Why Frohnmayer Balance may be Unimportant without High Levels of Voter Information

I don’t think those two modifications are of the same type. The modification you mentioned is only applicable to ranked choice systems or systems with a canonical compression into ranked choice, whereas the modification I suggest is applicable to any voting system. I would guess that independence of clones isn’t amenable to this kind of analysis.

I also don’t think the analogy is good. A better way would be to set a variable threshold for the proportion of voters needed to consider two candidates a “clone,” and then to perform the analysis over a range of reasonable thresholds. To me, the problem with your consideration is with how you are defining a clone.

I see what you mean. But my point is that the definition then doesn’t actually capture the intended spirit of the idea. For example, you mention “closeness,” but what if there is no canonical way to decide which ballots are “close”? The definition itself is the problem, and the way it is used to dismiss voting systems for not passing a “necessary” criterion. Some voting systems don’t fit within the domain of discourse used in defining Frohnmayer balance or its spirit.

I did mention that perhaps what is desired is for the ballot space to fit within a topological Abelian group, or more particularly one with a metric, and for certain ballots to be inverses of each other. But again, just because a voting system doesn’t conform to this restricted notion doesn’t mean it isn’t a good system worth considering.

With scores, you could consider candidates that are given the same score as eac other on every ballot.

But this was kind of the point. It was supposed to be an exaggerated version of your way of passing Frohnmayer Balance. A system that needs you to explicitly hunt out clones will always end up as a mess. Similarly I don’t think looking for ballots that exactly cancel each other out will work very well either.

But anyway, I don’t think we’re in particular disagreement over this. I think Frohnmayer Balance is better to have than not have all things being equal (see what I did there?), but I wouldn’t want to disqualify a system that didn’t pass it if it had other advantages.

3 Likes

That makes sense. In that case I think the definition of Frohnmayer balance isn’t really what people want, they want there to be a way to determine which votes are close to each other and which votes should cancel out fully or partially, which is a lot more complicated and much stronger of a condition than what the definition of Frohnmayer balance suggests. The natural mathematical setting is a topological Abelian group.

I don’t think we’re in much disagreement here either. In any case abstract properties should never be considered more important than how systems actually fair in practice with real human participants.

1 Like