[EM] IRV failure modes, vote splitting

robert bristow-johnson rbj at audioimagination.com
Wed Dec 19 21:15:54 PST 2018

---------------------------- Original Message ----------------------------

Subject: [EM] IRV failure modes, vote splitting

From: "John" <john.r.moser at gmail.com>

Date: Wed, December 19, 2018 10:34 pm

To: election-methods at electorama.com


> [I'm not subscribed, so please CC me on responses]


> After looking at Burlington, VT 2009, I've started to ask some questions

> about IRV.

what were you looking at?  this, from Warren Smith?:
It's a good analysis.  don't let this excellent analysis of the Burlington 2009 get conflated with all of Warren's claims about Score Voting or Approval Voting.
(other people on this list know this), i am a Burlington resident (i happen to live in Bernie's ward), politically active, and was there in 2009.  at the time Andy Montroll was a friend of mine.

> I strongly prefer Tideman's Alternative Smith.
personally, i think that Tideman Ranked Pairs (using margins) is just better.  and it's simpler.

> IRV eventually reduces to a three-way race, and I see some interesting

> things occur there.


> In Plurality, you can add a candidate on the same ideological end as your

> opponent—if your opponent is more-liberal than you, then add another

> more-liberal opponent—and you split the vote. This lets you win a close

> race when you can't get majority.


> In IRV, you also need to add a candidate, and the same rules kind of work.

> By adding a conservative to a two-liberal race, you siphon votes from your

> moderate (winning) opponent.
well, yes, but most of the moderate liberal voters had marked the more liberal as their second choice and also the reciprocal.

> That happened in 2009: Bob Kiss loses; add Kurt Wright and Kurt Wright

> wins plurality, Montroll has the fewest votes and is eliminated, Kiss beats

> Wright and wins.
Andy had the fewest 1st-choice votes of the three, but he was the 2nd-choice of most of Kurt's voters and nearly all of Bob's voters.


> Interesting thoughts.


> In the three-way race, it looks like Plurality without Majority elects the

> Condorcet loser. Kurt Wright lost to both Kiss and Montroll,
in a pair-wise comparison, yes.  loses to Andy by 929 votes and lost to Bob by 252 votes (out of nearly 9000).

> and didn't

> have a majority. Lacking a majority, pulling the center candidate would

> tend to favor your opponent. This is because Conservatives will roughly

> split between two Conservatives; Liberals will roughly split between two

> Liberals; and so the three-way race necessarily has an imbalance whereby

> there are more Conservatives or more Liberals, and so a split vote

> resulting in no majority winner implies that there are more of the group

> splitting the vote.
i would put it more simply:  if there *is* a single-dimensional political spectrum from left to right, the center candidate is far more likely to be preferred as a 2nd-choice to the voters on the extremes than the candidate at the opposite extreme.  both GOP
voters and Prog voters selected the Dem candidate as their second choice. 

> The plurality winner is smaller than this group, and

> so is the Condorcet loser.


> That's a logical outcome, not a mathematical one. We can construct

> situations where the liberals abandon the more-liberal candidate for the

> conservative; that's not likely in practice.


> As per vote splitting, above, this three-way situation would tend to take

> votes from the more-center candidate. The more-center candidate would be a

> second choice for both ends, and so typically has overwhelming support

> against each candidate WHEN THERE IS NO MAJORITY WINNER.
well, we need to define exactly what we mean by a "majority winner".  if there are three or more candidates it's possible no single candidate gets majority support.  but between any pair of candidates, there is a
majority winner unless they tie.
that's all Condocet does.  just pairs the candidates with all possible pair combinations and says consistently, "If more voters mark their ballots preferring Candidate A to Candidate B than voters marking the contrary, then Candidate B is not
elected."  that simple rule pretty much defines Condorcet.  and the problem in Burlington 2009 was 587 more voters marked their ballots that they preferred Andy over Bob than the number of voters preferring Bob over Andy, yet Bob was elected.

> That suggests IRV provides no real advantage in the three-way race:

IRV doesn't do too bad in a 3-way race if one of those three has far less support than the other two.  but in Burlington 2009, all three had approximately equal support.  the Prog was the IRV winner, the GOP was the FPTP winner, and the centrist Democrat was the Condorcet
winner.  any of those three were a plausible winner.
i don't know of another governmental race using Ranked-Choice Voting (what they now call it) where the method failed to elect the Condorcet winner.  but i think it will happen again.
When the spoiler has virtually no chance
in winning (but a good chance of spoiling), IRV will choose the same as the Condorcet.  it's only when there are 3 or more plausible contenders that this hiccup happens.
> - If Plurality isn't a Majority, IRV falls to vote-splitting and never
> elects the Condorcet candidate, but avoids the Condorcet loser.


> - If Plurality IS a Majority, IRV elects THE SAME CANDIDATE as Plurality,

> providing no advantage over Plurality in a three-way race. That candidate

> is the Condorcet candidate.


> - When encountering a three-way Smith Set, Tideman's Alternative Smith is

> identical to IRV after eliminating all non-Smith candidates.


> These are, again, practical outcomes, not mathematical ones.


> IRV's single advantage over Plurality appears to be that it mathematically

> avoids the Condorcet loser, although when doing so it practically

> eliminates the Condorcet winner.
no it doesn't.  not most of the time. 
again, Burlington 2009 is the only governmental election using RCV i am aware of in which the single-transferable vote method failed to elect the Condorcet winner.  I think all of the other RCV
elections have.
but that's still not a good reason to use IRV over a Condorcet-compliant method.
there are at least 4 solid reasons why IRV failed in Burlington in 2009.  the most important is that it failed to resist a spoiler.  because of that, a promise to the voters that
IRV made: that they would not need to vote tactically, they could serve their political interests well by voting for their favorite first, and marking their second favorite second.  but 1500 Wright voters found out that, simply by marking their favorite as #1, they caused the election of Bob
Kiss, where, if they had been tactical, they could have insincerely bumped Kurt down a notch and let Andy rise to the top and they would have prevented their lowest choice from winning.  it promised this spoiler thing would not happen.


r b-j                         rbj at audioimagination.com

"Imagination is more important than knowledge."

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