I want to preface this by stating that Keith has been an extremely valuable member of the Equal Vote Coalition Research Committee and has worked harder then anyone else to test various methods in a variety of ways.
Over my past 2 years on the Equal Vote Coalition Research Committee, I have given many criticisms about his vote unitary (latest revision here) concept. @Keith_Edmonds I know this is going to sound be harsh, but to me it seems like a pseudo-concept rather then something based in rigorous mathematics.
Keith talks about it as if it is a mathematically rigorous criterion for which he knows what methods pass or fail it. Can anybody write a computer program that takes in some election result (as well as the order the candidates were elected along with the weights of each voter throughout the process and the single winner selection method those weights effect if necessary even though to any mathematical criterion this information should be irrelevant and all that should matter is strictly the vote inputs and winner outputs) and determines whether that election violates vote unitary?
Another thing that bothers me about it is that it’s definition seems very inconsistant. When he describes the concept in his electowki page, he describes it as being about vote weight being able to be transferred to candidates but not being able to be created nor destroyed. If he applied this definition found at the top consistently, then all allocated systems like allocated score and sequential Monroe would also pass this criterion. However he doesn’t apply this definition throughout the page as latter when he gets to the compliance of multiwinner systems, he adds additional requirements to the criterion:
On the other side, a voter who has not been fully satisfied 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.
This is an additional requirement concept that has nothing to do with vote weights being conserved that could be better described as it’s own criteria. But it gets worse:
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.
This would imply that SSS fails vote unitary because even under SSS, voters whose favorite candidate is elected don’t always loose all their influence. When too much weight is exhausted this way, SSS has a check to make sure that it no more then a quota of weight is exhausted, at which point SSS reduces how much weight each vote would lose proportionally so that only a quota of weight is exhausted. In it’s current form, no voting method can satisfy this criteria without violating proportionality which is why even SSS (the voting method based off of it) fails it.
Finally, Keith makes the criterion means something completely different altogether for single winner elections:
In single member systems this property is defined by the Equal Vote Criterion.
It would be one thing if the criterion naturally reduced to this when applied to single winner elections, but you can’t just define one criterion to behave completely differently based on how many winners you have.
What concerns me the most about it is that Keith keeps describing it as the concept of one person one vote when I have yet to see any substantive argument for that perspective (which he states, not as a perspective but as a fact). The criterion has now ended up in various Equal Vote Coalition Research Committee reports.