[EM] Question to the Condorcetists

[Kristofer Munsterhjelm]

On 2024-02-28 19:36, Closed Limelike Curves wrote:
> Can Condorcet be weakened to comply with participation? Condorcet 
> methods have plenty of advantages, but systems failing participation are 
> vulnerable to court challenges or being struck down as unconstitutional, 
> as seen in Germany.

In the mathematical sense, there exists some voting method that 
maximizes the probability that when a random election is chosen, 
according to some election distribution, and that election has a CW, 
then that CW is elected -- while still respecting participation. In that 
sense, Condorcet can be weakened and such a method is the method that 
weakens it the least.

But what it actually looks like, or what its algorithm would be like, 
nobody knows. You could get a glimpse into how it behaves for low 
numbers of voters and candidates by using a variant of my integer 
programming approach, but it doesn't tell you much: it basically amounts 
to a gigantic lookup table.

In general, determining the minimal relaxations of some criterion 
required to pass some other criterion is very hard. I can really only 
think of two examples: Schulze STV's resistance to vote management 
except when it would conflict with Droop proportionality, and the 
independence of strongly dominated alternatives criterion of River as a 
monotone approximation to independence of covered alternatives. And I 
don't think Jobst set out to make a method to be close to IoCA while 
passing monotonicity, so Schulze's the only example I can think of where 
the designer set out to find a relaxation of that sort.

-km