[EM] Fwd: Election-Methods Digest, Vol 236, Issue 18

[Toby Pereira]

 As an example of a cycle inside a set of ballots where there is a Condorcet winner:
3: A>B>C2: B>C>A2: C>A>B2: B>A>C
A is the Condorcet winner (beating both others 5-4), so there's no cycle in that sense. But you can remove the following cycle within the ballots:
2: A>B>C2: B>C>A2: C>A>B
This leaves:
1: A>B>C2: B>A>C
B is now the Condorcet winner (and the Borda winner in the original set of ballots).
Toby
    On Monday, 18 March 2024 at 06:42:46 GMT, Closed Limelike Curves <closed.limelike.curves at gmail.com> wrote:  
 
 Only if there is a cycle involved.  Either the election was in a cycle in the first place or if the burial strategy is to push the election into a cycle.

If there never ever were any cycles, then Condorcet does not fail.
This is like saying that if there never were any odd numbers, 3 would be an even number. If Condorcet cycles were mathematically impossible, that would be great. Sadly, they aren't, so we have to deal with them. 
For strategy, the mathematical *possibility* of a cycle--not its actual occurrence in a set of results--is what matters, because threatening to create a cycle is what forces a Condorcet winner's supporters to vote strategically.
The system you're proposing--where we make cycles impossible--is Borda, not Condorcet. Saari shows that if you delete every subset of ballots that forms a cycle, then elect the Condorcet winner, you get Borda. If Condorcet is "strategyproof unless cycles are involved," then Borda is *always* strategy proof, because it's got none of them--but clearly it's not, and the reason why is because what matters is whether you *could*, hypothetically, have a cycle, not whether you actually *do*.
In reality, cycles are always involved. Sometimes it's a real cycle. Sometimes it's a theoretical cycle that someone *could* create, and that threat gives them leverage.


  
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