealthy to lose their risk-aversion for deicisions where they were sure there was no risk of losses cutting into what they need for personal use. Sounds pretty reasonable for a risk-averse agent to me.
Because if you don’t use Bayes’ Rule to navigate through conditional probabilities, you will come up with answers that are objectively wrong.
Did you see the disclaimer about how this is fictional?
Yes, but in any discussion about bias context matters. If people believe that real systems that serve real people work better with justice, but we can imagine a system in which there are no obvious defects from ignoring justice, that doesn’t mean those people are biased.
Constructing these sorts of policy questions, particularly centered around a single scenario, typically strikes me as motivated cognition. If we’d like to be kind to murderers (how nice of us!), we can come up with a scenario that suggests that option rather than seeking vengeance (how mean!).
But the same justifications can be applied in scenarios that are less contrived, where they look more questionable. Suppose a productive member of society, Mr. B, murders Mr. A because of a calculated defection and gets caught. Mr. B informs us that Mr. A was the only person he would want to murder, with several compelling reasons attached arguing the rest of us needn’t fear him. Should we forgive and forget? We don’t even need a 2 month training course, so it’s cheaper for society, and we have the assurance of experience that Mr. B is productive.
(I don’t particularly want to delve into casuistry. Suffice it to say there are reasons to say Mr. B should pay the price and Dan should not, but it seems to me that those reasons do not carve reality / game theory at the joints.)
Does it not? Do we know of a better basis for decision theory? Please tell me what you know.
... Suffice it to say there are reasons to say Mr. B should pay the price and Dan should not, but it seems to me that those reasons do not carve reality / game theory at the joints.
When we are faced with having to punish someone, we want to get out of it. Punishing people sucks. The question is whether we can avoid giving the punishment, and still credibly hold the threat of punishment against rational defectors. I think in Deadbeat Dan’s case, since he is not a rational defector, we can credibly hold the threat against defectors. In Mr. B’s case, we don’t care if he’ll never do it again, we have pre-committed to punish rational defectors, and must follow thru if we wish to maintain that threat.
I don’t think this is a case of carving reality into qualitative categories, because we have a quantitative analysis that solves the problem (utility of letting them go vs disutility of undermining rule of law).
The question is whether we can avoid giving the punishment, and still credibly hold the threat of punishment against rational defectors.
I know this reaction is not rational, but still, my first reaction was: In such environment (where it is possible to tell the difference between irrational and rational crime, and punish accordingly), becoming rational means losing your “get of out the jail once” card, and that’s not fair! The more rational you are, the wider range of your possible crimes becomes punishable. You are being punished for being rational.
Technically, a good person should not care about limiting their own crime range, and (if the good for everyone is their goal) they should be actually happy they have less chance to harm anyone. But still it somehow sucks to know that while I would be punished for doing X (because I am rational and see the consequences), other person would not be punished for doing a similar thing.
I guess this intuition is based on the real-world situations, where the psychologists are not perfect, the justice is not perfect, and therefore any rule like this has big chance to be heavily abused. (As in: If you have a good lawyer, your crimes will be declared irrational, and you will be sentenced to two weeks of group therapy. Meanwhile the average Joe does the same thing and gets hanged.)
I agree with everything you said, but don’t understand why you don’t think it’s “rational”.
Technically, a good person should not care about limiting their own crime range, and (if the good for everyone is their goal) they should be actually happy they have less chance to harm anyone. But still it somehow sucks to know that while I would be punished for doing X (because I am rational and see the consequences), other person would not be punished for doing a similar thing.
Remember “good” and “rational” are not the same thing.
I know this reaction is not rational, but still, my first reaction was: In such environment (where it is possible to tell the difference between irrational and rational crime, and punish accordingly), becoming rational means losing your “get of out the jail once” card, and that’s not fair! The more rational you are, the wider range of your possible crimes becomes punishable. You are being punished for being rational.
Maybe rational defector was the wrong way to put it. I don’t mean punish people who test high on rationality, I mean punish in the cases where it’s a calculated defection for personal gain. Punish in cases where tit for tat is actually an effective strategy.
