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Technical discussion of election methods

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Self/peer election methods

KM
Kristofer Munsterhjelm
Tue, Nov 14, 2023 1:43 PM

Let's say a group of people are voting on each other's suitability or on
their works. Then unless the method is modified to take this into
account, each candidate-voter has an incentive to rank himself highly
and everybody else low.

In Plurality voting, the common way to fix this is to bar a voter from
voting for himself. But that's not sufficient in other methods. Consider
Range, for instance. If A is barred from rating himself, but knows that
his most serious competitor is B, then he's incentivized to rate B zero.

But I think I've found a more general rule, which is simply this: when
the method determines whether A is higher ranked than B, it should
automatically disregard the ballots of both A and B.

For instance, in the Range example above, let A~>B if A's score (without
either A or B's ballots being counted) is greater than B's. Then elect
the candidate who beats everybody else by the ~> relation.

For Condorcet, this simply means that the magnitude A>B should not
include either A or B's preference; in practice that means that both A>B
and B>A will be down one (since given the opportunity, A would be likely
to vote himself top, as would B vote himself top).

More sophisticated strategy could still work, and ~> could even turn out
to be intransitive. In the Range example, perhaps one would need a
tiebreaker beyond what ordinary Range would need. But it should limit
the most obvious strategy.

-km

Let's say a group of people are voting on each other's suitability or on their works. Then unless the method is modified to take this into account, each candidate-voter has an incentive to rank himself highly and everybody else low. In Plurality voting, the common way to fix this is to bar a voter from voting for himself. But that's not sufficient in other methods. Consider Range, for instance. If A is barred from rating himself, but knows that his most serious competitor is B, then he's incentivized to rate B zero. But I think I've found a more general rule, which is simply this: when the method determines whether A is higher ranked than B, it should automatically disregard the ballots of both A and B. For instance, in the Range example above, let A~>B if A's score (without either A or B's ballots being counted) is greater than B's. Then elect the candidate who beats everybody else by the ~> relation. For Condorcet, this simply means that the magnitude A>B should not include either A or B's preference; in practice that means that both A>B and B>A will be down one (since given the opportunity, A would be likely to vote himself top, as would B vote himself top). More sophisticated strategy could still work, and ~> could even turn out to be intransitive. In the Range example, perhaps one would need a tiebreaker beyond what ordinary Range would need. But it should limit the most obvious strategy. -km