[EM] Example with most different results

Abel Stan stanabelhu at gmail.com
Sat May 25 03:35:36 PDT 2024


Greetings,

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

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

Wonder what's the highest we could get to.
Cheers,
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