Some crimes just aren’t done for personal gain, and those should have alternate strategy. Of course, what the alternate strategy is is still open, and distinguishing between them is difficult, as you say:
I guess this intuition is based on the real-world situations, where the psychologists are not perfect, the justice is not perfect, and therefore any rule like this has big chance to be heavily abused. (As in: If you have a good lawyer, your crimes will be declared irrational, and you will be sentenced to two weeks of group therapy. Meanwhile the average Joe does the same thing and gets hanged.)
At our level, I don’t think we are able to distinguish between crimes that should get punishment, and things where punishment is ineffective. It’s just useful to understand that justice is about game theory, not revenge.
Does it not? Do we know of a better basis for decision theory? Please tell me what you know.
I have not seen a satisfactory way to compare utilities, and so believe that actually running a utilitarian calculation is an unsolved (and I would suspect unsolvable) problem.
When we are faced with having to punish someone, we want to get out of it. Punishing people sucks.
Why should someone with this view ever be given the position of judge? I would even be leery of entrusting a child to their care for an afternoon, let alone an upbringing.
(I assume that by “want to get out of it” you mean “expected negative total value” not “expected negative short-term value.” One who delights in punishment is a brute, but one who shirks from meting out just punishment is infirm.)
The question is whether we can avoid giving the punishment, and still credibly hold the threat of punishment against rational defectors.
The question is whether we can avoid giving the punishment, and still credibly hold the threat of punishment against rational defectors.
No. Next question.
Not nearly straightforward enough to use the “No. Next question.” move on. Deception and various forms of active manipulation are possible. They are rational, not omniscient.
Why should someone with this view ever be given the position of judge? I would even be leery of entrusting a child to their care for an afternoon, let alone an upbringing.
(I assume that by “want to get out of it” you mean “expected negative total value” not “expected negative short-term value.” One who delights in punishment is a brute, but one who shirks from meting out just punishment is infirm.)
Punishing people sucks the same way paying for stuff you take sucks, or working hard to achieve your goals sucks. You should be able to conceive of the fact that short term suck can pay for long term good. Pretending that punishment is good because it pays for good is stupid and you will get confused if you think like that.
A judge or parent who understands that punishment is bad is not necessarily going to not do it. They may also understand that following thru on punishment threats is necessary to keep the threat credible.
One who delights in punishment is a brute, but one who shirks from meting out just punishment is infirm.
Those words are loaded with connotation. Why are you using them? Say what is bad about punishing too much or too little without using words like that. You may find that too much punishment is bad because punishment is bad, and not enough punishment is bad because it fails to follow thru on the precommitment to punish that holds up the rule of law.
No. Next question.
Really? So theres no such thing as extenuating circumstances where we let someone off, but everyone understands that the threat of punishment is still there?
Maybe it was an accident, maybe punishing the weather won’t make it sunnier, maybe we should deal with the insane a little bit differently.
You should be able to conceive of the fact that short term suck can pay for long term good.
Yes, of course. Indeed, there are few long term goods that can be purchased without short term suck.
But you weren’t arguing that punishing criminals was a long term bad, or even insufficiently good. You were arguing that it was short term suck.
Those words are loaded with connotation. Why are you using them?
Invert the order of the sentences, and you have your answer. But I will answer at length:
The history and law and order is one of long and painful experience. The common law definition of “assault” did not spring forth from first principles, it was learned.
The source of order is deterrence; deterrence rests on expectations; expectations rest on identities. The brute is resisted in a way that the even-handed is not; the infirm are flaunted in a way that the firm are not.
So theres no such thing as extenuating circumstances where we let someone off, but everyone understands that the threat of punishment is still there?
Accepting any excuse reduces the credibility of the commitment. Sometimes you may think that reduction is acceptable, but you should never pretend it was absent.
But you weren’t arguing that punishing criminals was a long term bad, or even insufficiently good. You were arguing that it was short term suck.
Yes? Punishing criminals sucks, but it pays for the rule of law. I miss your point.
Invert the order of the sentences, and you have your answer. But I will answer at length:
still don’t get it
The source of order is deterrence;
agree
deterrence rests on expectations;
agree
expectations rest on identities. The brute is resisted in a way that the even-handed is not; the infirm are flaunted in a way that the firm are not.
wat? I don’t understand. What has identity got to do with anything? And too many loaded words. What does “even-handed” even mean, apart from “vaguely good and something to do with justice”?
Accepting any excuse reduces the credibility of the commitment. Sometimes you may think that reduction is acceptable, but you should never pretend it was absent.
