Does anyone know the terms for the positions for and against in the following scenario?:
Let’s assume you have a one in a million chance of winning the lottery. Despite the poor chance, you pay five dollars to enter, and you win a large sum of money. Was playing the lottery the right choice?
I don’t know if there are terms for the positions, but it seems pretty obvious that this is just a question of how you define “right choice”. Not playing the lottery was the choice that seemed to maximize your utility given your knowledge at the time. Playing the lottery was the choice that actually maximized your utility. Which one you decide to call “right” is up to you. I think calling the former right is a little more useful because it describes how to actually make decisions, while the latter is only useful for looking back on decisions and evaluating them.
In decision theory, the “goodness” or “badness” of a decision is divorced from its actual outcome. Buying the lottery ticket was a bad decision regardless of whether you win.
However, don’t forget that the value of money doesn’t scale linearly with how much utility you assign to it. People tend to forget this. There is no rule that says you have to accept a certain $10 in exchange for a 10% chance at $100; on the contrary, it would be unusual to have a perfectly linear utility function in terms of money.
It’s possible that your valuation of $5 is essentially ‘nothing,’ while your valuation of $1 million is ‘extremely high.’ If you’ll permit me to construct a ridiculous scenario: let’s say that you’re guaranteed an income of $5 a day by the government, that you have no other way of obtaining steady income due to a disability, and that your living expenses are $4.99 per day. You will never be able to save $1 million; even if you save 1c per day and invest it as intelligently as possible, you will probably never accumulate $1 million. Let’s further assume that you will be significantly happier if you could buy a particular house which costs exactly $1 million. If we take this artificial example, then it may be rational, or “a good decision” to play the lottery some fraction of the time, since it is essentially the only chance you have of obtaining your dream house.
e: In case the downvote is due to a belief that I am wrong in my assertions, I am prepared to provide citations and calculations to verify everything in this comment. Unexplained downvotes drive me nuts particularly when I know I’m right.
Since we’re talking about probabilistic decision theories, if you consistently make “good decisions” you will still obtain “bad outcomes” some of the time. This should not be cause to start doubting your decision procedure. If you say you are 90% confident, you should be thrilled if you are wrong 10% of the time—it means you’re perfectly calibrated.
A perfectly rational agent working with incomplete or incorrect information will lose some of the time. The decisions of the agent are still optimal from the agent’s frame of reference.
In decision theory, the “goodness” or “badness” of a decision is divorced from its actual outcome.
How does this interact with the idea that rationalists should win?
Rationalists should follow winning strategies. If you followed a bad strategy and got lucky, that doesn’t mean you should keep following it. The relevant question is what strategy you should follow going forward.
Asking whether a particular past choice was “right” or “wrong”, if the answer has no impact on your future choices seems like a wrong question.
How does this interact with the idea that rationalists should win?
Rationalists win more by virtue of having a more accurate model of the world, and clearly this helps only in some domain, while in others only a favorable position in some kind of potential landscape would matter (e.g.: beauty contest).
Winning the lottery is one of those cases: buying the ticket is of course bad from a decision theory point of view, but one can always be luck enough to receive a great gain from those bad decisions. In the same way, an irrational person can have a correct belief by virtue of pure luck.
The “divorce” is logical/conceptual, not evidential. It remains true that “rationalists should win”, in the presumed intended sense that rationality wins in expectation, that winning is evidence of rationality, and that we should read the dictum a bit stronger to correct for our tendency to ascribe non-winning to bad luck.
More than two different positions, I think that’s two different senses of “right”. Once you replace it with “yielding a better expected outcome given what you knew when making the choice” or “yielding a better outcome given what we know now”, people wouldn’t actually disagree about anything.
(I myself prefer to use “right” with the former meaning.)
Yet Another Comment Not Answering Your Question ….
Let’s assume you have a one in a million chance of winning the lottery. Despite the poor chance, you pay five dollars to enter, and you win a large sum of money. Was playing the lottery the right choice?
A lot depends on whether this “large sum of money” is more or less than five million dollars.
Even with positive expected value, you may be better off passing up the bet depending on your tolerance for variance and the local shape of your utility-of-money function.
You won. Aren’t rationalists supposed to be doing that?
As far as you know, your probability estimate for “you will win the lottery” (in your mind) was wrong. It is another question how that updates the probability of “you would win the lottery if you played next week”, but whatever made you buy that ticket (even though the “rational” estimates voted against it… “trying random things”, whatever it was) should be applied more in the future.
Of course, the result is quite likely to be “learning lots of nonsense from a measurement error”, but you should definitely should update having seen that, and a decision you use for updates causing that decision to be made more in the future is definitely a right one.
If I won the lottery, I would definitely spend $5 for another ticket. And eventually you might realize that it’s just Omega having fun. (actually, isn’t one-boxing the same question?)
Playing the lottery was an irrational decision, but was the right choice. The outcome, as stated by moridinamael, is divorced from the decision making processes that went into it.
Assuming an unambiguous result that can only either be good or bad, and the most rational choice based upon the evidence then at hand led to a bad outcome, one still made the best (most rational) decision—but, considering the bad result, ’twas the wrong choice.
This classification if useful when determining the competency of a leader—they may have been an extremely rational decision maker but made nothing but wrong choices due to poor quality of information.
I forget my source—as for the terms, fubarofusco’s “Hindsight” fits well, while “Expected Value” does not.
Does anyone know the terms for the positions for and against in the following scenario?:
Let’s assume you have a one in a million chance of winning the lottery. Despite the poor chance, you pay five dollars to enter, and you win a large sum of money. Was playing the lottery the right choice?
