toony soprano
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Thanks very much for your reply Vladimir. But are you sure that is correct?
I have never seen that kind of restriction to a single choice-situation mentioned before when transitivity is presented. E.g. there is nothing like that, as far as I can see, in Peterson's Decision theory textbook, nor in Bonano's presentation of transitivity in his online Textbook 'Decision Making'. All the statements of transitivity I have read just require that if a is preferred to b in a pairwise comparison, and b is preferred to c in a pairwise comparison, then a is also preferred to c in a pairwise comparison. There is no further clause requiring that a, b, and c are all simultaneously available in a single situation.
Yes I phrased my point totally badly and unclearly.
Forget Rock Scissors paper - suppose team A loses to team B, B loses to C and C loses to A. Now you have the choice to bet on team A or team B to win/lose $1 - you choose B. Then you have the choice between B and C - you choose C. Then you have the choice between C and A - you choose A. And so on. Here I might pay anything less than $1 in order to choose my preferred option each time. If we just look at what I am prepared to pay in order to make my pairwise... (read more)
I would *really* appreciate any help from lesswrong readers in helping me understand something really basic about the standard money pump argument for transitivity of preferences.
So clearly there can be situations, like in a game of Rock Scissors Paper (or games featuring non-transitive dice, like 'Efron's dice') where faced with pairwise choices it seems rational to have non-transitive preferences. And it could be that these non-transitive games/situations pay out money (or utility or whatever) if you make the right choice.
But so then if these kinds of non-transitive games/situations are paying out money (or utility or whatever) I don't quite see how the standard money pump considerations apply? Sure, I might... (read more)
Also - if we have a set of 3 non-transitive dice, and I just want to roll the highest number possible, then I can prefer A to B, B to C and C to A, where all 3 dice are available to roll in the same situation.
If I get paid depending on how high a number I roll, then this would seem to prevent me from becoming a money pump over the long term.