[EM] Example with most different results

[Kevin Venzke]

Hi Abel, Kristofer,

Interesting idea.

> On 2024-05-25 12:35, Abel Stan wrote:
> > I have a challenge for all: I need a unified example where the most possible
> > voting systems lead to different results. I know it might be easy to construct
> > such a scenario with any number of runoffs and such, but that would not be in
> > the spirit of the game. This is the best I came up with so far, 8 different
> > winners, including a Condorcet-winner + 1 who could win under a dictatorship
> > (or a 4 round system).
> >
> > 1000:Plurality>Bucklin>Coombs>IRV>Anti>Borda>Runoff>Condorcet>Dictator
> > 999:Runoff>Condorcet>Bucklin>Anti>Dictator>Coombs>IRV>Borda>Plurality
> > 998:IRV>Condorcet>Borda>Coombs>Anti>Dictator>Plurality>Bucklin>Runoff
> > 997:Coombs>Borda>Bucklin>Anti>Dictator>Runoff>Plurality>Condorcet>IRV
> > 996:Dictator>IRV>Condorcet>Coombs>Anti>Runoff>Plurality>Bucklin>Borda
> > 995:Borda>Bucklin>Anti>Dictator>Coombs>IRV>Runoff>Plurality>Condorcet
> > 994:Anti>Condorcet>Borda>IRV>Coombs>Dictator>Runoff>Plurality>Bucklin
> > 993:Condorcet>IRV>Borda>Dictator>Runoff>Plurality>Anti>Bucklin>Coombs
> > 992:Bucklin>Borda>Dictator>Condorcet>Coombs>IRV>Runoff>Plurality>Anti
> 
> Incidentally IFPP (Carey, below-average Plurality elimination) elects
> Dictator :-)
> 
> https://munsterhjelm.no/km/rbvote/calc.html

On my calculator, votingmethods.net/calc , my "Cross Max" method also elects
Dictator. This is because Dictator has the greatest number of votes in a contest
involving the first preference winner, Plurality.

I match the result that there are 8 different winners. Only candidate Bucklin is
not elected anywhere.

Abel Stan <stanabelhu at gmail.com> a écrit :
> And one without a Condorcet-winner, 9 different result with 9 candidates:
> 
> 1000:Plurality>Bucklin>Coombs>IRV>Anti>Kemeny>Runoff>Schulze>Borda
> 999:Runoff>Schulze>Bucklin>Borda>Anti>Coombs>IRV>Kemeny>Plurality
> 998:IRV>Schulze>Coombs>Kemeny>Borda>Anti>Plurality>Bucklin>Runoff
> 997:Coombs>Kemeny>Bucklin>Borda>Anti>Runoff>Plurality>Schulze>IRV
> 996:Borda>IRV>Schulze>Coombs>Anti>Runoff>Plurality>Bucklin>Kemeny
> 995:Kemeny>Bucklin>Borda>Anti>Coombs>IRV>Runoff>Plurality>Schulze
> 994:Anti>Kemeny>Schulze>IRV>Coombs>Borda>Runoff>Plurality>Bucklin
> 993:Schulze>IRV>Borda>Kemeny>Runoff>Plurality>Anti>Bucklin>Coombs
> 992:Bucklin>Kemeny>Borda>Schulze>Coombs>IRV>Runoff>Plurality>Anti

Here I also have method(s) electing each of the nine.

The oddballs are:
Implicit approval elects Anti (makes sense).
Benham and Approval-Elim Runoff elect Coombs.
TACC and Chain Runoff elect Kemeny.

I really can't imagine how to make such scenarios without just running tons of
random scenarios until you find a good one. Is that what you did?

Kevin
votingmethods.net