IRV vs Condorcet Voting Methods

[MIKE OSSIPOFF]

There's a website called "Cal IRV",
that repeats all the old IRV arguments. The website says that there's
a small group who advocate Condorcet. "A small group"? Of those on this
mailing list who express a preference among Condorcet & IRV, what
percentage prefer IRV? Maybe one or two who periodically post to
repeat the IRV line.

At our websites, we regularly hear from people who previously had
only heard from the IRVists, but who then noticed our website. Nearly
all of those say that, having heard both sides, Condorcet is better,
and IRV is inadequate.

Among those who have heard both sides, few prefer IRV to Condorcet.

What the Cal IRV website actually says is that there are a small
group of people who "ardently" argue for Condorcet. "Ardently"?
How should we measure ardentness? If we measure it by promotional
busy-ness, the IRV people are many times more ardent. Likewise if
we measure ardentness by willingness to advance their proposal by
dishonesty or the giving of money to an organization conducting a study.

Here's their IRV vs Condorcet section, with comments by me:


A small group of people ardently supports pairwise methods. To that end, it 
ardently opposes IRV. Here's what the debate boils down to. An ideal voting 
system would allow voters to express their honest preferences, without 
having their second choice hurt their first choice, or the other way around 
if their first choice is not going to win. It turns out that this is 
mathematically impossible, and a tradeoff must be made.

Imagine that you are at a car auction, and you can only make one bid. If you 
hold out at $3000, you may get the car, but there is some risk that you will 
be walking home. On the other hand, if you offer $6000, you can be certain 
that you'll be driving home. Voting always involves a similar bargaining 
process between yourself and all other voters. Much of the bargaining is 
built into the system, including the bid amounts. With plurality voting, 
it's as if you can only make one bid. With IRV, you hold out on your bid if 
it is competitive, but you get your compromise bid if your first one is not. 
With a pairwise method, it's as if you announce both bids at the same time, 
so you almost always get the compromise bid.

[Only if the compromise win is the best that you can get]

So the voting method you prefer depends on which built-in strategy you 
prefer.

The pairwise methods work like this: voters' ballot rankings are used to 
determine the outcome of all one-on-one races. The candidate who beats all 
other candidates is the winner. There are often circular ties (that is, A 
beats B, B beats C, and C beats A); these are broken by successively 
ignoring the weakest victory. There are several variations on this, so we 
refer to pairwise 'methods' in the plural.

Imagine this hypothetical election:


Votes 1st 2nd 3rd
48 Reagan Anderson Carter
47 Carter Anderson Reagan
4 Anderson Reagan Carter
1 Anderson Carter Reagan


Reagan would win if this were an IRV election, because Anderson voters' 
second choices would give Reagan a majority. Anderson would win if this were 
a pairwise election, because Anderson would beat both Reagan or Carter if 
separate one-on-one races were tallied.

The difference is that with IRV, Reagan and Carter voters are taking a risk 
on Anderson voters' second choices (to those voters' knowledge, those second 
choices could have easily gone the other way, handing the election to 
Carter). A pairwise method would force a compromise

[Condorcet doesn't force compromise. Any voter can refuse to vote a
2nd choice if s/he doesn't want to compromise. For instance, in 2004,
if it's Nader, Gore, Bush, I won't vote a 2nd choice. I'm not interested in 
compromising with Gore, and no voting system except
Borda could force me to compromise].

, even if that compromise had very weak first-choice support. With IRV, only 
Anderson voters have to compromise.

At the cost of some distortion of one's expressed preferences, both methods 
allow for alternative strategies. With IRV, voters who prefer another 
candidate can always rank Anderson first if they accept this compromise

[Yes, they can bury their favorite, just as they do now. Thanks a
lot, IRV].

; their vote would go to their favorite if Anderson is eliminated.

[But if they succeed in making Anderson win, they might be unnecessarily 
giving the election away, where their favorite could
have otherwise won. Approval, like IRV, requires defensive strategy,
but with Approval it takes twice as many mistaken compromisers to
give away an election].

Voters can still gamble in a pairwise election: if Reagan and Carter voters 
list only their first choice, they surrender their ability to compromise, 
and gamble on Anderson voters' second choices. However, such gambling is 
more dangerous than it is in IRV - if it turns out that their favorite 
candidate is weak, their votes are wasted and their last choice wins.

[But wait...The ones who don't vote a 2nd choice are the ones who
don't want to compromise, so how can Irving say that they're taking
a risk by rejecting the compromise that they don't want, in Condorcet?

