4 ms·

That can't be correct as written because if I could magically extract everyone's scalar utility function from their minds, a mixture of utility functions would

by Eliezer 17y ago

That can't be correct as written because if I could magically extract everyone's scalar utility function from their minds, a mixture of utility functions would satisfy those three criteria. You need an additional requirement, "The citizen's true ordering of preferences is the only data presented to the algorithm." In other words the algorithm can't access the scalar utility function, only the ordering, and every similar ordering has to result in the same social ordering - no mixture of utility functions will satisfy this, obviously. If you want to prevent "strategic voting" that would impose other requirements as well. Impossibility theorems often aren't as impossible as they look, and indeed Arrow's Impossibility Theorem makes a good illustration of that, especially as the evasive answer is pretty obvious if you walk around thinking of expected utility maximizers all day long. Doesn't work for non-mind-reading applications because of the strategic voting problem, but in terms of whether it's possible for a society to aggregate the true utilities of its citizens, no sweat.

gojomo 17y ago
Of course, there are other specifics to the formal definition of Arrow's theorem. It's limited to situations where people express preference rankings -- as if on a ballot they fill out. It's not meant to describe situations where their perfectly-weighted preferences can be measured -- as if by some mind-reading utility-function-extraction-and-summation process. (Can two persons' Utils be meaningfully compared or summed?)
lmkg 17y ago
If you could magically extract everyone's scalar utility function, then it wouldn't be a voting system. The requirement that you state is in the definition. It's just implicit in the word "voting" rather than explicitly stated. Arrow's Theorem does rely on an explicit definition of voting, which is that voters make discrete choices about their candidates subject to certain criteria. Some theorem (possibly part of Arrow's Theorem) says that it's not possible to eliminate the potential for strategic voting in a 3+ party system without negating other desirable qualities like those listed above.

by Eliezer 17y ago

gojomo 17y ago

Of course, there are other specifics to the formal definition of Arrow's theorem. It's limited to situations where people express preference rankings -- as if on a ballot they fill out. It's not meant to describe situations where their perfectly-weighted preferences can be measured -- as if by some mind-reading utility-function-extraction-and-summation process. (Can two persons' Utils be meaningfully compared or summed?)

lmkg 17y ago

If you could magically extract everyone's scalar utility function, then it wouldn't be a voting system. The requirement that you state is in the definition. It's just implicit in the word "voting" rather than explicitly stated. Arrow's Theorem does rely on an explicit definition of voting, which is that voters make discrete choices about their candidates subject to certain criteria. Some theorem (possibly part of Arrow's Theorem) says that it's not possible to eliminate the potential for strategic voting in a 3+ party system without negating other desirable qualities like those listed above.