[EM] A rant about IRV and its recent history in Alaska

[Kristofer Munsterhjelm]

On 2025-03-30 03:17, robert bristow-johnson wrote:

>> We can expect the Democrats too will eventually learn the lesson that RCV is prone to spoiling.
> 
> I would say that IRV is more prone to spoiling than is Condorcet
> RCV.  I think that's obvious.   For the case of a Rock-Paper-Scissors cycle,
> *any* method will demonstrate the spoiler effect.  If the method elects
> Candidate Rock, then Candidate Scissors *must* be a spoiler.
> 
> But Condorcet RCV would have saved Burlington 2009 and Alaska 2022
> (August) from spoilage where Hare RCV (or IRV) failed to do so.

Yes: every[1] method fails IIA when there's a Condorcet cycle. Methods 
that fail Condorcet by definition also fail IIA in other cases.

>> By the way, my definition of "spoiler" is narrower than RBJ's
>> definition.  He calls X a spoiler if X, by running, causes the winner to
>> change from some Y to some Z.  I call X a spoiler if both of the
>> following conditions hold: (1) X, by running, causes the winner to
>> change from some Y to some Z.  (2) The number of voters whose order of
>> preference has X > Y > Z exceeds the number of voters whose order of
>> preference has X > Z > Y.
>>
>> In other words, X is a spoiler if X, by running, causes the
>>	election of a "greater evil" of most of X's supporters.

> But that is always the case when IRV fails to elect the Condorcet
> winner.  Then the loser in the IRV final round is the spoiler.  At least
> in the case of 3 significant candidates.
> 
> It's because many more of Palin voters preferred Begich over Peltola.
> Or in Burlington 2009, many more of Wright voters preferred Montroll 
> over Kiss.  In both cases, many more of the voters for Candidate
> Right preferred Candidate Center over Candidate Left.  That is the
> Center  Squeeze.
> 
> So your additional requirement adds no additional restriction.  When 
> IRV fails and spoils an election, it is *always* the Center
> candidate who is robbed, which means the candidate on the Right or
> Left is the spoiler and the opposite candidate on the Left or Right
> is the beneficiary of the spoiled election.
I just did a check using linear programming, and that seems to be true. 
My reasoning is as follows:

By Steve's definition, a spoiler is a candidate A who,
	(1) if he runs, changes the winner from B to C,
and	(2) has more A>B>C voters than A>C>B voters.

For IRV, if we want to find a counterexample where (1) holds but not (2):
	- B must beat C pairwise, so the winner without A is B.
	- After A is added, the finalists must be A and C, hence
	  B must be the plurality loser.
	  (A must be included to change the outcome, and C must be
            included to win)
	- C must beat A pairwise to win the second round, and
	- there must be at least as many ACB voters as ABC voters.

The polytope produced by these constraints is, unless I've made a 
mistake, empty.

>> We can also define a counterfactual spoiler: someone who would be
>> a  spoiler if s/he runs, but chooses not to run.  Similarly, we can define
>> a counterfactual Condorcet winner: someone who would be the sincere
>> Condorcet winner if s/he runs, but chooses not to run.
> 
> That's just so speculative that I don't feel safe speculating.

This is similar to Marcus Ogren's "primordial election": 
https://voting-in-the-abstract.medium.com/the-primordial-election-that-is-never-held-e019356faf90

By its nature, it's very hard to speculate about concrete examples, 
because we can't see what could possibly have happened. But it makes 
sense that there would be at least *some* primordial election effects. 
If it's too costly to run and you're not going to win, you're not going 
to run.

Marcus says that if candidates could run relatively unimpeded, we would 
expect to see a lot more center squeeze elections than Condorcet cycles, 
because in a spatial model, the former is more likely to occur than the 
latter. When the US ballot data shows a more even distribution between 
center squeezes and cycles, there are two possibilities:

- We only need two parties to accurately represent political opinion, so 
fringe parties will always be fringe; or

- Something deters candidates who would be closer to the median voter 
from running.

>> Spoiling (which violates the IIA criterion) isn't necessarily bad.
> 
> It's always bad for a larger number of voters than the spoiling
> favored.  More voters suffered from the spoilage than voters who benefited.
> 
>> For instance, if Scissors by running changes the winner from Paper
>> to  Rock, the additional preference information gained when Scissors runs
>> may suggest Rock is better than Paper. In this case, we should hope
>> Scissors isn't deterred from running.
> 
> Scissors has every right to run.  We must not deter Scissors from
> running.  But if Scissors is the spoiler (which is the case in a cycle
> and Rock is elected), it is simply in the numbers that Scissors running
> drew more 1st-choice support away from Paper than they did from Rock
> (and they would be Scissors' voters 2nd-choice votes).  That's how Paper
> got eliminated in the semi-final IRV round.

With a Condorcet cycle, every method would have an IIA failure, though. 
Suppose the jurisdiction used ranked pairs instead, then Scissors 
running could still change the election from Paper to Rock.

Since every method has to bite the IIA bullet in a cycle, it's not clear 
which way of resolving the cycle is best (in the senses of having 
legitimacy and not deterring candidates from running). Some approaches 
are better than others (ISDA would be better than something that fails 
Condorcet loser), but there's no obvious "best of the best".

-km

[1] With the usual caveats: determinism, neutrality and symmetry, etc.