MrAnchovy said:
I disagree again: we can replace the human state of mind with a utility function that provides numbers to distinguish between these four scenarios.
But that would make the theory useless. I'll give an example.
Suppose you have a classroom and you want to evaluate teaching methods. So you develop a theory about two styles of teaching and wonder which is better. Now if your theory says that the more visual method appeals to more visual learners and the more auditory method appeals to more auditory learners, and the success of either method will depend on the share of visual and auditory learners, it hasn't given you a prediction. You now need to input how many students are visual learners and how many are auditory learners. And you will get answer like this. "If 40% benefit more from visual learning and 60% benefit more from auditory learning, 40% will prefer the visual method and 60% will prefer the auditory method, and the expected value is 40% times the chosen method's effectiveness for visually preferred learners and 60% of the effectiveness of the chosen method for auditory-preferred learners. Do that calculation and you'll know which method is better." It's not a prediction. A prediction says "method X will be better". And if the theory must wait on psychological profiling of the agent, it isn't a useful theory.
It's like asking, what is the chance this person is lying, and getting the answer, if they have lied in the past, if they dislike you, if they are maniacal, if they distrust you, they are probably lying. But if they don't have those feelings or traits, they are probably telling the truth. This is not a prediction. And if you try to model all of that, you still have to feed in all that information, it's not predicting anything.
And it also makes a grave mistake. You may start to think that learners are either visual or auditory, or that people are either liars or truth tellers. But of course it may come down to the teacher which method is better. It may be that a good teacher can teach either method and a bad teacher can teach neither. It may be that pupils choose the auditory method on the survey because they think it'll mean easier homework, and pupils choose the visual method because they think it'll mean exams are easier to study for. Who knows, right? There is so much variation there, the theory becomes useless at predicting anything.
Yes, it gives you a number that looks good but that number is meaningless and useless, it means nothing.
And in this case, the answer that the gamble, if Poisson, would mean leaving empty-handed 60% of the time, is useless. One doesn't know if it is Poisson because that is a real concern and the whole idea was to not have real concerns be involved. One has to say, "what if the scenario is Roulette, what if the scenario is a claw game?" And then the answer is, take multibets in a claw game and single bets in Roulette. But to me that is not an answer when one has decided not to deal with real concerns. And anyway, it is only useful when one has a real concern in mind and then the question should have been, "How can I maximise my odds at Roulette?", "How can I beat this claw game?", etc. The question as posed is unanswerable and it is wrong to suppose that one can simply add a utility function and have a useful theory. If one has to add a utility function, that means the theory can't predict anything and is splintering into many pieces that each predict one tiny thing, but together they are simply a questionaire awaiting the real concerns to be supplied.
And, the view that if one plugs in the real concerns, the theory will model the real world, is called Aristotleanism. It says the world is black and white, yes or no, there are no mixtures, no shades. But we know that's not true. Is an apple really red? Is a wave in the ocean really a sine wave or a Fourier composite of sinusoids? Isn't that just an excuse to say it is unpredictable? We still predict the height of the waves when there is an earthquake but is there any theory that predicts how many waves will arrive in an hour and the spacing of them? I think not. And for similar reasons, I reject the height prediction as well. The real world is never going to match the model, the world is not Aristotelian.
When it comes to gambling, there is nothing predictable about it. The whole point is to be unpredictable. If there is ever a game that becomes predictable, it'll be changed or updated so that it isn't anymore. There's a kind of uncertainty principle: as soon as you can predict, you can predict that you will lose.
There is market research that looks at number of houses, buyers in a vicinity, competition, etc, that can produce a number of dollars of potential spend on a product type. But I class that as something different, I don't think of it as the probability of making X dollars selling this product. And I would argue that any theory like that is useless.