Agreed. I thought you meant there weren’t cases that were worth it.
Even if it does exist, and we have a way to restore people to normalcy, are there strong game theoretic reasons to?
It seems like it depends on whether or not we can easily distinguish between “irrational” crime and calculated defections. In the current world, we can’t, so there are game-theoretic reasons to justify similar treatment. But if we could relatively reliably differentiate, it seems like a large waste of resources avoid a cheap treatment that reduces the risk of future irrational crime to negligible levels. And I suspect that’s true even if our test was only 75% accurate at telling the difference between “irrational” criminals and calculated defections.
My impression is that violent criminals often have suffered head injuries, not just poor upbringings.
That’s an interesting impression to have. Not that I know any better, but I’m doubtful of the reliability of any data because it is irrelevant to the US legal system (except for insanity type defenses, and mitigation in death penalty litigation).
But if we could relatively reliably differentiate, it seems like a large waste of resources avoid a cheap treatment that reduces the risk of future irrational crime to negligible levels.
Yep. But I don’t see significant reason to expect detection systems to outpace tricking systems.
I’m doubtful of the reliability of any data
25 to 87% of inmates report suffering a head injury, compared to 8.5% of the general population. The high variation in reports suggests that the data isn’t the best quality / most general, but with the most conservative estimate prevalence is at three times higher.
“Risk Aversion,” as a technical term, means that the utility function is concave with respect to its input
Risk aversion is separate from the properties of utility function. Being risk-averse rather means preferring a guaranteed payoff to a bet with the same expected utility. See here for a numerical example. It is possible to be risk averse even with a convex utility function.
That is a non-standard definition. (Standard definition.) Agents should always be indifferent between bets with identical expected utilities. (They do not always have to be indifferent between bets with identical expected payoffs.)
Preferring a guarantee to a bet is the certainty effect, like I claimed in the grandparent.
Rational agents should be. Irrational agents—in this case, prone to risk aversion—would instead be willing to pay a finite cost for the bet to be replaced with the sure deal, thus losing utility. You can fix this by explicitly incorporating risk in the utility function, making the agent rational and not risk-averse any more.
This strikes me as, though I’m unsure as to which technical term applies here, ‘liking your theory too much’. ’Tis necessary to calculate the probability of payoff for each of two exclusive options of identical utility in order to rationally process the choice. If Option A of Utilon 100 occurs with 80% probability and Option B also of Utilon 100 occurs with 79.9% probability, Option A is the more rational choice. To recognise the soundness of Vaniver’s following statement, one must acknowledge the necessity of calculating risk. [Additionally, if two options are of unequal utility, differences in payoff probabilities become even more salient as the possible disutility of no payoff should lower one’s utility estimate of whichever choice has the lower payoff probability (assuming there is one).]*
(They do not always have to be indifferent between bets with identical expected payoffs.)
Honestly the above seems so simple that I very much think I’ve misunderstood something, in which case please view this as a request for clarification.
[...]* This also seems obvious, but on an intuitive mathematical level, thus I don’t have much confidence in it; it fit better up there than down here.
Again, what you are saying is a non-standard definition. The commonly used term for the bias you’re describing is certainty effect, and risk aversion is used to refer to concave utility functions.
First, concave utility function is just a model for risk aversion which is “the reluctance of a person to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff.” (wiki)
Second, the certainty effect is indeed one of the effects that is captured by my preferred model, but of course it’s not limited to it, because it’s possible to behave in a risk-averse manner even if none of the offered bets are certain.
This! If you’re risk averse, then you want to avoid risk, and so in the real utility calculation upon which you base your decisions the risk-averse option gets a little extra positive term for being, well, risk-averse. And then the two options no longer have the same expected utility.
Unfortunately, under your new “fixed” utility function there will again be a point of indifference at some slightly different probability/payoff combination, where you, being risk-averse, have to go for the sure deal, so you will end up stuck in an infinite recursion trying to adjust your utility function further and further. I tried to explain this more clearly here.
I don’t think that follows. The risk-aversion utility attaches to the choice, not the outcome: I get extra utility for having made a choice with lower expected variance, not for one of the outcomes. If you then offer me a choice between choices, then sure, there will be more risk aversion, but I don’t think it’s viciously recursive.
