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Algorithmic Asset Voting: Difference between revisions

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Algorithmic Asset Voting (view source)

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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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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 A
 
26.5 C
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In the single-winner case, if the negotiators are honest, strictly follow voter preferences, and have enough time to negotiate, then Asset becomes a Smith-efficient [[Condorcet method]], and in the multiwinner case, resembles Condorcet PR methods such as [[CPO-STV]] and [[Schulze STV]] (these transformations can be observed by turning Asset Voting into an algorithm using various assumptions, as mentioned below). The reasoning for this can in part be linked to the fact that Asset is an iterative voting method (it is almost like an iterative version of FPTP; iterative voting methods are generally more Condorcet efficient than their non-iterative equivalents<ref>[https://link.springer.com/chapter/10.1007/978-3-642-41575-3_14]</ref>) where the voters/negotiators are constantly updated on who is about to win if no change in votes occur (i.e. which set of candidates of a size equal to the number of seats to be filled have more votes committed to them than all other candidates so far), and they can therefore plan to defeat such candidates. Pairwise comparison is implicitly involved in this planning, as the negotiators must see if the candidates they prefer over those about to win can obtain more votes from all negotiators than those who are about to win.
 
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:
 
|2|A>B>C|
 
|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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== Lewis Carroll's own likely observations that Asset is intended to be Condorcet-efficient ==
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