Vote unitarity: Difference between revisions
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3.) Unitary Transformations: A voter's total vote weight cannot be created or destroyed but may be spent to elect winners who represent them through the rounds of tabulation, winner selection, and reweighting. The amount of remaining vote weight available to be used by any voter at any stage in the tabulation must always be their initial vote weight minus the amount they have spent. A voter who has achieved full representation by electing their favorite will have no vote weight left in play in subsequent rounds unless their favorite candidate received a surplus of votes and didn't need the full weight of their supporters votes to be elected.
== Rationale and Critique ==
When [[Single Transferable Vote]] allocates entire voters to winners it can violate vote unitarity by over removing influence in some cases. This occurs in all allocation systems; for example in [[Allocated Score]] somebody who only gave a score of 1 to the winner could lose all future influence. [[Reweighted Range Voting]] on the other hand only reduces influence fractionally, so a voter who got a candidate they gave max score in the first round would only have their ballot weight reduced to 1/2.
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This rational became the foundation of a new class of Unitary Proportional voting methods which were invented to satisfy Vote Unitarity and Hare Proportionality, including [[Sequentially Spent Score|Sequentially Spent Score Voting]].
The principle of proportionate spending can also be critiqued in that it increases strategic incentives. Note that "proportionate spending" only refers to how a ballot is reweighted ''after'' a candidate is elected. This leaves open the question of how much power a vote has to elect a candidate in the first place. Thus, there are two possibilities.
# If a rating of (for example) 3 out of 5 has only 3/5 the power (or less) to elect a candidate in the first place, then the strategic incentive is to give higher ratings to your favorite among the most borderline-viable candidates, in order to get that candidate elected.
# Following the same example, if a rating of 3 out of 5 has more than 3/5 the power to elect a candidate in the first place, the strategic incentive is to give lower ratings, so that the amount of your ballot that is used up when a candidate is elected is less than the voting power you exerted in electing them.
This leads some voting theorists, such as Jameson Quinn, to consider vote unitarity an actively harmful criterion, as opposed to otherwise-similar methods which tend to allocate votes more fully.
== Compliant Voting Methods ==
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== Discussion of Common Failure Modes ==
=== Failure to
Most voting methods and implementations ensure that the initial weight of a vote is equal between voters, but in order to ensure that it's possible to cast an equally powerful vote, there can be no caps on the number of candidates who can be ranked or rated, and there can be no limit to the number of candidates who can be ranked or rated at any level.
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==History==
[[Keith Edmonds]] saw a unification of [[Proportional representation|Proportional Representation]] and the concept of one person one vote which was maintained throughout winner the winner selection method. He coined the term "vote unitarity" for the second concept.<ref>https://groups.google.com/forum/#!topic/electionscience/Tzt_z6pBt8A</ref> and designed a score reweighting system which satisfied both Hare Quota Criterion and Vote Unitarity. As such it would preserve the amount of score used through sequential rounds while attributing representation in a partitioned way. It would assign Hare Quotas of score to winners which allowed for a voters influence to be spread over multiple winners. The final system was originally proposed in a late stage of the [[W: 2018 British Columbia electoral reform referendum]] but was not selected for the referendum ballot. This system, [[Sequentially Spent Score]], was the first sequential [[Multi-Member System | Multi-Winner]] [[Cardinal voting systems |Cardinal Voting System]] built on [[Score voting|Score Voting]] ballots to satisfy Vote Unitarity. Variants were soon found.
== Definitions
Vote Weight = The weight and worth of a person's vote. The amount of power that a voter has to elect candidates in each round. Ballots are fully weighted at the beginning of tabulation, and ballots may be reweighted to reflect that some or all of a vote's weight has been spent to win representation.
== Priceability ==
Vote Unitarity is related to the more recent concept of [[priceability]]<ref>D. Peters and P. Skowron. Proportionality and the limits of welfarism. In Proceedings of the 2020 ACM Conference on Economics and Computation, pages 793–794, 2020. Extended version [https://arxiv.org/pdf/1911.11747.pdf arXiv:1911.11747].</ref> A committee is priceable if there is a price such that voter spending can be arranged in such a way that each committee member gets a total spending of exactly the price, and voters do not have enough money left to buy additional candidates. The intuition behind this condition is that it encodes that each voter has (approximately) equal influence on the committee (since each voter starts out with an equal budget), and this ensures proportionality.
== References ==
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