[EM] IRV failure modes, vote splitting

John john.r.moser at gmail.com
Wed Dec 19 19:34:36 PST 2018

[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.  I strongly prefer Tideman's Alternative Smith.

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.

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.

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, 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.  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.

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

 - 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.
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