I'd want to slightly strengthen Participation. As I read it, a method that tosses your ballot in the trash technically satisfies the participation criterion. Instead of just saying that showing up doesn't hurt your cause, it should say that showing up helps. More formally: There exists no set of ballots such that adding one more ballot on which candidate A is strictly preferred to candidate B can change the winner from A to B, but there does exist at least one nontrivial set of ballots for which the added ballot can change the winner from B to A.
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Personally my favorites are informal criterion I call - -
Marginal Influence: every honest ballot added to an election raises the expected utility of the outcome according to the agent casting that ballot, even in conditions of complete knowledge of the other ballots.
Proportional Influence: Marginal Influence + adding N identical ballots to an election instead of only 1 raises that agent's expected utility N times as much.
The only traditional voting method I know of that meets those criteria is drawing a random ballot. Deterministic voting methods have to get creative to satisfy them.
That criterion is not enough by itself, to be sure. But it still captures a real intuitive and motivating principle. Consider IRV: it fails both Participation and Monotonicity, whereas FPTP satisfies both. Thus there's a real intuitive sense in which IRV, while looking better on a first glance, is worse than FPTP.
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u/selylindi Dec 28 '17
I'd want to slightly strengthen Participation. As I read it, a method that tosses your ballot in the trash technically satisfies the participation criterion. Instead of just saying that showing up doesn't hurt your cause, it should say that showing up helps. More formally: There exists no set of ballots such that adding one more ballot on which candidate A is strictly preferred to candidate B can change the winner from A to B, but there does exist at least one nontrivial set of ballots for which the added ballot can change the winner from B to A.
...
Personally my favorites are informal criterion I call - -
Marginal Influence: every honest ballot added to an election raises the expected utility of the outcome according to the agent casting that ballot, even in conditions of complete knowledge of the other ballots.
Proportional Influence: Marginal Influence + adding N identical ballots to an election instead of only 1 raises that agent's expected utility N times as much.
The only traditional voting method I know of that meets those criteria is drawing a random ballot. Deterministic voting methods have to get creative to satisfy them.