Asset voting: Difference between revisions
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If used as a [[Multi-Member System|multi-winner voting method]], it obeys most [[PSC|proportionality criteria]], if the requisite assumptions about coalitions are extended to include candidates as well as voters. For example, since Asset allows a negotiator or group of negotiators who hold a certain number of Droop Quotas of votes to guarantee the election of up to that number of their preferred candidates (see [[SNTV]]), if the negotiators follow voter preferences then proportionality for Droop solid coalitions is satisfied. In such use, it is similar to [[delegable proxy]] systems except that, unlike such systems, it has public elections only at regularly scheduled intervals (proxies are not "revocable") and elects a fixed number of representatives with equal power.
Note that several assumptions are made throughout the article to make Asset comparable to other [[voting method]]<nowiki/>s; specifically, sometimes Asset is discussed as if the voters themselves are trading votes.
== Connection to Condorcet ==
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3: C>A>B
4: D </blockquote>D starts out with the most votes in the negotiation, but the ABC bloc is a [[mutual majority]], so they have an incentive to put their 9 votes behind one of ABC because they prefer any of them to D winning. In general, the idea is that because Smith candidates [[pairwise beat]] non-Smith candidates, this means that by definition more voters have an incentive to elect Smith candidates than non-Smith candidates. This has interesting extensions to the PR case (see [[Condorcet PR]]), because voters must sometimes keep their vote with a favorite candidate to make their favorite win, preventing them from also supporting their 2nd choice to beat their 3rd choice.
=== Contrast with IRV ===
10 B
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44 C>B </blockquote>A starts out with the most votes in the negotiations, but C-top voters can end that by giving their 44 votes to B, making B have more votes (54 total). A-top voters can't do anything to stop B from winning, C-top voters have no ability to elect C, and prefer B over A, and B-top voters are getting their 1st choice, so no voters have both incentive and ability to change the outcome, and so B would win. This is an example of the negotiation process averting the [[center squeeze effect]] and electing the [[Condorcet winner]].
Note that in [[IRV]], once B was eliminated, C would have a majority of votes; the 56 voters who prefer B to C wouldn't be able to overpower the 44 that prefer C by transferring their votes toward B.
=== Majority-beat constraint ===
However, this doesn't apply when some candidates in the Smith set don't have at least a Droop quota of all voters preferring them in some comparisons; example:
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== Connection to utilitarianism ==
Because the [[utilitarian winner]] can be thought of as a "weighted" [[Condorcet winner]], if the negotiators only use parts of their votes (like [[cumulative voting]]) to support their preferred candidates, then Asset may begin to resemble a [[Cardinal PR]] method. Single-winner example: <blockquote>51 A:5 B:4
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49 B:5 </blockquote>If the max score is 5, then A 100% supports himself and 80% supports B. In general, to solve these situations, each voter should only give to their favorite candidate as much of their vote as their strength of preference for them i.e. someone who only 80% supports their favorite and 60% supports their second choice gives their favorite 80% of a vote, leaving 20% unusable. Then, to determine how the votes are transferred in head-to-head matchups, you find the fraction for the support for the less-preferred candidate divided by the support for the more-preferred candidate, and divide this by 2; this is the fraction of the more-preferred candidate's votes you transfer to the less-preferred candidate for that voter. This will replicate the utility margin between the two candidates. So here, for the 51 voters, the fraction is 80/100=(4/5)/2=2/5 so they transfer 2/5ths of their votes for A to B. The 49 B voters' fraction is 0/100 i.e. they don't support A at all, so they don't give any of their votes for B to A. So the final vote total is A 30.6 B 69.4, creating a vote margin of 38.8 in favor of B. This replicates the utility margin, which was A 51 subtracted from B (49 + 51*0.8)=89.8, which is 38.8.
This example is somewhat farcical, but in general, [[utilitarianism]] can be viewed through an Asset lens as negotiators only weakly pushing for some preferences. Asset may even be modelable as one of the cardinal PR methods when all negotiators' preferences are cardinal and not ranked. Also see the [[utility]] article for discussion on the connection between majority rule and utilitarianism. It is also worth looking into how negotiators can have weak preferences in some pairwise matchups but strong preferences in others, which all together could not be written on a rated ballot as a rated utility; see [[
== Notes ==
Asset voting's [[party list case]] is [[D'Hondt]]. This is because negotiators can always split votes per seat in an optimal fashion to get as many seats as they'd get in D'Hondt.
Independence properties
Asset passes [[Independence of Smith-dominated Alternatives]], because once the negotiators start discussing electing Smith set members, they won't be able to form a coalition in favor of a non-Smith candidate, and any Smith candidate is likely to be viable since there is a [[beat-or-tie path]] between all of them.
Under certain assumptions, Asset passes [[Pareto|Independence of Pareto-dominated alternatives]]. This is because the Pareto-dominating alternative will [[pairwise beat]] the Pareto-dominated alternative, and there is no incentive for any negotiator to elect the Pareto-dominated alternative instead of the Pareto candidate. So the negotiators would have an incentive to discard consideration of any Pareto-dominated alternatives.
Presentation
Asset negotiations can be modeled similarly to [[IRV]] i.e. every round, the number of votes pledged or offered to each candidate are counted. With such a presentation, it would then be shown who would win in a given round if that was the final round. This can be used to explain why the negotiators shifted their votes in a later round. In this sense, Asset, and by extension, [[Condorcet]] or [[Condorcet PR]], can be thought of as superior to [[STV]] because it allows voters to get a better deal for themselves by pivoting back towards candidates who seemed unattractive in earlier rounds but are found to be more viable than the voter's favorite, whereas STV just eliminates such candidates.
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