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Odd that they didn't mention Arrow's impossibility theorem: https://en.wikipedia.org/wiki/Arrow's_impossibility_theorem https://en.wikipedia.org/wiki/Arrow's_i

Odd that they didn't mention Arrow's impossibility theorem: https://en.wikipedia.org/wiki/Arrow's_impossibility_theorem https://en.wikipedia.org/wiki/Arrow's_impossibility_theorem https://plato.stanford.edu/entries/arrows-theorem https://plato.stanford.edu/entries/arrows-theorem

WillDaSilva 6y ago
From the Quadratic voting Wikipedia page: Quadratic voting is a variant of cumulative voting in the class of cardinal voting. From the Arrow's impossibility theorem Wikipedia page: Cardinal voting electoral systems are not covered by the theorem, as they convey more information than rank orders.
godelski 6y ago
You want Gibbard's. It is an extension for cardinal systems. [0] https://en.wikipedia.org/wiki/Gibbard%27s_theorem https://en.wikipedia.org/wiki/Gibbard%27s_theorem
naniwaduni 6y ago
Arrow's theorem is an interesting result on its own, but its practical applicability is kind of undermined by the fact that the dictatorship criterion is actually pretty rarely interesting (and is almost totally irrelevant to a ballot).
- contravariant 6y ago
  You do realise that the dictatorship criterion simply replicates the vote of one particular voter no matter what? [1] In most realistic implementations this is likely either the first or the last voter. Surely we can agree that those wouldn't really be desirable? [1]: See here for a somewhat easy to follow proof: https://www.math.ucla.edu/~tao/arrow.pdf https://www.math.ucla.edu/~tao/arrow.pdf
  - naniwaduni 6y ago
    The dictatorship criterion is slightly more wide-reaching than that specific construction which makes it sound silly (though, honestly, not really tremendously unfair). Your link gives a decent enough definition: > (No dictators) If a single voter prefers X to Y, but all other voters disagree, then the voting system should override the wishes of that single voter and rank Y higher than X.
    - contravariant 6y ago
      The problem is that that criterion combined with the other conditions becomes equivalent to there being no 1-man quorums. As the rest of the proof shows the negation of this implies that there is a dictator, who completely determines the result for all votes. I guess in a ballot system it might be pretty tricky to figure out who this person is, but in the end it just boils down to the order in which the votes are put into the sorting system. No while sortition has it's advantages it goes against most people's intuition of what a fair voting system is. And technically arrow's definition of voting systems is deterministic, although you could always shuffle the votes beforehand.

WillDaSilva 6y ago

From the Quadratic voting Wikipedia page: Quadratic voting is a variant of cumulative voting in the class of cardinal voting. From the Arrow's impossibility theorem Wikipedia page: Cardinal voting electoral systems are not covered by the theorem, as they convey more information than rank orders.

godelski 6y ago

You want Gibbard's. It is an extension for cardinal systems. [0] https://en.wikipedia.org/wiki/Gibbard%27s_theorem https://en.wikipedia.org/wiki/Gibbard%27s_theorem

naniwaduni 6y ago

Arrow's theorem is an interesting result on its own, but its practical applicability is kind of undermined by the fact that the dictatorship criterion is actually pretty rarely interesting (and is almost totally irrelevant to a ballot).

contravariant 6y ago
You do realise that the dictatorship criterion simply replicates the vote of one particular voter no matter what? [1] In most realistic implementations this is likely either the first or the last voter. Surely we can agree that those wouldn't really be desirable? [1]: See here for a somewhat easy to follow proof: https://www.math.ucla.edu/~tao/arrow.pdf https://www.math.ucla.edu/~tao/arrow.pdf
- naniwaduni 6y ago
  The dictatorship criterion is slightly more wide-reaching than that specific construction which makes it sound silly (though, honestly, not really tremendously unfair). Your link gives a decent enough definition: > (No dictators) If a single voter prefers X to Y, but all other voters disagree, then the voting system should override the wishes of that single voter and rank Y higher than X.
  - contravariant 6y ago
    The problem is that that criterion combined with the other conditions becomes equivalent to there being no 1-man quorums. As the rest of the proof shows the negation of this implies that there is a dictator, who completely determines the result for all votes. I guess in a ballot system it might be pretty tricky to figure out who this person is, but in the end it just boils down to the order in which the votes are put into the sorting system. No while sortition has it's advantages it goes against most people's intuition of what a fair voting system is. And technically arrow's definition of voting systems is deterministic, although you could always shuffle the votes beforehand.