# All of LimberLarry's Comments + Replies

A simple game that has no solution

You seem to be treating the sub-problem, "what would Player 2 believe if he got a move" as if it is separate from and uninformed by Player 1's original choice. Assuming Player 1 is a utility-maximizer and Player 2 knows this, Player 2 immediately knows that if he gets a move, then Player 1 believed he could get greater utility from either option B or C than he could get from option A. As option B can never offer greater utility than option A, a rational Player 1 could never have selected it in preference to A. But of course that only leaves C as ... (read more)

A simple game that has no solution

Exactly, but B is never a preferable option over A, so the only rational option is for Player 1 to have chosen A in the first place, so any circumstance in which Player 2 has a move necessitates an irrational Player 1. The probability of Player 1 ever selecting B to maximize utility is always 0.

1James_Miller8y
But this does not make sense because then player 1 will know that player 2 will play X, so Player 1 would have been better off playing A or B over C.
A simple game that has no solution

If Player 2 gets to move, then the only possible choice for a rational Player 1 to have made is to pick C, because B cannot possibly maximize Player 1's utility. The probability for a rational Player 1 to pick B is always 0, so the probability of picking C has to be 1. For Player 1,there is no rational reason to ever pick B, and picking C means that a rational Player 2 will always pick X, negating Player 1's utility. So a rational Player 1 must pick A.

1James_Miller8y
So are you saying that if Player 2 gets to move he will believe that Player 1 picked C?
A simple game that has no solution

Well, as i said I'm not familiar with the mathematics or rules of game theory so the game may well be unsolvable in a mathematical sense. However, it still seems to me that Player 1 choosing A is the only rational choice. Having thought about it some more I would state my reasoning as follows. For Player 1, there is NO POSSIBLE way for him to maximize utility by selecting B in a non-iterated game, it cannot ever be a rational choice, and you have stated the player is rational. Choosing C can conceivably result in greater utility, so it can't be immediatel... (read more)

1James_Miller8y
Then please answer the question, "if Player 2 gets to move what should he believe Player 1 has picked?" Until you can answer this question you can not solve the game. If it is not possible to answer the question, then the game can not be solved. I know that you want to say "Not picking A would prove Player 1 is irrational" but you can't claim this until you tell me what Player 2 would do if he got to move, and you can't answer this last question until you tell me what Player 2 would believe Player 1 had done if Player 1 does not pick A.
A simple game that has no solution

To formulate this mathematically you would need to determine the probability of making a false prediction and factor that into the odds, which I regret is beyond my ability.

A simple game that has no solution

Because for Player 1 to increase his payoff over picking A, the only option he can choose is C, based on an accurate prediction via some process of reasoning that player 2 will pick X, thereby making a false prediction about Player 1's behaviour. You have stated both players are rational, so I will assume they have equal powers of reason, in which case if it is possible for Player 2 to make a false prediction based on their powers of reason then Player 1 must be equally capable of making a wrong prediction, meaning that Player 1 should avoid the uncertainty and always go for the guaranteed payoff.

0LimberLarry8y
To formulate this mathematically you would need to determine the probability of making a false prediction and factor that into the odds, which I regret is beyond my ability.
A simple game that has no solution

Right that makes sense, but wouldn't Player 1 simply realize that making an accurate forecast of player 2's actions is functionally impossible, and still go with the certain payout of A?

-1James_Miller8y
By definition of rationality in game theory, Player 1 will maximize his expected payoff and so need to have some belief as to the probabilities. If you can't figure out a way of estimating these probabilities the game has no solution in classical game theory land.
A simple game that has no solution

I'm not overly familiar with game theory, so forgive me if I'm making some elementary mistake, but surely the only possible outcome is Player 1 always picking A. Either other option is essentially Player 1 choosing a smaller or no payoff, which would violate the stated condition of both players being rational. A nonsensical game doesn't have to make sense.

1James_Miller8y
To know that A gives you a higher payoff than C you have to know what Player 2 would do if he got to move, but since Player 2 expects to never move how do you figure this out?
This is why we can't have social science

Well fair enough. His use of nutrition science as an example was probably poorly chosen.

This is why we can't have social science

I don't think we actually disagree on anything, the only point I was making was that your reply to Lightwave, while accurate, wasn't actually replying to the point he made.

2ChristianKl8y
I did reply to his point. He spoke about nutrition science. That field has it's own problems that psychologists don't have to deal with. It's a bad example if he wanted to make the point you think he wanted to make.
This is why we can't have social science

Obviously if you can control for a confounding factor then its not an issue, I was simply stressing that the nature of human sciences means that it is effectively impossible to control for all confounding factors, or even be aware of many of them.

6ChristianKl8y
To the extend that's true careful replication of studies to identify factors is important if you don't want to practice what Feymann described as Cargo Cult science [http://neurotheory.columbia.edu/~ken/cargo_cult.html]. If you follow Feymann argument physicists also would get a bunch of bad results if they would work with the scientific standards used in psychology. Feymann on rat psychology: Nutrition is really a different case than a lot of psychology. There are question in psychology such as whether doing certain things to a child in it's childhood effect whether that child is a healthy adult. Those questions are hard to investigate scientifically because of time lag. The same isn't true for many psychology experiments.
Welcome to Less Wrong! (6th thread, July 2013)

I'm Tom, 23 year old uni drop out (existential apathy is a killer), majored in Bioscience for what its worth. Saw the name of this site while browsing tvtropes and was instantly intrigued, as "less wrong" has always been something of a mantra for me. I lurked for a while and sampled the sequences and was pleased to note that many of the points raised were ideas that had already occurred to me.

Its good to find a community devoted to reason and that seems to actually think where most people are content not to. I'm looking forward suckling off the collective wisdom of this community, and hopefully make a valuable contribution or two of my own.

2[anonymous]8y
Hello and welcome to LessWrong! We have something of a crosspollination with tvtropes as well as a few other sites. The similar "archive diving" structures probably don't hurt. Glad you decided to join in! The site always needs some bioscience to collaborate with our high computer science population. Look forward to seeing your contributions.
This is why we can't have social science

I think he is more suggesting that the number of confounding factors in psychology experiments is generally far higher than in the natural sciences. The addition of such uncontrollable factors leads to a generally higher error rate in human sciences.

0ChristianKl8y
The number of confounding factors isn't that important if it's possible to do controlled experiments that control for them. Nutrition science has the problem that you usually can't do good controlled experiments or those are very expensive.