[EM] serious strategy problem in Condorcet, but not in IRV?

[James Green-Armytage]

Dear election methods fans,

There is a fellow named Burt Monroe who has a theory that he calls "turkey
raising." I have read a sort of paper of his on the subject, called
"Raising Turkeys: An Extension and Devastating Application of
Myerson-Weber Voting Equilibrium." Looking back into the archives, I found
that Kevin brought the paper up in March, but nobody commented on it. I
don't know if it is on the web, but if anyone wants it, I can send it as
an attached pdf file.

I think that the paper overstates its case, and focuses mostly on voting
systems that nobody really pays attention to now, such as Borda, Nanson,
etc. However, I think that the central idea is worth taking quite
seriously.

The idea seems to be that methods that are sensitive to lower preferences
produce strategy incentives which can result in the likely election of a
candidate who has no sincere support at all, that is, who is ranked dead
last in every voter's sincere preferences.

Monroe says that a method which has this effect fails a criteria he has
made up, called NIA, or nonelection of irrelevant alternatives. According
to him, Condorcet methods fail this criteria, as does Borda, Coombs, and
some others, but it is passed by IRV / the alternative vote, approval
voting, plurality, and runoff. He looks at a bunch of different Condorcet
versions, none of which are beatpath or ranked pairs, but one of which is
Simpson, which to my knowledge is the same as minimax aka sequential
dropping aka successive reversal, and which is equivalent to beatpath and
ranked pairs in most simple cases.

My main concern at this point is with Condorcet and IRV. I have taken the
common wisdom that Condorcet is more resistant to strategy manipulation
than IRV, but this idea challenges that notion. I guess that my goal here
is to reaffirm it, or to accept that IRV is more strategy proof. I am
asking for all of your help in finding out which it is.

Without further ado, let me try to get into an example. This illustrates
my interpretation of the implications of the Monroe paper, which is not
necessarily the same as his intention, but which should be close enough
for starters.

Sincere preferences
46: A>B
44: B>A
5: C>A
5: C>B

It is extremely clear here that C seriously does not deserve to win, as he
is ranked last by 90% of the voters. Also, it is clear that A deserves to
win, albeit by a narrow margin.
Now, if the method is Condorcet (minimax, Schwartz / minimax, ranked
pairs, or beatpath), and if everyone voted sincerely, A would win.
However, if the 44 B>A voters strategically vote B>C (offensive order
reversal), a cycle is formed, in which the defeat of B is now the defeat
of least magnitude, and so B wins.

46: A>B
44: B>C
5: C>A
5: C>B

A:B = 51:49
A:C = 46:54
B:C = 90:10

This is already very unfair, and a clear subversion of the democratic
process.
What can the offended A>B voters do about this? Assuming that the other
preferences are constant they have no way of electing A. Their only
option, other than allowing B to steal the victory, is to truncate or
order-reverse themselves, leading to the election of C. For example,

46: A
44: B>C
5: C>A
5: C>B

A:B = 51:49
A:C = 46:54
B:C = 44:10

The B-->C defeat is the defeat of least magnitude, and so C wins.
The only hope of A voters is that their truncation will deter the B voters
from their order reversal.
Thus the A and B voters have entered a game of chicken. A voters swerving
is their voting sincerely and allowing B to win. B voters swerving is
their voting sincerely and allowing A to win. The car crash is the
election of C. 
The outcome is unpredictable. It is quite possible that C will be elected,
despite the fact that he so clearly does not deserve to win. This is not a
pleasant scenario at all from the point of view of democracy, utility,
majority rule, public trust in government, etc.


However, let's say that you have the same sincere preference rankings
while using an IRV system.

46: A>B
44: B>A
5: C>A
5: C>B

In this case, there is nothing that the B voters can do to get B elected,
as long as the other votes are constant. If they vote B>C, it doesn't
matter, as C is eliminated first anyway. So, it looks as though IRV is
more strategy resistant in these sorts of situations than Condorcet is,
unless...

