Algorithmic Asset Voting: Difference between revisions
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Some optional assumptions are:
* When a negotiator is indifferent between certain outcomes (i.e. because their voters equally ranked those outcomes), they use their assets to help pick the socially best of those outcomes. As an example, if the voters cast rated ballots <blockquote>49 A5 B4 3 A5 B5 48 B5</blockquote>then treat the 3 A=B votes as preferring B, because B has the most points, giving B 51 > A 49 votes, making B the winner even though more voters actually prefer A.
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(A, C, D) vs. (A, C, S):
'''26 A
26.5 C
26.5 D'''
21 S
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5 B
47 C </blockquote>There's a Condorcet cycle here between all 3 candidates. But note that if the 47 A>B voters vote B>A, then B is the Condorcet winner. Notably, there is no way for any other voter to improve the outcome for themselves (the A>B preferring voters can't make A CW and neither can the C>B preferring voters), so B is a strategically stable winner. Using AAV along with a cycle resolution method that would elect C would automatically elect B because of this. This step might be usable solely to shrink the Smith Set at times rather than find a single strategic CW.
Another example: <blockquote>6 A>C>B>D
2 B>C>A>D
3 B>A>C>D
2 C>D>A>B
2 C>B>A>D
5 D>C>A>B
1 D>A>C>B </blockquote>C is the CW. But if the top line of 6 A>C>B>D voters vote A>B>D>C instead, then there will be a cycle, and most cycle resolution methods would elect A. With AAV, it's possible to note that such a cycle can be stably resolved in C's favor if every voter who prefers C>A votes C top A bottom. This allows voters to not have to actually vote that way in the election, avoiding any possible two-party domination effects. <ref>https://rangevoting.org/CondStratProb.html</ref>
But note that with a Condorcet cycle of <blockquote>1 A>B>C
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