[EM] Another IRV failure

[Ken Taylor]

I was thinking about this problem today, in a discussion with some people
from the [instantrunoff] mailing list (an off-list discussion, because they
have extremely tight moderation over there).

Basically, what happens if you run the IRV until you have 3 candidates left,
two of which are tied for last place? If you eliminate both, you're
basically selecting the winner without looking at any next-choice votes,
eliminating any benefit that IRV may have, and also picking a winner without
a "majority" to support him or her. But which one of the last-place
candidates you choose to eliminate could drastically affect the outcome of
the election depending on what their next-choice votes were.

For example, say there were 3 candidates left, A B and C.

A is currently winning with 36% of the vote.
B and C have 32% of the vote exactly.
For the C supporters, almost all of them list B as a next-choice.
But the B supporters are split approximately evenly between A and C as their
next-choice.

(mapping this example on to the real world is an exercise left for the
reader ;) )

In other words, the current tally looks like this:
36% - A
16% - B A
16% - B C
32% - C B

If C is eliminated, B wins the election. But if B is eliminated, A wins the
election. It seems that, from objectively looking at the votes, the majority
prefers B to A, and B should be the winner. But can we count on the person
who makes an arbitrary decision here to be objective?

Perhaps it's possible to create a tie-breaking mechanism for IRV which
allows it to produce an ideal democratic winner more often in these
situations. Maybe even by calculating the IDW and making sure you don't
eliminate them! (If this were applied to *every* elimination, however, and
not just ties, then you'd basically be doing Condorcet...)

The *interesting* thing here is that if you don't only look at exact ties,
but also near-ties (say within a certain percentage of eachother), then the
spoiler-effect-returns problem described at http://www.electionmethods.org/I
RVproblems.htm can be treated as a problem of a near-tie-for-last-place.

For example, assume that in the discussion above A and B are from the
"major" parties, and C is from a "minor" party that has views similar to B.
If some more people vote for C, the election could be something like:

35% - A
16% - B A
16% - B C
33% - C B

In which case A wins -- B and C lose. So people will have reason to vote the
major party B over their first-choice minor party C, keeping third parties
down just as our current system does.

*HOWEVER*, if there was a good system to resolve ties for last place which
took into account voter preferences, and the situation above was treated as
a "near-tie" between B and C, then the spoiler-effect-returns problem could
be solved, while keeping the general sense of IRV intact (for those people
who like IRV's general sense -- ie, requiring not only wide support but also
strong first-choice support, and also being analogous to a voting system
that already exists (runoff voting)).

This issue will require some more thought, though...

Ken


----- Original Message ----- 
From: "James Gilmour" <jgilmour at globalnet.co.uk>
To: "'Eric Gorr'" <eric at ericgorr.net>; <election-methods at electorama.com>
Sent: Tuesday, March 09, 2004 1:40 PM
Subject: RE: [EM] Another IRV failure


> Eric Gorr asked:
> > First, is there an official method for how to deal with the case
> > where two or more candidates are tied for least votes? My current
> > implementation throws them all out at the same time, but I have seen
> > another implementation (demochoice.org) which selects one at a time.
>
> In UK legislation for preferential vote elections tied candidates must be
excluded one at a time.
> The legislation says the returning officer shall determine by lot which
candidate to exclude and the
> candidate on whom the lot falls is the one to be excluded.
> James
>
> ----
> Election-methods mailing list - see http://electorama.com/em for list info