The only way I can see IRV producing a similar result in this situation is
if a lot of B voters initiate the chicken game by taking a loss
themselves, by voting a combination of C>B and B>C instead of B>A.  For
example, 

46: A>B
26: B>C
5: C>A
23: C>B

Now, the winner is C. The A voters cannot do anything to elect A if the
other voters' rankings remain unchanged, so they have to choose between B
and C. As they do prefer B, they may be moved to switch around their own
preferences so that he is elected instead of C. For example,

35: A>B
11: B>A
26: B>C
5: C>A
23: C>B

B wins. If the A voters are cowed into going along with this, then indeed
the B voters' strange strategy will have paid off in spades.
I believe that this sort of possibility did not occur to Monroe, and I
think that it does contradict his point that IRV can *never* produce
voting games that lead to the election of "irrelevant alternatives."

However, I have to admit that the strategy incentive in the IRV scenario
seems significantly less direct, and less obvious. The B voters have to
start by taking a loss, whereas in the Condorcet scenario, the B voters
can snatch the election away from A without losing anything. This is a
serious point to consider.

The likelihood of the different strategies may depend on what sort of
election scenario the system is being applied to. 

One possibility is a series of polls leading up to an actual election,
such as a presidential election. (That is, voters can lie about their
sincere preferences in the polls and thus try to manipulate the rankings
of other voters.) If this is the situation, then I believe that the IRV
strategy and the Condorcet strategy would both work, and both result in a
game of chicken, although admittedly the IRV strategy requires more
imaginative and violent manipulation. 

Another possibility is that the voters are going into the election
completely blind to the relative support of the three candidates. I am not
quite sure what would happen in this case, although I would tend to
imagine that voters would vote sincerely. For example, a B voter, not
knowing whether a B>C vote would help elect B over A in a cycle, or just
straight-up elect C, should in theory just tend to vote sincerely. Monroe
might disagree with me here, however. Probably, it depends somewhat on the
relative marginal utility, that is their marginal gain of electing B
instead of A, versus their marginal gain of electing A instead of C. If
their perceived marginal utility of B over A is much greater than that of
A over C, they might be more willing to risk an insincere vote for B>C>A.

There are quite a few different possible scenarios between these two
extremes of totally expressive polls and total blindness before the
election. Maybe voters know that C has very little first place support,
and that A and B are very close.

There is a question of whether strategic conspiracies are allowed to take
place. Is it considered politically acceptable for a party to call up all
of its supporters and ask them to vote insincerely? Also, can they do so
without non-party members finding out about it? Are members of one party
able to send messages to the members of the other party, in order to play
mind games with them and influence their votes?

Unfortunately, I think that these questions will have to be dealt with if
Condorcet is to be applied to the level of public elections.


So, that is my concern. Perhaps Monroe's paper is one of the best
arguments I've heard against Condorcet and against IRV. Hence, it is a
crucial point for any IRV-Condorcet debate. I have very little doubt that
Condorcet produces more fair results than IRV when the votes are sincere,
but is it possible that Condorcet has more serious strategy problems than
IRV?
How can Condorcet advocates respond?

First, I would like to know if anyone has a way to blow Monroe's argument
out of the water, beyond my own relatively lukewarm counter.
Second, I would like to know the logic behind the common wisdom that
Condorcet is more strategy resistant than IRV.
Third, I would like to see the worst (and most likely to occur) strategy
flaws of the IRV system. I would like to see if they can truly be said to
be as serious, and as likely to occur as the Condorcet strategy flaws
given here. I am aware of some of them perhaps, but it would be nice to
try and condense the examples in one place.

I hope that we can make some progress in the strategy debate, which is the
real meat of the IRV-Condorcet issue.


Sincerely (no pun intended),
James





P.S. By the way, here is another example similar to the one I used in this
posting, where C is a less wretched loser, but where manipulation is
easier:

Sincere preferences
30: A>B
25: B>A
23: C>A
22: C>B