Algorithmic Asset Voting: Difference between revisions
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(Work in progress)[[File:Algorithmic Asset Voting description.png|thumb|A flowchart explaining how Algorithmic Asset works. ]]
[[Asset Voting]] can, depending on which relevant assumptions are made about how negotiators act, be turned into a [[Generalized Condorcet criterion|Smith-efficient]] [[Condorcet method]] in the single-winner case, and a Condorcet PR method in the multiwinner case (akin to [[CPO-STV]] and [[Schulze STV]]). Its variants, [[Sequential Asset Voting]] and Bloc Asset Voting, can also be algorithmized.
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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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10 F>E
Condorcet PR methods should probably pick (B, E) as the winner set, because both candidates in the set are the Condorcet winners within their respective Hare Quotas (the top 3 lines and bottom 3 lines), so if for example you tried to go with (A, E), the 10 totally unrepresented C voters could give B their votes, giving B 10+5=15 votes total to beat A's 11. But if say all voters indicate that B and E are only 10% better than less-preferred candidates, this is no longer the case (B and E actually become Condorcet losers in their quotas, because they get only 5 + 1 or 1.1 votes in their pairwise matchups against their quota competitors, who have 10 or 11 votes) and then (A, D) looks like a better Condorcet PR winner set, since C and F, the only viable competitors left, simply have fewer voters preferring them than A and D.<ref>https://www.reddit.com/r/EndFPTP/comments/ep0tq1/using_weak_preferences_in_condorcet_pr_methods/</ref></blockquote>Note that a voter could even be allowed to give less than a full vote to any candidate, even their 1st choice, in all pairwise matchups.
The use of the [[KP transform]] on rated ballots and then converting those Approval ballots to ranked ballots allows voters to submit, for example, a rated ballot A5 B4 C3, and have it treated either as 0.2 votes A>B, 0.2 votes B>C, and 0.4 votes A>C (score for preferred candidate minus score for less preferred candidate divided by max score yields the number of votes in each matchup) or 1 vote A>B, 1 vote B>C, 1 vote A>C.
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The Smith Set in Algorithmic Asset PR:<blockquote>
8 D>A>B>C
7 B>C>A>D
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5 C2>B2>A2>D2
Initializing an algorithmic Asset negotiation, D and D2 have the most votes (1st choices). But within each Hare Quota, ABC and A2 B2 C2 are in a Condorcet cycle. Therefore, once a few negotiating moves (pairwise comparisons) have been done, D and D2 won’t be in any of the 2-winner winner sets the negotiators cycle through. For example, if the negotiators are currently supporting (B, B2), and D and D2 attempt to gather enough support to win, 12 ballots prefer B to 8 for D or D2, and the same for B2. So the Smith Set here is all of the outcomes in the Condorcet cycles, which is a proper subset of all possible 2-winner sets.[https://forum.electionscience.org/t/free-and-private-cardinal-polling/536/11]</blockquote>
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.
== Resisting Favorite Betrayal and burying ==
In some cases, it's possible to use the concept of AAV to reduce Favorite Betrayal incentive. For example: <blockquote>48 A>B
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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
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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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It may be possible to make AAV always elect proportionally from Droop semi-solid coalitions. If so, then this may greatly speed up computation of the result, as only winner sets that satisfy all semi-solid coalitions need be considered; discovering semi-solid coalitions can be done by checking ballots and observing which candidates are ranked higher than others and by which voters. <ref>https://www.removeddit.com/r/EndFPTP/comments/euiup2/a_new_pr_concept_of_semisolid_coalitions/</ref> Semi-solid coalitions may overlap.
== References ==
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