“Risk Aversion,” as a technical term, means that the utility function is concave with respect to its input, like in thelittledoctor’s example. I think you’re thinking of something else, like the certainty effect. But I don’t know of anyone who considers the certainty effect to be a terminal goal rather than an instrumental one (woo, I don’t have to compute probabilities!).
And we should be proper utilitarians… why?
Then we have evidence they will strike again.
Does that exist? My impression is that violent criminals often have suffered head injuries, not just poor upbringings.
Even if it does exist, and we have a way to restore people to normalcy, are there strong game theoretic reasons to? There could still be calculated defections, which we should attempt to deter by punishing violent crime. The rehab program also seems far more useful before crimes happen, rather than after.
Oh, ok. I mean the affect where people make their utility functions “risk averse” to avoid bad possibilities, or just go ahead and avoid bad possibilities, and I have seen people on LW take “risk aversion” (whatever that means to them) as terminal.
Because it works better for achieving values that don’t include “non-utilitarianism”? Why should we be Bayesians either?
Did you see the disclaimer about how this is fictional? I put that there to avoid this...
The fictional psychologists assure us that Dan is curable.
It would be nice to avoid murders by putting people through the course preemptively, but it’s no good to give up on the course afterwards.
You don’t “make” your utility function anything; it is what it is. “Risk aversion” just means that the most obvious scale for measuring your utility isn’t proportional to your true utility scale. For example, one’s utility for money is generally not proportional to the amount of money, and is approximately proportional only if the amount is not large compared to your current wealth.
For larger quantities of money it’s not even close to proportional. In particular, I—and most people, for that matter—do not value $2 billion twice as much as $1 billion. The positive impact on my life of gaining $1 billion dollars at my current level of wealth is vastly greater than the additional positive impact of going from $1 billion to $2 billion. Hence if I were offered a choice between a guaranteed $1 billion dollars vs. a 90% chance of gaining $2 billion dollars, I would choose the sure thing—the expected utility of the second option is greater than 90% but less than 91% of the expected utility of the first option for me.
Likewise, suppose that my net worth is $100,000. An extra $100,000 would be great, but losing $100,000 would be disastrous; it would wipe me out. So my gain in utility from gaining $100,000 is considerably less than my loss of utility from losing $100,000… and it makes sense for me to do things like insure my home.
Both of these examples show me to be risk averse. It is not a strategy I have chosen; it is simply a statement of my personal utility function.
I know your position is dominant around here, but I intended to tackle it anyway. If you care about doing good, once you’ve handled your personal expenses, additional marginal dollars have fixed marginal utility (until you’re dealing with enough money to seriously impact the global market for marginal utility).
Money utility is linear between the amounts where you’re worrying about personal expenses, and the amounts where you’re impacting the global market for marginal utility. That’s most of the range.
This may be true, and so we might expect someone who was very wealthy to lose their risk-aversion for deicisions where they were sure there was no risk of losses cutting into what they need for personal use. Sounds pretty reasonable for a risk-averse agent to me.
The flaw in this theory is that it assumes the extra money actually gets donated.
humph. if we are not assuming the money gets used, I’m not sure how we can apply any particular utility to it at all.
We can assume the money gets used on oneself, which is much more likely to happen in the stated scenario.
Does it?
Because if you don’t use Bayes’ Rule to navigate through conditional probabilities, you will come up with answers that are objectively wrong.
Yes, but in any discussion about bias context matters. If people believe that real systems that serve real people work better with justice, but we can imagine a system in which there are no obvious defects from ignoring justice, that doesn’t mean those people are biased.
Constructing these sorts of policy questions, particularly centered around a single scenario, typically strikes me as motivated cognition. If we’d like to be kind to murderers (how nice of us!), we can come up with a scenario that suggests that option rather than seeking vengeance (how mean!).
But the same justifications can be applied in scenarios that are less contrived, where they look more questionable. Suppose a productive member of society, Mr. B, murders Mr. A because of a calculated defection and gets caught. Mr. B informs us that Mr. A was the only person he would want to murder, with several compelling reasons attached arguing the rest of us needn’t fear him. Should we forgive and forget? We don’t even need a 2 month training course, so it’s cheaper for society, and we have the assurance of experience that Mr. B is productive.
(I don’t particularly want to delve into casuistry. Suffice it to say there are reasons to say Mr. B should pay the price and Dan should not, but it seems to me that those reasons do not carve reality / game theory at the joints.)
