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. It 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 methods 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 which are compatible with Vote Unitarity are those which follow a Largest remainder method like the Hamilton method. This is because it apportions evenly

Creation

Since Single Transferable Vote allocates voters it violates vote unitarity by over removing influence in some cases. 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 they ballot weight is 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 (note that if a Bloc Score election is treated as a sequential method, then every time a candidate is elected, a voter who got one of their max-scored candidates is actually allowed to vote with full weight in later rounds, Thiele methods such as RRV are more proportional than Bloc elections because they at least reduce ballot weight to some degree). Proponents of Single Transferable Vote would use this argument for its superior fairness over Reweighted Range Voting. Keith Edmonds wanted to design a score reweighting system which had neither of these flaws. As such it would preserve the amount of score used through sequential rounds. He was also unhappy with Allocated Score since somebody who only gave a score of 1 to the winner could lose all future influence. Sequentially Spent Score is the sequential Multi-Winner Cardinal voting system built on Score voting ballots to follow this principle.

Relation To Similar Concepts

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.