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

[robert bristow-johnson]

> On 03/18/2024 2:27 AM EDT 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.

No, there are about as many odd numbers as there are even numbers.  Odd integers are common.  Condorcet cycles are extremely uncommon.  Circa 0.4%.

> If Condorcet cycles were mathematically impossible, that would be great. Sadly, they aren't, so we have to deal with them.
> 

I completely agree.

> 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.
> 

Well, actually, I think it's a loser in a Condorcet RCV election that would threaten to create a cycle.  A good example *is* the Alaska 2022 special election.  With Condorcet, Begich wins.  If it were Plurality, Peltola wins.

Then if it were Condorcet-Plurality (or Bottom-Two Runoff, they both elect the same candidate in a 3 candidate race), if the Peltola campaign organized supporters to bullet-vote Peltola (not ranking Begich over Palin), they would have pushed the election into a cycle and then Peltola wins.  But that can backfire, if Palin had a little more support, then this burial strategy could end up electing Palin.

> The system you're proposing--where we make cycles impossible--

I never once said that.  I said, if cycles never happened, Condorcet would never fail and there would be no reason for any voter to vote tactically.  We know cycles can happen and we have to deal with it.  But to fail to elect the Condorcet Winner when such candidate *does* exist, is inexcusable.  There is no benefit in that at all.

> 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*.
> 

If you have a Condorcet election that does not demonstrate a cycle, I'm sure there are examples where Borda would turn out differently.

> In reality, cycles are always involved.

No.  They're not always involved.  Cycles are rare.  But Arrow and Gibbard prevail, so cycles, even though they are rare, are unavoidable, so a ranked-ballot method has to be able to elect someone that

> Sometimes it's a real cycle. Sometimes it's a theoretical cycle that someone *could* create, and that threat gives them leverage.
> 

I know there are real cycles.  In the U.S. 2 out of circa 500 RCV elections had no Condorcet Winner.  These are Minneapolis Ward 2 city councilor in 2021 and Oakland School Board District 4 in 2022.

But they're rare.

--

r b-j . _ . _ . _ . _ rbj at audioimagination.com

"Imagination is more important than knowledge."

.
.
.