# [EM] Draft of CVD analysis about IRV vs. Condorcet Voting

Ken Taylor taylok2 at alum.rpi.edu
Sat Apr 3 08:44:02 PST 2004

```James Wrote, responding to me:
> >I may have worded my response to the article too strongly. However, your
> >example, reposted here:
> >46: A>B
> >44: B>C (instead of B>A)
> >5: C>A
> >5: C>B
>
> Please note that there is a second example at the end of that posting;
> one which is stronger in that it is harder to deal with.
30: A>B
25: B>A
23: C>A
22: C>BAs it stands, A wins:
A/B  53/47
B/C  55/45
A/C  55/45

If B insincerely ranks C over A, a cycle is produced, just as before:

A/B 53/47
B/C 55/45
C/A 70/30

If this cycles is broken with SSD, then B wins, just as before. I'm not sure
why this is harder to deal with than your first example, since different
cycle breaking methods lead to different results. Resloving it with IRV
would elect C -- basically giving the "insincere" B voters what they ask for
(in fact, B has no chance if IRV is used as the resolution method).

> Yes, but that's just it. No matter what the cycle breaking method is, it
> will under some circumstances reward those who have strategically created
> the cycle to begin with. Your argument is dependent on this point, and
> since you are wrong on this point, your argument is wrong.

My *main* argument was that you can never use strategic voting to change the
condorcet winner, as was implied by the original article; at best you can
create a cycle, and that the strategic incentives depend heavily on the
actual cycle resolution method used. Please explain to me how your assertion
that there is no perfect resolution method makes this wrong? I believe you
are misrepresenting my argument by giving my parenthetical statement more
strength than it was intended to have.

Furthermore, I contend that "under some circumstances reward[ing] those who
have strategically created the cycle to begin with" does not necessarily
mean there is a strategic incentive to create the cycle. Whether there's an
incentive depends heavily on what those circumstances are, how likely it is
to be in your favor without backfiring, and how well you can predict those

With SSD, for example, a very small change in the voting numbers could
result in the B/C defeat being broken instead of the A/B defeat, causing C
to win. I contend that this is *not* a result B would have wanted, given
that their true preference was A>C. If B voters truly would rather have A
lose at all costs, then I contend that their true preference is B > C > A,
as they voted.

And finally, as IRV is immune to this particular strategy (a claim made both
by you and by the author of the article I was responding to), using IRV as a
completion method would also be immune to this particular strategy. And so,
my argument against the contention that Condorcet falls prey to this
particular strategy is not ultimately wrong.

> The strategic incentives in Condorcet-completed-by-IRV are still very
> substantial. Basically the incentive is for people who favor a candiate
> who is the IRV winner but not the Condorcet winner to strategically alter
> their ballots so that no Condorcet winner emerges. Comparing this
> strategic liability to the strategic liability of SSD is apples and
> oranges: they are both serious, but in different ways.

I also contend that it is a much less serious strategic problem than that I
was arguing against. First off, Whether the IRV winner is going to be
preferable to the Condorcet winner is much harder to predict before the
election. In fact, IRV may even be *worse* for your candidate than
condorcet, as in the example above, and exactly how your strategic voting is
going to result depends, to quote electionmethods.org, "in a very quirky way
on the order in which candidates are eliminated."  I believe such
uncertainties all but dissolve any real-world strategic incentive to such a
method. The article I was originally responding to also makes this
strategy-too-hard-to-predict argument.

This stands in stark contrast to a method such as Bourda count, where
strategic order reversal is almost always going to come out in your favor
(as long as your opponent doesn't do it, too!). The original article's
wording seemed to imply that the flaw was just as serious in Condorcet as it
is in Bourda, and I believe I'm correct in stating that it's not.

Secondly, since the original article was comparing Condorcet vs IRV, it
seems odd to claim that selecting the IRV winner is a flaw in a condorcet
method. This of course only applies to the original article in question, and
not Condorcet in general.

Ken

```