[EM] Keeping Candidates in Subsequent Rounds of Instant Runoff Voting

[Kristofer Munsterhjelm]

On 08/12/2016 10:24 PM, York W. &/or Lois G. Porter wrote:
> Friday, August 12, 2016
> 3:05 pm CDT
> 
> Hi,
> 
> I'm a big time "newbie" here. Wasn't able, for some reason, to search
> the existing messages so I thought I'd stick my neck out and ask a
> probably stupid question.
> 
> In the IRV election method, I don't understand the rationale of
> eliminating the lowest vote getter in each round. In a simple example,
> let's say there are four candidates. Let's say A, B, and C get thirty
> percent of the vote on the first round. Candidate D gets ten percent.
> Normally Candidate D is eliminated even though s/he might be the choice
> of 90 percent of folks in the second round.

I'm not really a fan of IRV, and you're right that that is a problem.
IRV's elimination process ensures that you can't get the Condorcet
loser, but it by no means guarantees that you'll get the Condorcet
winner, as the Burlington election very easily shows.

I think IRV can be traced to STV, and that STV (the multiwinner version)
came first. STV's logic is to assign each vote to one of s candidates
(if there are s seats), and then elect those s candidates.

Finding out when a candidate has got enough voters to be elected is easy
enough: you just check if it's got a Droop quota or more of first
preferences. If so, exactly a Droop quota of votes can be considered to
have elected that candidate, and those votes are removed. This works
because if there are s seats, you can have no more than s Droop quotas'
worth of ballots in total.

However, when every candidate has fewer than a Droop quota's worth of
first preference votes, the above doesn't work. The easiest way to make
it work is to eliminate someone, because then the remaining votes will
be distributed over fewer candidates. But how?

STV chooses to resolve the problem by eliminating the candidate with
fewest first preference votes. It's the most natural way of doing it,
because then the criterion for who is going to be eliminated is based on
the same score (the plurality count) as the criterion for who is going
to be elected. For that reason, it's also relatively easy to manually
implement by shifting bundles of ballots around.

So if I were to guess, IRV is the way it is because it's a
specialization of a more general method (STV). And STV is the way it is
because it's based on quotas for election.

> Wouldn't it make sense to simply just leave everyone in each round and
> continue to run the tally until someone has a majortity? If more than
> one candidate, if the thing drug out, got a majority, one could use the
> one that was the "most popular" (had the greatest total) at that point.
> If there was a tie after at least two candidates had a majority, one
> could use "drawing lots".

That's more like Bucklin, which goes:

First round: count every voter's first preferences. If any of the
candidates has a majority, elect him.
Second round: count every voter's first and second preferences. If any
of the candidates has a majority, elect him.

.. and so on.

You could imagine this as holding multiple rounds where the voters
become less choosy as time goes on, and the moment someone gets a
majority, he wins.

> I'm sure there is something I'm missing here but the eliminating of a
> candidate that might be basically relatively popular and a good
> compromise candidate seemed to be a problem to me. Apologies if this one
> is totally stupid. I've searched on-line without success at finding the
> answer. One expert wrote back that it would cause problems but didn't
> specify what the problems would be. Any help clarifying this for me will
> be appreciated.

Only taking first preferences into account makes IRV rather resilient to
strategic voting. But resistance to strategy isn't the only important
factor: performance under relative honesty is also important, and IRV
leaves something to be desired in that department.