Does it not? Do we know of a better basis for decision theory? Please tell me what you know.
When we are faced with having to punish someone, we want to get out of it. Punishing people sucks. The question is whether we can avoid giving the punishment, and still credibly hold the threat of punishment against rational defectors. I think in Deadbeat Dan’s case, since he is not a rational defector, we can credibly hold the threat against defectors. In Mr. B’s case, we don’t care if he’ll never do it again, we have pre-committed to punish rational defectors, and must follow thru if we wish to maintain that threat.
I don’t think this is a case of carving reality into qualitative categories, because we have a quantitative analysis that solves the problem (utility of letting them go vs disutility of undermining rule of law).
About excuses
I know this reaction is not rational, but still, my first reaction was: In such environment (where it is possible to tell the difference between irrational and rational crime, and punish accordingly), becoming rational means losing your “get of out the jail once” card, and that’s not fair! The more rational you are, the wider range of your possible crimes becomes punishable. You are being punished for being rational.
Technically, a good person should not care about limiting their own crime range, and (if the good for everyone is their goal) they should be actually happy they have less chance to harm anyone. But still it somehow sucks to know that while I would be punished for doing X (because I am rational and see the consequences), other person would not be punished for doing a similar thing.
I guess this intuition is based on the real-world situations, where the psychologists are not perfect, the justice is not perfect, and therefore any rule like this has big chance to be heavily abused. (As in: If you have a good lawyer, your crimes will be declared irrational, and you will be sentenced to two weeks of group therapy. Meanwhile the average Joe does the same thing and gets hanged.)
I agree with everything you said, but don’t understand why you don’t think it’s “rational”.
Remember “good” and “rational” are not the same thing.
Maybe rational defector was the wrong way to put it. I don’t mean punish people who test high on rationality, I mean punish in the cases where it’s a calculated defection for personal gain. Punish in cases where tit for tat is actually an effective strategy.
Some crimes just aren’t done for personal gain, and those should have alternate strategy. Of course, what the alternate strategy is is still open, and distinguishing between them is difficult, as you say:
At our level, I don’t think we are able to distinguish between crimes that should get punishment, and things where punishment is ineffective. It’s just useful to understand that justice is about game theory, not revenge.
I have not seen a satisfactory way to compare utilities, and so believe that actually running a utilitarian calculation is an unsolved (and I would suspect unsolvable) problem.
Why should someone with this view ever be given the position of judge? I would even be leery of entrusting a child to their care for an afternoon, let alone an upbringing.
(I assume that by “want to get out of it” you mean “expected negative total value” not “expected negative short-term value.” One who delights in punishment is a brute, but one who shirks from meting out just punishment is infirm.)
No. Next question.
Not nearly straightforward enough to use the “No. Next question.” move on. Deception and various forms of active manipulation are possible. They are rational, not omniscient.
Punishing people sucks the same way paying for stuff you take sucks, or working hard to achieve your goals sucks. You should be able to conceive of the fact that short term suck can pay for long term good. Pretending that punishment is good because it pays for good is stupid and you will get confused if you think like that.
A judge or parent who understands that punishment is bad is not necessarily going to not do it. They may also understand that following thru on punishment threats is necessary to keep the threat credible.
Those words are loaded with connotation. Why are you using them? Say what is bad about punishing too much or too little without using words like that. You may find that too much punishment is bad because punishment is bad, and not enough punishment is bad because it fails to follow thru on the precommitment to punish that holds up the rule of law.
Really? So theres no such thing as extenuating circumstances where we let someone off, but everyone understands that the threat of punishment is still there?
Maybe it was an accident, maybe punishing the weather won’t make it sunnier, maybe we should deal with the insane a little bit differently.
Yes, of course. Indeed, there are few long term goods that can be purchased without short term suck.
But you weren’t arguing that punishing criminals was a long term bad, or even insufficiently good. You were arguing that it was short term suck.
Invert the order of the sentences, and you have your answer. But I will answer at length:
The history and law and order is one of long and painful experience. The common law definition of “assault” did not spring forth from first principles, it was learned.
The source of order is deterrence; deterrence rests on expectations; expectations rest on identities. The brute is resisted in a way that the even-handed is not; the infirm are flaunted in a way that the firm are not.
Accepting any excuse reduces the credibility of the commitment. Sometimes you may think that reduction is acceptable, but you should never pretend it was absent.
