Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

# Slider comments on The Number Choosing Game: Against the existence of perfect theoretical rationality - Less Wrong

-1 29 January 2016 01:04AM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Sort By: Best

Comment author: 07 January 2016 09:12:47PM 0 points [-]

What you are saying would be optimising in a universe where the agent gets the utility as it says the number. Then the average utility of a ungoer would be greater than that of a idler.

However if the utility is dished out after the number has been spesified then an idler and a ongoer have exactly the same amount of utility and ought to be as optimal. 0 is not a optimum of this game so an agent that results in 0 utility is not an optimiser. If you take an agent that is an optimiser in other context then it ofcourse might not be an optimiser for this game.

There is also the problem that choosing the continue doesn't yield the utilty with certainty only "almost always". The ongoer strategy hits precicely in the hole in this certainty when no payout happens. I guess you may be able to define a game where concurrently with their actions. But this reeks of "the house" having premonition on what the agent is going to do instead of inferring its from its actions. if the rules are "first actions and THEN payout" you need to be able to do your action to get a payout.

In the ongoing version I could think of rules that an agent that has said "9.9999..." to 400 digits would receive 0.000.(401 zeroes)..9 utility on the next digit. However if the agents get utility assigned only once there won't be a "standing so far". However this behaviour would then be the perfectly rational thing to do as there would be a uniquely determined digit to keep on saying. I am suspecting the trouble is mixing the ongoing and the dispatch version to each other inconsistently.

Comment author: 08 January 2016 08:49:09AM 0 points [-]

"However if the utility is dished out after the number has been spesified then an idler and a ongoer have exactly the same amount of utility and ought to be as optimal. 0 is not a optimum of this game so an agent that results in 0 utility is not an optimiser. If you take an agent that is an optimiser in other context then it ofcourse might not be an optimiser for this game."

The problem with this logic is the assumption that there is a "result" of 0. While it's certainly true that an "idler" will obtain an actual value at some point, so we can assess how they have done, there will never be a point in time that we can assess the ongoer. If we change the criteria and say that we are going to assess at a point in time then the ongoer can simply stop then and obtain the highest possible utility. But time never ends, and we never mark the ongoer's homework, so to say he has a utility of 0 at the end is nonsense, because there is, by definition, no end to this scenario.

Essentially, if you include infinity in a maximisation scenario, expect odd results.