In that example, with Condorcet, the only voters who could need strategy are 
the Anderson voters, if they felt that offensive order-reversal were going 
to be used against them. They could refuse to vote
a 2nd choice. But in that election they have no reason to vote a 2nd
choice anyway, since if one side has a 1st chioce majority it's a done
deal, and since otherwise one side needs Anderson more than Anderson's
voters need that side's candidate.]

So if you prefer an election method that compels voters to compromise, you 
should prefer pairwise methods.

[Again, Condorcet doesn't compel anyone to compromise. No one forces
you to vote a 2nd choice. But Condorcet will reliably count your
preference for 2nd choice over last choice if you choose to vote such
a preference. But, with IRV, if you want to protect the CW's win,
or protect majority rule, IRV forces you to compromise by burying
your favorite].

If you prefer a method that makes you compromise [by favorite-burial]
when your candidate is weak, and lets you gamble on others' second-choice 
votes when your candidate is strong, you should prefer IRV.

If you do prefer pairwise methods, it's important to note that IRV has a lot 
more political momentum because it is similar to existing methods

[IRV isn't similar to existing methods. IRV would be a completely
different voting system, with a completely different and costly
balloting system. In comparison, Approval uses existing ballots
and is nothing other than a minimal, but powerful, improvement on
the existing Plurality voting system].

, and that implementation of IRV would create opportunities for pairwise and 
other methods, should they ever gain popular support. So, as a compromise, 
it would make sense to show support for IRV!

[Just as Irving believes that Condorcet forces you to compromise, he
thinks you need to compromise on an absurdly inadequate voting system.
IRV won't facilitate Condorcet. It will merely get us stuck in IRV,
till such time as IRV discredits itself and its promoters. And,
at that time, how likely is it that people will be willing to listen
to, accept, and work for, another rank-count proposal?]



What about approval voting?

Approval voting is like plurality except that you vote for as many 
candidates as you support

[It isn't clear what Irving means by "support". Irving hasn't a clue
about who people would vote in Approval. The obvious strategy, and
most likely the popular one, will be to vote for whichever of the
perceived 2 frontrunners the voter prefers to the other, and for
everyone whom s/he likes better. More Approval strategies are
described at http://www.barnsdle.demon.co.uk/vote/sing
at the Approval Strategy page.]

, not just your favorite. It suffers from the same problem as the pairwise 
methods: if you vote for a compromise candidate, it works against your 
favorite.

[When you vote for Middle and Favorite, you aren't casting a vote
for Middle over Favorite. You merely aren't voting between them.
At least Approval reliably counts every pairwise preference that you
choose to vote. You're the one who decides which of your pairwise
preferences will be counted. With IRV, IRV decides which of your
preferences it will count. As I said, Approval requires twice as
many mistaken compromisers to give away an election, as compared to
IRV].



But IRV isn't even monotonic!

"Monotonicity" may sound intimidating, but it is not a big deal. The term 
actually has several definitions.
Pairwise voting methods are monotonic with respect to swapped pairs. This 
means that, on a ballot marked "Anderson,Reagan,Carter", if you swap Reagan 
and Carter so the ballot reads "Anderson,Carter,Reagan", the voting method 
ensures that Carter will not lose if he were already the winner, and Reagan 
will not win if he were a loser. IRV does not satisfy this, because this may 
cause Reagan to be eliminated, and the next choices of Reagan's voters could 
cause someone other than Carter to win.

IRV is monotonic with respect to added rankings. If you add a ranking to the 
end of the list on your ballot, or you add a ballot with a single ranking, 
it will always help that candidate win, and never hurt any higher-ranked 
candidates. Pairwise methods do not satisfy this, as demonstrated in a 
previous answer.


[With IRV, as with any rank method except Borda, adding to the
count a ballot that votes Smith over Jones can change the winner
from Smith to Jones:

35: ABC
33: BAC
32: CBA

But now 2 more voters arrive at the last minute, to vote CBA. They
finally decided to vote in order to do their part to keep their
last choice from winning. But by showing up to vote, they made
their last choice win. Approval will never do that.]

The fact that each of these voting methods satisfies one type of 
monotonicity and not the other is just another reflection of the tradeoff 
between compromising and gambling on a higher payoff that is inherent to all 
voting methods.

[The IRV promoters don't have a clue about what Monotonicity means]


Mike Ossipoff



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