Vote unitarity

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.

Rationale

Since Single Transferable Vote allocates voters it violates 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 person would essentially be allowed to vote with half weight in later rounds. 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.

On an even further extreme, Bloc voting when treated as a sequential method often violate 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 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 reweight on their ballot. This also has the added effect that makes outcome of 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.

The test of balance

The test of balance is defined as the following "Any way I vote, you should be able to vote in an equal and opposite fashion. Our votes should be able to cancel each other’s out."

Vote Unitarity is not incompatible with this but the concept of a Utilitarian Multi-Winner score system is. These systems do not aim to cancel out the will of opposing groups and leave them with nothing. They aim to find an compromise for all conflicting voters. Vote Unitarity helps to ensure fairness in the compromise.

Compliance

Vote unitarity can be turned into a criterion in specific ways for specific classes of systems.

Single member systems

In single member systems this property is trivially satisfied due to the simplicity of such systems.

Multi-member systems

In sequential 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 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.

Partisan systems

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

History

Keith Edmonds saw a unification of Proportional representation and the concept of one person one vote. 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. As such it would preserve the amount of score used through sequential rounds which attributing representation in a partitioned way. It would assigne 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-Winner Cardinal voting system built on Score voting ballots to satisfy Vote Unitarity. Variants were soon found.