Well, I would call them “expected value” and “hindsight”.
Hindsight says, “Because we got a good result, it’s all good.”
Expected value says, “We got lucky, and cannot expect to get lucky again.”
Rational Inquirer says “The world gave me a surprise. Is there something I can learn from this surprise?”
And then it says. “We learned something about the random variables that led to that lottery draw. This doesn’t generalize well.”
I don’t know if there are terms for the positions, but it seems pretty obvious that this is just a question of how you define “right choice”. Not playing the lottery was the choice that seemed to maximize your utility given your knowledge at the time. Playing the lottery was the choice that actually maximized your utility. Which one you decide to call “right” is up to you. I think calling the former right is a little more useful because it describes how to actually make decisions, while the latter is only useful for looking back on decisions and evaluating them.
In decision theory, the “goodness” or “badness” of a decision is divorced from its actual outcome. Buying the lottery ticket was a bad decision regardless of whether you win.
However, don’t forget that the value of money doesn’t scale linearly with how much utility you assign to it. People tend to forget this. There is no rule that says you have to accept a certain $10 in exchange for a 10% chance at $100; on the contrary, it would be unusual to have a perfectly linear utility function in terms of money.
It’s possible that your valuation of $5 is essentially ‘nothing,’ while your valuation of $1 million is ‘extremely high.’ If you’ll permit me to construct a ridiculous scenario: let’s say that you’re guaranteed an income of $5 a day by the government, that you have no other way of obtaining steady income due to a disability, and that your living expenses are $4.99 per day. You will never be able to save $1 million; even if you save 1c per day and invest it as intelligently as possible, you will probably never accumulate $1 million. Let’s further assume that you will be significantly happier if you could buy a particular house which costs exactly $1 million. If we take this artificial example, then it may be rational, or “a good decision” to play the lottery some fraction of the time, since it is essentially the only chance you have of obtaining your dream house.
e: In case the downvote is due to a belief that I am wrong in my assertions, I am prepared to provide citations and calculations to verify everything in this comment. Unexplained downvotes drive me nuts particularly when I know I’m right.
How does this interact with the idea that rationalists should win?
Since we’re talking about probabilistic decision theories, if you consistently make “good decisions” you will still obtain “bad outcomes” some of the time. This should not be cause to start doubting your decision procedure. If you say you are 90% confident, you should be thrilled if you are wrong 10% of the time—it means you’re perfectly calibrated.
A perfectly rational agent working with incomplete or incorrect information will lose some of the time. The decisions of the agent are still optimal from the agent’s frame of reference.
Rationalists should follow winning strategies. If you followed a bad strategy and got lucky, that doesn’t mean you should keep following it. The relevant question is what strategy you should follow going forward.
Asking whether a particular past choice was “right” or “wrong”, if the answer has no impact on your future choices seems like a wrong question.
Rationalists win more by virtue of having a more accurate model of the world, and clearly this helps only in some domain, while in others only a favorable position in some kind of potential landscape would matter (e.g.: beauty contest). Winning the lottery is one of those cases: buying the ticket is of course bad from a decision theory point of view, but one can always be luck enough to receive a great gain from those bad decisions. In the same way, an irrational person can have a correct belief by virtue of pure luck.
The “divorce” is logical/conceptual, not evidential. It remains true that “rationalists should win”, in the presumed intended sense that rationality wins in expectation, that winning is evidence of rationality, and that we should read the dictum a bit stronger to correct for our tendency to ascribe non-winning to bad luck.
“Should” != “will always”. Once in a while, unlikely things do happen.
More than two different positions, I think that’s two different senses of “right”. Once you replace it with “yielding a better expected outcome given what you knew when making the choice” or “yielding a better outcome given what we know now”, people wouldn’t actually disagree about anything.
(I myself prefer to use “right” with the former meaning.)
(I’ve seen people using “right” for the former and “lucky” for the latter, and people using “rational” for the former and “right” for the latter.)
Yet Another Comment Not Answering Your Question ….
A lot depends on whether this “large sum of money” is more or less than five million dollars.
I guess that in most ordinary situations the utility of $5M isn’t anywhere near 1M times the utility of $5.
Even with positive expected value, you may be better off passing up the bet depending on your tolerance for variance and the local shape of your utility-of-money function.
You won. Aren’t rationalists supposed to be doing that?
As far as you know, your probability estimate for “you will win the lottery” (in your mind) was wrong. It is another question how that updates the probability of “you would win the lottery if you played next week”, but whatever made you buy that ticket (even though the “rational” estimates voted against it… “trying random things”, whatever it was) should be applied more in the future.
Of course, the result is quite likely to be “learning lots of nonsense from a measurement error”, but you should definitely should update having seen that, and a decision you use for updates causing that decision to be made more in the future is definitely a right one.
If I won the lottery, I would definitely spend $5 for another ticket. And eventually you might realize that it’s just Omega having fun. (actually, isn’t one-boxing the same question?)
Playing the lottery was an irrational decision, but was the right choice. The outcome, as stated by moridinamael, is divorced from the decision making processes that went into it.
Assuming an unambiguous result that can only either be good or bad, and the most rational choice based upon the evidence then at hand led to a bad outcome, one still made the best (most rational) decision—but, considering the bad result, ’twas the wrong choice.
This classification if useful when determining the competency of a leader—they may have been an extremely rational decision maker but made nothing but wrong choices due to poor quality of information.
I forget my source—as for the terms, fubarofusco’s “Hindsight” fits well, while “Expected Value” does not.