[EM] Reply to Tom Mull, re: IRV

[MIKE OSSIPOFF]

Tom--

Thanks for writing to the list. You came to the right place, and
just in time.

We discuss the relative merits of single-winner voting systems. As
an advocate of single-winner election reform, it's a good thing that
you take an interest in the discussion of voting system merit
differences. The leaders of the organizations that promote IRV regrettable 
don't seem interested in the merit differences between
IRV and other single-winner methods. That's why those organizations
are still promoting IRV.

You've heard their IRV promotional arguments. If you've been in
contact with CVD or other IRV promotion organizations, it's a safe
bet that they haven't told you about disadvantages of IRV with
respect to other voting systems. Now, by writing to this list,
you'll hear the other side of the IRV issue.

Where to start? With IRV, you can change a losing candidate to
a winning candidate by moving him lower in your ranking. Approval
will never do that.

In fact,
in IRV, you can do that by moving him from 1st place to last place--
something that won't happen with Approval or Condorcet, the favorite
methods here.

With IRV, by showing up and voting a ballot that ranks X over Y,
you can thereby change the winner from X to Y. If you'd stayed home,
X would have won. That will never happen with Approval.

The most popular methods on this list are Approval and Condorcet
(Condorcet has a number of versions).

I and many others value majority rule, and the standard of getting
rid of the notorious lesser-of-2-evils problem. We have some criteria
that measure for those popular standards, at:

http://www.electionmethods.org

and

http://www.barnsdle.demon.co.uk/vote/sing.html

Approval and Condorcet do well by at least some of those criteria.
IRV fails every one of them.

In the following example, the numbers on the left represent the numbers
of voters who vote the rankings that follow the numbers. So that
100: ABC means that 100 people vote the ranking ABC.

Here are a set of sincere rankings:

40: ABC
25: B (No 2nd choice, which, in IRV, is as if they're equally divided
       between A & B)
35: CBA

Notice that B would win a 2-candidate race against any one of the
other candidates. He's what is called the Condorcet winner.

So what happens in IRV if people vote sincerely? B is immediately
elimianted, even though 60% of the voters rank him over A, and
65% of the votes rank him over C.

That's a major violation of majority rule. To prevent it, the C
voters need to insincerely rank B in 1st place, above their favorite.
We call that "favorite-burial". It happens in Plurality, and it
will happen in IRV. That's the only way that the C voters can avoid
the election of their last choice, A.

On this list we've discussed Nash equlibrium with various voting
systems. A Nash equilbirium is a configuration of strategies used
by players, and the resulting outcome, such that no player can improve
his outcome, when he's the only player to do so.

When talking about elections, we consider as a player a set of voters
who share the same preferences and vote in the same way.

Some have objected that people don't vote in blocs, but the fact is
that, in any of our elections, there are indeed lots of people who
share the same preferences and vote in the same way in a particular
election. It's clear that there's something unstable about an
outcome that such a group of voters can improve on by voting differently, 
and that there's something more secure and stable about
an outcome in which that isn't so.

In IRV, there are situations (configurations of candidates, voters,
and voters' sincere rankings) in which the only Nash equilibria are
ones in which some voters defensively reverse a sincere preference
ordering, when making out their rankig.

In contrast, with Approval and Condorcet (when Condorcet is done
right), every situation has Nash equilibria in which no one
order-reverses.

The better Condorcet versions measure defeats by "winning-votes",
abbreviated "wv". That means that if X pairise-beats Y, the
strength of that defeat is defined as the number of voters who
ranked X over Y.

If defeats are measured in other ways, as by margin-of-defeat, then
, as with IRV, there will be situations in which the only Nash equilibria 
are ones in which some voters defensively order-reverse.

Likewise, when defeats in Condorcet are measured in ways other than
wv, Condorcet then fails every one of the defensive strategy criteria
listed at the 2 above-named websites.

Anyway, thanks again for writing to this list. I wanted, in this
message, to tell you of the disadvantages of IRV, and of the worse
versions of Condorcet

A number of Condorcet versions are defined and described at
http://www.barnsdle.demon.co.uk/vote/sing.html

My favorite for public elections is Ranked-Pairs, with defeats measured by 
wv.

I like RP for public elections because of its brief definition:

Ranked-Pairs:

In order of stronger defeats first, consider each defeat in turn as
follows: Keep it if it doesn't contradict already-kept defeats, by
forming a cycle with them--i.e. by being in a cycle consisting only
of it and some already-kept defeats.

When all defeats have been so considered, a candidate wins if he
has no kept defeats.

[end of definition]

In our most recent poll here about the best method, Approval won.

Approval:

Using the same ballot now used for 1-vote Plurality, each voter may
mark as many candidates as s/he wishes. The candidate with the most
marks wins.

Mike Ossipoff










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