Yes? Punishing criminals sucks, but it pays for the rule of law. I miss your point.
still don’t get it
agree
agree
wat? I don’t understand. What has identity got to do with anything? And too many loaded words. What does “even-handed” even mean, apart from “vaguely good and something to do with justice”?
Agreed. I thought you meant there weren’t cases that were worth it.
If you consider “not being a brute” part of your identity, you are less likely to act like a brute.
It seems like it depends on whether or not we can easily distinguish between “irrational” crime and calculated defections. In the current world, we can’t, so there are game-theoretic reasons to justify similar treatment. But if we could relatively reliably differentiate, it seems like a large waste of resources avoid a cheap treatment that reduces the risk of future irrational crime to negligible levels. And I suspect that’s true even if our test was only 75% accurate at telling the difference between “irrational” criminals and calculated defections.
That’s an interesting impression to have. Not that I know any better, but I’m doubtful of the reliability of any data because it is irrelevant to the US legal system (except for insanity type defenses, and mitigation in death penalty litigation).
Yep. But I don’t see significant reason to expect detection systems to outpace tricking systems.
25 to 87% of inmates report suffering a head injury, compared to 8.5% of the general population. The high variation in reports suggests that the data isn’t the best quality / most general, but with the most conservative estimate prevalence is at three times higher.
Risk aversion is separate from the properties of utility function. Being risk-averse rather means preferring a guaranteed payoff to a bet with the same expected utility. See here for a numerical example. It is possible to be risk averse even with a convex utility function.
That is a non-standard definition. (Standard definition.) Agents should always be indifferent between bets with identical expected utilities. (They do not always have to be indifferent between bets with identical expected payoffs.)
Preferring a guarantee to a bet is the certainty effect, like I claimed in the grandparent.
Rational agents should be. Irrational agents—in this case, prone to risk aversion—would instead be willing to pay a finite cost for the bet to be replaced with the sure deal, thus losing utility. You can fix this by explicitly incorporating risk in the utility function, making the agent rational and not risk-averse any more.
That sounds like a …drumroll… terminal bias.
Enshrining biases as values in your utility function seems like the wrong thing to do.
This strikes me as, though I’m unsure as to which technical term applies here, ‘liking your theory too much’. ’Tis necessary to calculate the probability of payoff for each of two exclusive options of identical utility in order to rationally process the choice. If Option A of Utilon 100 occurs with 80% probability and Option B also of Utilon 100 occurs with 79.9% probability, Option A is the more rational choice. To recognise the soundness of Vaniver’s following statement, one must acknowledge the necessity of calculating risk. [Additionally, if two options are of unequal utility, differences in payoff probabilities become even more salient as the possible disutility of no payoff should lower one’s utility estimate of whichever choice has the lower payoff probability (assuming there is one).]*
Honestly the above seems so simple that I very much think I’ve misunderstood something, in which case please view this as a request for clarification.
[...]* This also seems obvious, but on an intuitive mathematical level, thus I don’t have much confidence in it; it fit better up there than down here.
Again, what you are saying is a non-standard definition. The commonly used term for the bias you’re describing is certainty effect, and risk aversion is used to refer to concave utility functions.
First, concave utility function is just a model for risk aversion which is “the reluctance of a person to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff.” (wiki)
Second, the certainty effect is indeed one of the effects that is captured by my preferred model, but of course it’s not limited to it, because it’s possible to behave in a risk-averse manner even if none of the offered bets are certain.
Another way to interpret this situation is that the “utility function” being used to calculate the expected value is a fake utility function.
This! If you’re risk averse, then you want to avoid risk, and so in the real utility calculation upon which you base your decisions the risk-averse option gets a little extra positive term for being, well, risk-averse. And then the two options no longer have the same expected utility.
Unfortunately, under your new “fixed” utility function there will again be a point of indifference at some slightly different probability/payoff combination, where you, being risk-averse, have to go for the sure deal, so you will end up stuck in an infinite recursion trying to adjust your utility function further and further. I tried to explain this more clearly here.
I don’t think that follows. The risk-aversion utility attaches to the choice, not the outcome: I get extra utility for having made a choice with lower expected variance, not for one of the outcomes. If you then offer me a choice between choices, then sure, there will be more risk aversion, but I don’t think it’s viciously recursive.