Algorithmic Asset Voting: Difference between revisions
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Some reasoning for why this method is most likely Droop-proportional and even Hagenbach-Bischoff-proportional: mathematically, if any candidate has an HB quota, no matter how the votes are arranged among other candidates, the quota-preferred candidates can guarantee they are are or are tied to be one of the (number of winners) top candidates. Examples: with 1 winner, HB quota is 1/2 (half), and even if a non-quota candidate has all of the other 1/2 of the votes, the quota-preferred candidate is at least tied for being the top candidate. With 2 winners, HB quota is 1/3rd, and even if two non-quota candidates split the remaining 2/3rd of the votes perfectly evenly, the quota-preferred candidate is still tied to be one of the top two. And so on. It would appear that so long as you always elect from the Smith Set of winner sets, HB-proportionality is guaranteed, because winner sets that pass HB ought to always beat winner sets that don't. Consider that Minimax, a Condorcet method, fails Smith and happens to also fail mutual majority<ref>https://en.m.wikipedia.org/wiki/Mutual_majority_criterion#Minimax</ref>, and in the single-winner case mutual majority is equivalent to Droop proportionality.
In some cases, it's possible to use the concept of AAV to reduce Favorite Betrayal incentive. For example: <blockquote>48 A>B
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.
But note that with a Condorcet cycle of <blockquote>1 A>B>C
1 B>C>A
1 C>A>B </blockquote>there is no strategically stable winner, because if any voter attempts Favorite Betrayal to make their preferred candidate the CW, then 2 other voters have incentive to alter their votes to make someone they prefer the CW, and so on.
== References ==
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