Vote unitarity: Difference between revisions

'''Vote unitarity''' is the concept that each person should have one vote and that vote should not change in power during the tabulation in any system. More mathematically, it is the condition that the time evolution of the vote according to the tabulation procedure is mathematically represented only by [[W : Unitary transformation | Unitary transformations]]. This means that ballot weight can be split between winners but never created or destroyed during the voting systems calculation of winners.

SinceWhen [[Single Transferable Vote]] allocates voters to winners it violatescan 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. This violates the principle of one person one vote since this personvoter would essentially be allowed to vote with half weight in later rounds after "winning". Proponents of [[Single Transferable Vote]] would use this argument for its superior fairness over [[Reweighted Range Voting]] and the [[Reweighted Range Voting]] use the opposite argument. Since [[Reweighted Range Voting]] and [[Single Transferable Vote]] are very popular systems which violate Vote Unitarity in opposite ways it should be possible to find a balanced middle ground which maintaining their other desirable features.

On an even further extreme, [[Bloc voting]] when treated as a sequential method often violateviolates Vote Unitarity even more than [[Reweighted Range Voting]] since a voter can fully influence the election of multiple candidates independently without any reweighing. [[Cumulative voting | Cumulative Voting]] attempts to mitigate this by giving voters the same amount of vote beforehand with the understanding that it is up to them to chose how to reweightdistribute their vote's weight on their ballot. This also has the added effect thatwhich makes outcomeoutcomes of [[Cumulative voting | Cumulative Voting]] have higher [[Proportional representation]] than standard Bloc Systems. Thiele methods such as [[Reweighted Range Voting]] violate Vote Unitarity less than Bloc elections because they at least reduce ballot weight to some degree. In addition they do this reweigting in such a way to satisfy the Hare Quota Criterion.

In sequential [[Multi-Member System|multi-member systems]] this concept become especially relevant due to the different rounds of tabulation. Specifically, a voter whose favorite has been elected should not have influence over subsequent rounds. On the other side, a voter who has not been fully statisfied should still have some level of influence. This means that systems which allocate votes such as [[Single transferable vote]] and [[Sequential Monroe]] violate vote unitarity if they allocate the whole vote weight to a candidate the voter did not express maximal endorsement for. In [[Ordinal systemvoting | ordinal systems]] it is not possible to know how much influence should be lost at each round since only relative endorsement is given. In [[cardinal voting systems]] the influence of each voter in each round goes down proportionally in relation to the amount of representation they have won in previous rounds.

The versions of [[Party-list proportional representation |party-list proportional represenationrepresentation]] which comply with vote unitarity are those which follow a [[largest remainder method]] like the [[Hamilton method]]. This is because it apportions evenly.

[[Keith Edmonds]] saw a unification of [[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 and designed a score reweighting system which satisfied both Hare Quota Criterion and Vote Unitarity.{{Citation needed}} As such it would preserve the amount of score used through sequential rounds whichwhile attributing representation in a partitioned way. It would assigneassign 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]] ballots to satisfy Vote Unitarity. Variants were soon found.