[EM] Centrifugal Margins

[Kristofer Munsterhjelm]

On 11/26/23 23:31, Joshua Boehme wrote:
> 
> Hello everyone. I've lurked in the archives off and on for a while. I 
> finally decided to join since I've been playing around with a method and 
> I'm at a point where outside feedback/criticism could help. Also, 
> someone might have already described this in some paper I don't know about.
> 
> I'm calling it centrifugal margins for now, and it stochastically 
> chooses an ordering based on ordinal ballots. (Since single-outcome 
> methods can be contentious, assume multiple outcomes wouldn't make sense 
> in the particular context or we're satisfying some external constraint.) 
> Centrifugal margins generally requires ballot-level detail, but 
> sometimes the head to head margins suffice.
> 
> The reason for the name is that it tries to maximize winning 
> comparisons' margins and minimize them for losing ones. Majority voting 
> with 2 candidates is the prototype: a candidate with >50% of the votes 
> wins 100% of the time. Although cycles can prevent us from reaching 
> 100%, the method tries to push non-ties away from the tie point. Ties 
> remain perfectly balanced, like a pencil on its tip.
> 
> Let E be the set of non-losing edges over the ballots B. Centrifugal 
> margins looks for new ballots B' that leximax (the margins of E over B') 
> - (the margins of E over B). Note that E is determined solely by the 
> actual ballots. For simple elections this suffices. Otherwise, we do the 
> same for 3-candidate subgraphs after leximaxing the edges, then 
> 4-candidate subgraphs, etc. The final ballots B' give the distribution.
> 
> The actual calculation resembles the nucleolus in game theory (a big 
> inspiration) and has similar pitfalls. It involves iterated linear 
> programming problems and using the duals to lock constraints.

I'm not quite sure what you mean. Could you give a simple example, say 
where the first step suffices so we don't have to get into linear 
optimization nitty-gritty?

-km