# [EM] pairwise comparisons

robert bristow-johnson rbj at audioimagination.com
Thu Apr 19 01:32:09 PDT 2018

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Subject: [EM] pairwise comparisons

From: "Curt" <accounts at museworld.com>

Date: Wed, April 18, 2018 7:19 pm

To: "EM" <election-methods at lists.electorama.com>

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> ... But for the rest of you, I’m interested in your thoughts.
dunno if you'll like mine.

>

> Imagine a set of six candidates, and one voter. The voter is asked to determine their views of these candidates. But instead of just being asked to rank them in order, the voter is asked to judge them pairwise.
that seems to be both a complicated ballot and a setup for possible
silliness.

>

> For six candidates, this means 15 questions. Each question being a comparison of A and B, with the voter picking their favorite of the two.

>

> First question, is it possible for a voter to generate a cycle?
of course it is.  but this voter is schitz.  maybe a little psychopharmocology or a little electricity in the brain might do that voter some good.
> We know it is technically possible, trivially
demonstrated. But is it possible that a voter, using some internal set of principles, would also generate a cycle? I would argue yes.
only if the voter is jerking our chain or is schizoid.  (this, plus the fact of limited real-estate on the ballot, is why i would never offer pair-wise
binary choices, but just offer full ranking, which would require five levels for six candidates.)
here is what the voter should be thinking about for a single-winner race:  "Who do I like best?  Who do I think is the best person for this single seat office?"
Mark that
candidate #1.  The ask "If this person were taken out of the race and didn't exist at all, of the remaining candidates who do I think is the best person for this office?"
Mark that candidate #2.  Then take both #1 and #2 out of the race and ask oneself who is best in the
remaining field.

I just cannot see the psychology of if a voter thinks that Candidate A is better than Candidate B, and also thinks that Candidate B is better than Candidate C, there is no way that the same *sane* voter would decide that Candidate C is better than Candidate
A.
Now a voter can have tied preferences and rank Candidates A, B, and C all #1, but that is saying "I don't care which of those three are elected, but I sure as hell don't want the losers Candidates D or E or F to take this office.  but that is different than a circular preference
with A, B, and C.

We should do some Condorcet voting system for general elections in a multiparty and multi-candidate context.  but it should be a ranked ballot for each voter.  only let the voter express linear preferences.

>

> If the voter does generate a cycle via these pairwise comparisons, what does this mean? Does it mean the voter is confused? Does it mean the voter is inconsistent?
yes and yes.
> Does it mean that this cycle or cycles are an accurate depiction of the voter’s actual
views?
only if he's wack.

>

> Say that we then ask the voter to create an actual ranked ballot out of these six candidates, and the voter manages to do so. What happened in that process of the voter deciding the rankings? Was it a clarifying experience? Did the voter’s preferences change? Did the voter compromise? Did
the voter lie?
we want a system where there is no incentive for the voter to have to vote tactically (i.e. compromise) or lie.

>
> And finally, say that a collection of these voters submit their ranked ballots (not just their pairwise comparisons), and the votes are tabulated, and the result is a three-candidate Smith Set, where each candidate defeats all other candidates outside the Smith Set.

>

> What does that Smith Set mean?
it means that there is a problem.  it means that these voters that voted for Nader in 2000 and preferred Bush over Gore have a much different way of thinking than the Nader voters who preferred Gore over Bush.
BTW, the Burlington 2009 IRV election
had 5 candidates, 3 of which any one could have credibly won the election, but one of the 3 was the Plurality (of 1st choice) winner, another was the IRV winner, and another was the Condorcet winner.  all three had some legit claim to being the "people's choice".  but, from a
Condorcet POV, it was perfectly ordered and there was no ambiguity of the voter preference.
i **really** think that if governments started using a Condorcet-compliant method regularly, a cycle would be very rare.  i think the possibility of a cycle as a reason not to go with Ranked-Choice
Voting and a Condorcet-compliant method, is a red herring.

> Is the electorate confused? Is the electorate inconsistent? Or is the Smith Set an accurate depiction of the electorate’s actual views?
it depicts a problem.  since a 3-candidate cycle is decided the
same way with MinMax or RankedPairs or Schulze, the defeat that is the weakest is the defeat that doesn't count and that will resolve the circular preference and the election.
but it won't stop the burning trash cans in the street.
ever since Nov 2016, we're all friggin' toast
anyway.

--

r b-j                         rbj at audioimagination.com

"Imagination is more important than knowledge."

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