Algorithmic Asset Voting: Difference between revisions
Added example for Algorithmic Asset in the PR case.
(Added section on how an inventor of Asset, Lewis Carroll, likely believed Asset was the most Condorcet-efficient PR method of his time.) |
(Added example for Algorithmic Asset in the PR case.) |
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- A resolution method is applied when there are multiple outcomes in the Smith Set, and the candidates' preferences can change in order to change the Smith Set in favor of maximizing their voters' satisfaction (though this might break the algorithm or make it fail to be Condorcet-efficient in certain scenarios). As a further possibility, the candidates might also be allowed to try to induce Condorcet cycles or otherwise grow the Smith Set in ways that allow them to then resolve the election in favor of their voters' satisfaction (though this also might break the algorithm).
=== Procedure ===
Do pairwise matchups between all possible outcomes. (To speed up computation, some matchups can be ignored if the outcome is certain. Also, some outcomes can be checked first if they're more likely than others).
When doing a matchup, transfer votes in such a way as to ensure a voter gets as many of their favorite candidates as possible. (If the voter submitted a rated ballot, optionally attempt to instead maximize their overall utility i.e. if electing their 1st choice is worth 9 utility points, and electing their 2nd and 3rd choice is 8+5= 13, prioritize electing the latter two).
=== Example ===
3-winner election, Hagenbach-Bischoff quota 25:
26 A
34 CBD
6 BD
8 DB
5 DS
21 SD
It can immediately be observed that A and C have over a quota of 1st choices, so they will win. (D, S) form a Droop solid coalition of 26 votes, so one of them must win. Therefore, the only outcomes to compare are (A, C, D), (and (A, C, S).
(A, C, D) vs. (A, C, S):
26 A
26.5 C
26.5 D
21 S
Here, 7.5 CBD votes and the 19 other votes that prefer D to S give their votes to D. A, C, and D are then the 3 candidates with the most votes, and since the voters who prefer S>D don't have enough votes to change the outcome, (A, C, D) win this matchup. Since we already know (A, C, D) can win all other matchups, (A, C, D) is the Condorcet winner and wins.
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== Explanation of how Asset Voting is, under certain assumptions, a Condorcet method (and how this enables it to be done as an algorithm) ==
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Asset Voting can be done algorithmically on ranked or rated ballots when certain assumptions are applied, such as the ones mentioned above (here is a [https://www.removeddit.com/r/EndFPTP/comments/eac87u/demonstrating_condorcet_pairwise_counting_with_an/ visualization] of the algorithm). One main assumption is that every negotiator attempts to maximize their assigned voters' satisfaction with the outcome. When there is a Condorcet cycle of negotiating outcomes in this algorithm that would give a voter incentive for Favorite Betrayal in most Condorcet methods, it is sometimes possible to prevent that in Algorithmic Asset if a cycle resolution method is applied and the algorithmic negotiators are then allowed to optimize their preferences for candidates in the cycle in response to the cycle resolution method's chosen winner. As an example:
|3|C>A>B|
|4|C=B>A|
|2|A>B>C|
All 3 candidates are in a Condorcet cycle. Schulze picks C, so that would be the default outcome if no negotiation occurs. Based off of this, the algorithm can flip the 4 A>B>C voters to B>A>C to help resolve the cycle and elect B (since B would then be the only member of the Smith Set, B can't be overtaken by anyone else), because this change in expressed preference benefits these voters' actual preferences. Then, not enough C voters would have an incentive to negotiate to elect someone other than B. It may be possible for some cycles to only be resolvable when certain cycle resolution methods are used as default methods in Algorithmic Asset and not others.
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