Anonymity-proof voting rules
A (randomized, anonymous) voting rule maps any multiset of total orders (aka. votes) over a fixed set of alternatives to a probability distribution over these alternatives. A voting rule f is false-name-proof if no voter ever benefits from casting more than one vote. It is anonymity-proof if it satisfies voluntary participation and it is false-name-proof. We show that the class of anonymity-proof neutral voting rules consists exactly of the rules of the following form. With some probability k f ∈ ∈[0,1], the rule chooses an alternative uniformly at random. With probability 1∈-∈k f, the rule first draws a pair of alternatives uniformly at random. If every vote prefers the same alternative between the two (and there is at least one vote), then the rule chooses that alternative. Otherwise, the rule flips a fair coin to decide between the two alternatives. We also show how the characterization changes if group strategy-proofness is added as a requirement. © 2008 Springer Berlin Heidelberg.
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