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.
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.