Example with most different results
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,
On 2024-05-25 12:35, Abel Stan wrote:
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
-km
The more interesting question is what makes voting systems agree when so
many of them can be made to disagree (and why?)
The answer I found for a single vacancy was that an ordinal count is
less accurate than a rational count, and the disagreement in results
was merely caused by discrepancies in ordinal counts. This was shown by
changing the unweighted Condorcet count to a weighted Condorcet count,
whereupon it agreed with the only other rational count (Borda method),
in a finely balanced vote.
Therefore, I concluded that such alleged demonstrations that there is
"no perfect voting system" were an imposition on readers.
For that matter, no scientific (or knowledgable) endeavor ever claims
perfection, but to seek unambiguous results, that could not mean
anything one wants.
Moreover single vacancies may not offer more than half a democracy.
(Known in ancient times as a tyranny.) With more seats per constituency,
in a proportional election, the inaccurate "last past the post"
exclusion count becomes less important. (As well as being unnecessary.)
Regards,
Richard Lung
On 25/05/2024 11:35, Abel Stan wrote:
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,
Election-Methods mailing list - seehttps://electorama.com/em for list info
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@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
On 2024-05-25 17:05, Kevin Venzke wrote:
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?
I think you can do some of them with mixed integer programming. But it
would be pretty cumbersome - just running tons of scenarios would be easier.
(For instance, for Kemeny, you could enumerate every permutation with
Kemeny first and then add constraints that the minimum Kendall tau
distance of these must be less than every other permutation's Kendall tau.)
Weighted positional methods are easy to do, at least :-)
-km
I mostly did it semi-manually, just trying in excel to better understand
each (the first example, with Condorcet). I then checked it with one site,
probably when I changed something up because of that is when Bucklin
switched.
The second example case from just modifying the first one. I also thought
if I'd really get into it I'd just try random ones, but with certain
restrictions to make it faster. That's what I did when I did the same thing
for different PR apportionment formulas.
On 2024-05-25 17:05, Kevin Venzke wrote:
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?
I think you can do some of them with mixed integer programming. But it
would be pretty cumbersome - just running tons of scenarios would be
easier.
(For instance, for Kemeny, you could enumerate every permutation with
Kemeny first and then add constraints that the minimum Kendall tau
distance of these must be less than every other permutation's Kendall tau.)
Weighted positional methods are easy to do, at least :-)
-km