Algorithmic Asset Voting: Difference between revisions
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Some of the assumptions are:
▲- The negotiators strictly follow the preferences of those ballots and try to maximize those ballots' satisfaction with the outcome i.e. if a negotiator is asked to negotiate on behalf of a voter whose ballot was A>B>C, and the negotiations are at such a stage that the negotiator can use their assets to decide which of A, B, or C will win, then the negotiator must help elect A.
▲- The candidates with the most votes at the end of the negotiations are sequentially elected until all seats are filled.
▲- The negotiators have as much time as necessary to reach a final outcome or set of outcomes.
▲- The negotiators move one negotiating step at a time (i.e. if some negotiators agree to support a candidate, they must first all give their votes to that candidate before any further negotiating actions occur)
Some optional assumptions are:
▲- In the multiwinner case, when a voter submits a rated ballot, and their negotiator can choose between electing, say, the voter's first choice, or both of their second and third choices, the negotiator somehow uses the rated information to decide which outcome is preferable (i.e. they might add up the utilities for the voter in either outcome and pursue the higher-utility outcome.)
▲- A resolution method is applied when there are multiple outcomes in the Smith Set, and the candidates' preferences can change in order to change the Smith Set in favor of maximizing their voters' satisfaction (though this might break the algorithm or make it fail to be Condorcet-efficient in certain scenarios). As a further possibility, the candidates might also be allowed to try to induce Condorcet cycles or otherwise grow the Smith Set in ways that allow them to then resolve the election in favor of their voters' satisfaction (though this also might break the algorithm).
=== Procedure ===
Line 34 ⟶ 28:
3-winner election, Hagenbach-Bischoff quota 25:
26 A
34 C>B>D▼
6 B>D▼
8 D>B▼
5 D>S▼
21 S>D▼
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),
▲34 C>B>D
▲6 B>D
▲8 D>B
▲5 D>S
▲21 S>D
▲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
26.5
21 S▼
▲26.5 D
▲21 S
Here, 7.5 CBD votes and the 19 other votes that prefer D to S give their votes to D. A, C, and D are then the 3 candidates with the most votes, and since the voters who prefer S>D don't have enough votes to change the outcome, (A, C, D) win this matchup. Since we already know (A, C, D) can win all other matchups, (A, C, D) is the Condorcet winner and wins.
== Explanation of how Asset Voting is, under certain assumptions, a Condorcet method (and how this enables it to be done as an algorithm) ==
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.
== Lewis Carroll's own likely observations that Asset is intended to be Condorcet-efficient ==
Lewis Carroll is the first known inventor of Asset Voting. In a passage in an article<ref>[https://www.rangevoting.org/BlackCarrollAER2.pdf
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