Asset voting

From Electowiki
Jump to navigation Jump to search

Asset voting is used to refer to a voting system in which votes are considered as "assets" given to candidates. If no candidate gets more than the winning threshold (i.e., a majority, in the single winner case; generally speaking, a Droop or Hare Quota), then the candidates can redistribute "their" votes to other candidates until a winner exists. Variations exist with different constraints on transfers - for example, the candidate with the fewest votes might be forced to redistribute their votes first. There need not be any threshold either i.e. for however many seats there are to be filled, for that number of candidates with the most votes, they are elected. This variation means that, in this single-winner example:

51 A

49 B

10 C

Candidate C can't prevent A from winning by denying them a Droop quota, since A has the most votes overall.

Asset voting was invented in 1874 by Lewis Caroll (Charles Dodgson), and independently reinvented and named by Forest Simmons and Warren Smith.[1][2]

If used as a multi-winner voting method, it obeys most 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 methods; specifically, sometimes Asset is discussed as if the voters themselves are trading votes. In practice however, Asset could fail just about every criterion and yield any type of election result.

Connection to other voting methods[edit | edit source]

Connection to Condorcet[edit | edit source]

Asset always picks a winner or winner set that is in the Smith Set based on negotiators' preferences (which is not necessarily the same as the voters' preferences, since the negotiators may be corrupt, change preferences mid-negotiation, not know the voters' full preferences, etc.) if the negotiators are given enough time to negotiate, are honest with each other in their negotiating moves, don't attempt to strategically alter their preferences,[dubious ] and if each candidate in the Smith set is preferred by at least a Droop quota of all voters in every pairwise comparison, meaning that if the negotiators have discussed every relevant permutation of winners or winner sets, Asset will always produce an outcome that can earn more votes from the negotiators during the negotiations than any other possible outcome, unless certain outcomes earn more votes than each other in a Condorcet cycle, in which case one of those cycling outcomes will win.

Example:

3: A>B>C

3: B>C>A

3: C>A>B

4: D

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[edit | edit source]

46 A>B

10 B

44 C>B

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[edit | edit source]

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:

25 A>B

26 B>A

3 C>A

46 C

A is the CW. However, C starts out with the most votes; if a B vs C matchup is done first, then B will beat C, and then if an A vs B matchup is done, if the A-top voters try to make A win, then C will have the most votes (more than A or B), whereas if they continue to support B (as they did during the B vs C match-up), they ensure B wins. So in this circumstance, because A wasn't a Majority Condorcet winner (A got 28 votes against B's 26, but this is less than a majority of all voters, which is 51), the chicken dilemma allowed B to win.

Connection to utilitarianism[edit | edit source]

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:

51 A:5 B:4 49 B:5

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 Rated pairwise preference ballot for discussion on this. 


Free-riding[edit | edit source]

Asset can, under ideal conditions in the multiwinner case, render many free-riding strategies needless; this is because, in some sense, the negotiators can do vote management themselves. Consider the example of three parties, A, B and C, where 51 voters vote for B candidates, 49 vote for A candidates, and 10 for C candidates, and there are 5 seats to be elected. Supposing every voter gives maximal support to all of the candidates of their chosen party, and no support for any other candidate, Party B will win 3 seats in most PR methods. However, if the 49 A voters divide themselves as evenly as possible between 3 of their candidates (17 of them bullet vote the first, 16 each bullet vote the second and third candidates), and a Droop quota is spent every time someone is elected in the PR method, then Party A will be able to win 3 seats instead. With Asset, the B candidates can agree to divide their 51 votes evenly between 3 of them (17 each), ensuring that their candidates will be 3 of the 5 candidates with the most votes when the negotiations end and thus win. [3]

Note however that free riding still can work if a voter honestly supports both a candidate with a small base and a candidate with the same small base combined with other bases, as the voter may wish to give their vote to the first candidate to elect them and hope the other bases will elect the second candidate, giving the voter two rather than only one of their preferred candidates. This type of free riding can lead to popular candidates losing to candidates equally preferred to them by smaller groups of voters if too many voters attempt it.

Extensions[edit | edit source]

Asset Voting also has sequential and Bloc versions of itself, which are generally less proportional and more majoritarian than regular Asset in the multiwinner cases (with Bloc Asset, a majority can win every seat). All of these various forms of Asset Voting can be algorithmized, and under certain (relevant) assumptions, become some type of Condorcet or Condorcet PR method.

Notes[edit | edit source]

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[edit | edit source]

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 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[edit | edit source]

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.

References[edit | edit source]

  1. "Asset voting was invented by Lewis Carroll (Charles L. Dodgson)!". RangeVoting.org. Retrieved 2019-03-02.
  2. Black, Duncan (May 1969). "Lewis Carroll and the Theory of Games" (PDF). The American Economic Review. 59 (2): 206–210.
  3. "Different reweighting for RRV and the concept of Vote Unitarity". The Center for Election Science. 2019-06-29. Retrieved 2020-02-19.