Pairwise Additivity (for single-winner systems)
In a single-winner election, let's consider the candidates in their ordered pairs.
Suppose there is a way to interpret each ballot as assigning a number to each ordered pair of candidates, such that doing this preserves all the information the ballot provides that would be relevant to the electoral outcome.
Further suppose that without changing the outcome, we can rewrite the tally in such a way that its first step is to sum up for each ordered pair of candidates, the numbers given to that ordered pair by the ballots. The rest of the tally then depends only on those results, and reproduces the outcome that the tallying procedure originally described for the voting system would have produced, electing the same candidate, and reporting equally about how well or poorly the losing candidates did.
Then the voting system meets a constraint I am introducing here, of "pairwise additivity".
I suggest that any pairwise-additive system that also meets Frohnmayer balance suffices to defeat the absolute dictatorship of capital (in large elections).
I believe the following systems are among those that are pairwise additive and Frohnmayer balanced:
- Ranked Robin
- Reverse STAR