Talk:Asset voting: Difference between revisions
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::: Suppose at every point in the negotiations, the negotiators are keeping track of the candidate (candidates equalling the number of seats, in the multiwinner case) with the most votes committed to them, and consider such a candidate "the one to beat", because this is the one who will win if the negotiators do nothing. Then, all it takes for Asset to elect a CW with no votes is for the other negotiators to keep looking for candidates who they a) prefer over "the one to beat" and who b) can get more votes to be committed to them. As an example:
:::* 26 AB
:::* 26 CB
:::* 48 D
::: It's clear that even without any 1st choice support, if no negotiator preferences change here, eventually A and C's votes will go to B, because there's no other way to beat D, and because once B becomes the one to beat, there's nobody that can get more votes committed to them and is preferred over B by those committing the votes. If, let's say, A and C made no move to elect B (even despite having a weak preference for B), then we could say their functional preferences (their mental preferences modified to fit their negotiating behavior) were
:::* 26 A>B=D
:::* 26 C>B=D
::: in which case B isn't the CW or in the Smith Set of negotiator preferences.
::: I did add to my claim that the negotiators must be honest in their negotiating moves; in other words, they can't promise to give their votes to someone at the end of negotiations and then not do so, since that breaks this mechanism.
::: Also, it's worth pointing out that the more candidates there are, the more negotiation is required to find the Smith Set, since the negotiators are in essence doing pairwise comparisons. Even if given enough time to theoretically reach the optimal negotiating outcome, they may simply stop after a while when they've reached a satisfactory enough outcome, which is conceptually similar to an optimal PR algorithm getting a very good bit not best winner set because of long computations. Note that this still would be an outcome in the Smith Set, since the negotiators' functional preference is to equally rank the outcomes they would prefer negotiating for with the outcome they reached, or said differently, they're equally ranking the candidates they prefer over the ones in the final winner set with those ones in the final winner set. Some of the negotiators might even rank the final outcome as being better than what they earlier preferred, perhaps because they really want to finish the negotiations quickly.
::: Here is a visualization of Asset done algorithmically if it helps support my claim: https://www.reddit.com/r/EndFPTP/comments/eac87u/demonstrating_condorcet_pairwise_counting_with_an/ [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 14:53, 16 December 2019 (UTC)
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