Interpretations of one person, one vote


I’ve noticed that people have used the phrase “one person, one vote” to mean different things. This can lead to confusing situations, such as when Equal Vote references the U.S. Supreme Court’s interpretation but goes on to interpret it as requiring Frohnmayer balance. Because of this, I think it would be useful to identify the different levels of “one person, one vote” that an electoral system can meet. Here’s what I’ve come up with:

Level 1: each voter gets one vote/ballot

This is the most literal interpretation, and it’s passed by pretty much every serious option. I believe quadratic voting would be a notable exception, though.

Level 2: each vote/ballot has the same weight

This is the interpretation that the U.S. Supreme Court holds states to. It’s passed by every proportional method and every single-winner method using equally-sized districts. It’s failed by single-winner methods that use unequally-sized districts and the Electoral College.

Level 3: Frohnmayer balance/Equality Criterion

This is the interpretation pushed by Equal Vote. It’s passed by approval, score, and STAR. It’s failed by plurality, RCV, and 3-2-1. (Do any proportional methods pass this?)

Does this structuring of “one person, one vote” interpretations make sense? Do you see any mistakes regarding which methods pass which interpretations? Any other suggestions or feedback?

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Frohnmayer Balance and Proportional Representation are mutually incompatible.
For example, in the following election:
10 votes: {A5, B5, C5, D0} (Max is 5; there are 3 winners)
By PR, the winners must be A,B,C.
On the other hand, in the following election:
10: {A5, B5, C5, D0}
10: {A0, B0, C0, D5}
10: (Votes countering the previous 10, which must exist by Frohnmeyer Balance.)
By PR, D must be elected. By Frohnmeyer Balance, the winners must be the same as those from the first election, that is, A,B,C. So D cannot be elected.


This is an interesting topic and one that I dealt with while designing my system.

In the article you cite, what is talked about at the beginning where “vote weight” =1/“Number you like” is normally referred to as “vote splitting”. I would love a more formalized definition of this that spells out if ordinal voting has vote splitting.

I like the idea of Frohnmayer Balance in principle but keep in mind that some systems have the property that a single voter who gives the same score to all candidates can alter the outcome. I am pretty sure outcomes would differ in such systems with the addition of two people who vote with counter balancing ballots. The flaw @Marylander brilliantly points out may be related to this. For those who missed it the counter balancing votes are also 10: {A5, B5, C5, D0}.

My approach to the problem of “one persons one vote” was a little different. I look at a vote as a conserved property. Think about money or a fluid. You only have so much. A sequential proportional system obeys “Vote Unitarity” if the amount of this quantity is the same for all voters at each stage. This does not mean that everybody gets to spend all their vote but that nobody gets more as part of the counting process. RRV violates this. It is worth pointing out that this automatically satisfies proportional representation.

There are more details in my post here: Different reweighting for RRV and the concept of Vote Unitarity

Also, I chose the name Vote Unitarity because I was sure it was not already used and it is a term used in quantum mechanics for this property. Warren hates the term but his conservative vote juice is no better. I am open to suggestions.