3 ms·

When reading about voting systems, I'm always reminded of Arrow's impossibility theorem, which everybody should be aware of: http://en.wikipedia.org/wiki/Arrow

by Maro 17y ago

When reading about voting systems, I'm always reminded of Arrow's impossibility theorem, which everybody should be aware of: http://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem http://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem In short, no "fair" voting system can satisfy these three criteria: - If every voter prefers X over Y, then the group prefers X over Y. - If every voter prefers X over Y, then adding Z to the slate won't change the group's preference of X over Y. - There is no dictator.

ComputerGuru 17y ago
Never knew about this - thanks for the most interesting read. Is the 2nd factor a problem with the voting system or with the psychology of the voters though?
- huangm 17y ago
  This is a desirable property of a voting system. If we prefer X over Y (X > Y), then adding Z can give: Z > X > Y, X > Z > Y, or X > Y > Z. Adding Z ought not change the ordering of X and Y.
huangm 17y ago
And to relate specifically to Instant Runoff Voting, IRV fails to satisfy monotonicity. It also fails to satisfy the Condorcet Criterion (a commonly held desirable property that the person with the majority #1 votes should be ranked 1st). There exist `better' ranking systems such as ones involving markov chains (http://www10.org/cdrom/papers/577/ http://www10.org/cdrom/papers/577/), but I'd imagine that the Oscar Committee requires their voting/ranking scheme to be palatable to the general public. Using IRV is a good step in the direction of `better' voting, while still being explainable in a few sentences.
- tel 17y ago
  Slight nitpick: the Condorcet Criterion doesn't actually specify that the one with the majority #1 votes is first ranked. It explicitly states that the candidate that, when compared pairwise with each other candidate, wins most frequently should win overall. http://en.wikipedia.org/wiki/Condorcet_criterion http://en.wikipedia.org/wiki/Condorcet_criterion
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 Maro 17y ago

ComputerGuru 17y ago

Never knew about this - thanks for the most interesting read. Is the 2nd factor a problem with the voting system or with the psychology of the voters though?

huangm 17y ago
This is a desirable property of a voting system. If we prefer X over Y (X > Y), then adding Z can give: Z > X > Y, X > Z > Y, or X > Y > Z. Adding Z ought not change the ordering of X and Y.

huangm 17y ago

And to relate specifically to Instant Runoff Voting, IRV fails to satisfy monotonicity. It also fails to satisfy the Condorcet Criterion (a commonly held desirable property that the person with the majority #1 votes should be ranked 1st). There exist `better' ranking systems such as ones involving markov chains (http://www10.org/cdrom/papers/577/ http://www10.org/cdrom/papers/577/), but I'd imagine that the Oscar Committee requires their voting/ranking scheme to be palatable to the general public. Using IRV is a good step in the direction of `better' voting, while still being explainable in a few sentences.

tel 17y ago
Slight nitpick: the Condorcet Criterion doesn't actually specify that the one with the majority #1 votes is first ranked. It explicitly states that the candidate that, when compared pairwise with each other candidate, wins most frequently should win overall. http://en.wikipedia.org/wiki/Condorcet_criterion http://en.wikipedia.org/wiki/Condorcet_criterion

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.