[EM] Condorcet Loser, and equivalents

robert bristow-johnson rbj at audioimagination.com
Tue Jun 4 12:39:49 PDT 2019

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

Subject: [EM] Condorcet Loser, and equivalents

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

Date: Tue, June 4, 2019 11:50 am

To: election-methods at electorama.com


> [Not subscribed, please CC me]


> Andy Montroll beats Bob Kiss.

> Andy Montroll beats Kurt Wright.

> Bob Kiss beats Kurt Wright.

> Montroll, Kiss, and Wright beat Dan Smith.

> Montroll, Kiss, Wright, and Smith beat James Simpson.


> James Simpson is the Condorcet Loser.


> …is that right?
yes.  and he was also an absent candidate.  most of us didn't even know he was a candidate until election day.  he got only about a dozen voters ranking him at all.
however, Dan Smith was a serious candidate.  he is now the president of
some small Vermont college, i think.
now it looks like he's going back to Burlington.


> In the race {Montroll, Kiss, Wright}, Kurt Wright is the Condorcet Loser.


> Let's say candidate D appears. D signs up, becomes a candidate, is on the

> ballot, and never campaigns.

you mean like James Simpson?

> D loses horribly, of course.


> D is now the Condorcet Loser. Kurt Wright isn't.
you mean like James Simpson?

> Does this change the nature of the candidate, Kurt Wright, or the social

> choice made?


> Think about it. Without Simpson, Smith is the Condorcet Loser. Without

> Smith, Wright is the Condorcet Loser. You have a chain of absolute

> Condorcet Loser until you have a tie or a strongly connected component

> containing more than one candidate which is not part of the Smith or

> Schwartz set.


> This is important.
I've always said (maybe not in these circles) that even though the Burlington 2009 race was close enough to have one Plurality Winner (Wright), a different IRV Winner (Kiss), and a yet different Condorcet Winner (Montroll), that the outcome was well ordered, from a
Condorcet POV.

Andy was unambiguously preferred over all of the candidates.
Remove Andy from the slate and Bob is preferred over all of the remaining candidates.
Remove Andy and Bob from the slate and Kurt is preferred over all of the remaining candidates.
Remove Andy and Bob and Kurt from the
slate and Dan is preferred over the only other remaining candidate.
But there were three plausible winners.  There was a spoiler (Kurt) but usually the "spoiler" is someone who is way below the top two candidates, yet has enough votes to be far more than the margin of the top
Ironically, in the 2014 governor's race in Vermont, we had a serious spoiler candidate, but this time it was the Republican candidate who got screwed.  The spoiler was a Libertarian who got 3 times more votes than the margin between the GOP and Dem.  Since there was no majority,
it went to the Vermont Legislature who routinely picks the plurality winner.  the guv was reelected.
that's when i started lecturing the GOP that sometimes they get hoisted by their own petard.

> We say Instant Runoff Voting passes the Condorcet Loser criterion, but can

> elect the second-place Condorcet Loser. That means Kurt Wright is the

> Condorcet Loser and IRV can't elect Wright; but in theory, you can add

> Candidate D and get Kurt Wright elected.
Only if Candidate D can get into the final round with Kurt.  If either Andy or Bob do, they beat Kurt in the final round.
we had a Candidate D (his name is Dan).

> In practice, between two candidates, the loser is the Condorcet loser.

> Montroll beats Kiss, so Kiss is the Condorcet Loser. By adding Kurt

> Wright, you have a new Condorcet Loser. This eliminates Montroll and,

> being that Kurt Wright is now the Condorcet Loser and is one-on-one with

> another candidate, Bob Kiss wins.
oh, so you're saying that Candidate D has more first-choice votes than either Andy or Bob?
doesn't sound like a "spoiler" to me.  sounds like a "winner".

> It seems to me the Condorcet Loser criterion is incomplete and inexact: a

> single Condorcet Loser is meaningless. The proper criterion should be ALL

> Condorcet Losers, such that eliminating the single Condorcet Loser leaves

> you with exactly one Condorcet Loser, thus both of them are the

> least-optimal set.


> I suppose we can call this the Generalized Least-Optimal Alternative

> Theorem, unless somebody else (probably Markus Schulze) came up with it

> before I did. It's the property I systematically manipulate when breaking

> IRV.


> Thoughts? Has this been done before? Does this generalize not just to

> IRV, but to all systems which specifically pass the Condorcet Loser

> criterion proper (i.e. they have no special property like Smith-efficiency

> that implies Condorcet Loser criterion, but CAN elect the second-place

> Condorcet loser)? That last one seems like it must be true.
i don't worry too much about the Condorcet Loser.


r b-j                         rbj at audioimagination.com

"Imagination is more important than knowledge."

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