I noticed recently is that there are two types of preference and that confusing them leads to some of the paradoxes described here.
Desires as preferences. A desire (wanting something) can loosely be understood as wanting something which you currently don’t have. More precisely, a desire for X to be true is preferring a higher (and indeed maximal) subjective probability for X to your current actual probability for X. “Not having X currently” above just means being currently less than certain that X is true. Wanting something is wanting it to be true, and wanting something to be true is wanting to be more certain (including perfectly certain) that it is true. Moreover, desires come in strengths. The strength of our desire for X corresponds to how strongly you prefer perfect certainty that X is true to your current degree of belief that X is true. These strengths can be described by numbers in a utility function. In specific decision theories, preferences/desires of that sort are simply called “utilities”, not “preferences”.
Preferences that compare desires. Since desires can have varying strengths, the desire for X can be stronger (“have higher utility”) than the desire for Y. In that sense you may prefer X to Y, even if you currently “have” neither X nor Y, i.e. even if you are less than certain that X or Y is true. Moreover, you may both desire X and desire Y, but preferring X to Y is not a desire.
Preferences of type 1 are what arrows express in your graphs (even though you interpret the nodes more narrowly as states, not broadly as propositions which could be true). A→B means that if A is the current state, you want to be in B. More technically, you could say that in state A you disbelieve that you are in state B, and the arrow means you want to come to believe you are in state B. Moreover, the desires inside a money pump argument are also preferences of type 1, they are about things which you currently don’t have but prefer to have.
What about preferences of type 2? Those are the things which standard decision theories call “preferences” and describe with a symbol like “≻”. E.g. Savage’s or Jeffrey’s theory.
Now one main problem is that people typically use the money pump argument that talks about preferences of type 1 (desires/utilities) in order to draw conclusions about preferences of type 2 (comparison between two desires/utilities) without noticing that they are different types. So in this form, the argument is clearly confused.
I noticed recently is that there are two types of preference and that confusing them leads to some of the paradoxes described here.
Desires as preferences. A desire (wanting something) can loosely be understood as wanting something which you currently don’t have. More precisely, a desire for X to be true is preferring a higher (and indeed maximal) subjective probability for X to your current actual probability for X. “Not having X currently” above just means being currently less than certain that X is true. Wanting something is wanting it to be true, and wanting something to be true is wanting to be more certain (including perfectly certain) that it is true. Moreover, desires come in strengths. The strength of our desire for X corresponds to how strongly you prefer perfect certainty that X is true to your current degree of belief that X is true. These strengths can be described by numbers in a utility function. In specific decision theories, preferences/desires of that sort are simply called “utilities”, not “preferences”.
Preferences that compare desires. Since desires can have varying strengths, the desire for X can be stronger (“have higher utility”) than the desire for Y. In that sense you may prefer X to Y, even if you currently “have” neither X nor Y, i.e. even if you are less than certain that X or Y is true. Moreover, you may both desire X and desire Y, but preferring X to Y is not a desire.
Preferences of type 1 are what arrows express in your graphs (even though you interpret the nodes more narrowly as states, not broadly as propositions which could be true). A→B means that if A is the current state, you want to be in B. More technically, you could say that in state A you disbelieve that you are in state B, and the arrow means you want to come to believe you are in state B. Moreover, the desires inside a money pump argument are also preferences of type 1, they are about things which you currently don’t have but prefer to have.
What about preferences of type 2? Those are the things which standard decision theories call “preferences” and describe with a symbol like “≻”. E.g. Savage’s or Jeffrey’s theory.
Now one main problem is that people typically use the money pump argument that talks about preferences of type 1 (desires/utilities) in order to draw conclusions about preferences of type 2 (comparison between two desires/utilities) without noticing that they are different types. So in this form, the argument is clearly confused.