Approval is Sincere
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Quick post but I thought readers here might like to see the paper I just came across:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3265187
Main result is that a 'sincere' ballot (i.e. one for which if A > B and B is approved then A is also approve) is always among the set of best-response strategies for a voter under Approval.
Note that this does not necessarily mean that all Nash equilibria consist of only sincere ballots, and there might be other best-responses which have a more elaborate strategy. However, you can interpret it to mean that for any complicated strategy a voter might wish to employ, there exists a sincere ballot they can submit with which they will fare at least as well.
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@brozai Its worth pointing out that this is just a restatement of Monotonicity by their definition of sincere. If A > B and B is approved then A is also approved. The " B is approved " part is crucial because the form of insincere voting in Approval is understood through the chicken dilemma. So there is a strategic problem with approval
Another interesting point is that you can use mathematical induction to take the approval case and expand it to Score voting
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I think it might be a little stronger than just Monotonicity? There are monotonic methods for which an analogous result would not hold, e.g. Borda
Another way to see that they are different is that in fact a best response might include a ballot with skipped rankings! It will just also include a sincere ballot
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@brozai said in Approval is Sincere:
I think it might be a little stronger than just Monotonicity?
Yes, I think you are right