[EM] majority rule, mutinous pirates, and voter strategy

[James Green-Armytage]

Hi Juho,
	Very interesting post; glad you to decided to write. My preliminary
thoughts on three topics...

1. The Smith set.
	My attachment to the Smith set stems in part from a desire to satisfy
majority rule to the maximum possible extent. If you are willing to agree
that majority rule should be upheld, then it doesn't matter whether the
majority is small (e.g. a margin of only a few votes) or large (e.g. a 2:1
ratio). If you agree that majority rule should be upheld, you can only
reasonably ignore a majority preference if it is contradicted by another
majority preference. In your ABCX example, there is in each case a clear
majority who prefer A>X, B>X, and C>X. It is true that these majorities
are narrow, but the important thing is that they are not contradicted by
other majorities. Keep in mind that if X ran in an election with any of
the other candidates, X would lose. 
	This is the nature of the beast, i.e. the democracy beast: majority rule
is obviously imperfect, but once you have accepted the need to vote, it
seems necessary to accept the will of the majority, so long as majority
can be distinguished from minority. Among candidates A, B, and C, this
distinction cannot be made. However, it can be made between any of these
candidates and candidate X. Hence, I think that selecting X would violate
majority rule.

2. Pirates
	I like your pirate example. :-) 

3. Strategy
>In the election methods mailing list I have in the recent months observed
>lots of discussion on criteria that are related to making the voting
>methods as strategy free as possible. Sometimes I have even gotten the
>impression that when electing the winner from the candidates in the top
>loop (Smith set) it could be anyone in the top loop, as long as the
>numerous strategy criteria are fulfilled. I guess this has not really
>been the case, but my point is that one should give high priority to
>selecting the candidate that we think is best, and maybe a bit less
>priority to all the strategical considerations. 
	I am perhaps more actively interested in voter strategy than most voting
theorists. I consider strategy resistance to be a very high priority for a
method that will be used in contentious elections, although I don't rely
heavily on criteria in my strategic analyses.
	Again, I am assuming that the first priority is majority rule, which
dictates that we should select a member of the top cycle. So, I think that
it is extremely important to have a methods that not only identify Smith
members when voting is sincere, but also prevent sincere Smith members
from being obscured by strategic incursion. This is the first priority.
	However, that said, I am interested in the question of how to determine
which of the Smith set members is the "best". I'm hoping that you might be
interested in my "cardinal pairwise" method, which attempts to get a rough
measure of the relative priority of different defeats to the voters. Given
a sincere majority rule cycle, I suggest that this gives us a more
meaningful way to determine the "best" candidate. However, the method
requires cardinal ballots (e.g. 0-100) and the tally rule takes a bit of
explaining, which is why I don't consider it to be a likely "first wave"
Condorcet method. Anyway, here is a link to my write-up (and to my web
site in general).
http://fc.antioch.edu/~james_green-armytage/cwp13.pdf
http://fc.antioch.edu/~james_green-armytage/voting.htm

>This is based on the assumption that strategical voting is not that easy
>in real life, at least not in elections where the number of voters is
>large. Many of the strategical voting cases are problematic only in
>situations where the voting behaviour of the voters is known. In real
>life this is seldom the case. 
	I am skeptical of the statements above. First, the prevalence of
strategic voting depends on how broadly you define strategy. Many would
define it to include voting for a Democrat or Republican when you actually
prefer a third party candidate. This kind of strategy is obviously quite
common, and it has a significant impact on the political landscape. I
follow Blake Cretney in referring to this generally as the "compromising
strategy", which I define as follows:
	"Insincerely ranking an option higher in order to decrease the
probability that a less preferred option will win. For example, if my
sincere preferences are R>S>T, a compromising strategy would be to vote
S>R>T or R=S>T, raising S’s ranking in order to decrease T’s chances of
winning. (The drawback is that this often decreases R’s chances of winning
as well.)"
	The nice thing about Condorcet-efficient methods is that they tend to
minimize the need/incentive for compromising strategies. The tradeoff is
that we have to consider the possibility of "burying" strategies, which I
define as follows:
	"Insincerely ranking an option lower in order to increase the probability
that a more-preferred option will win. For example, if my sincere
preferences are R>S>T, a burying strategy would be to vote R>T>S or R>S=T,
lowering S’s ranking in order to increase R’s chances of winning. (The
drawback is that this often increases T’s chances of winning as well.)"
	There is no incentive for the burying strategy in plurality, two-round
runoff, or IRV. The incentive does exist, however, in Condorcet methods,
as well as in Bucklin and Borda. This makes it somewhat more of a
theoretical entity (difficult to study empirically), because there is much
less real public election data for these methods. (Although I can tell you
that the college where I went as an undergraduate uses Borda, and I talked
to several people who admitted (often with some embarrassment) to using
the burying strategy, although of course they didn't use that terminology)
Since we lack empirical data, I think it is premature to conclude that
burying will not be a problem if Condorcet methods do rise to use in
highly contentious elections. Of course I hope that it will not be, but I
prefer to err on the side of caution. This means keeping an eye on the
problem, and identifying methods that keep the possibility for a
successful burying within acceptable bounds. If regular winning votes
methods are found to not be sufficiently strategy resistant, then I would
advocate an additional anti-strategy measure.

>(And cycles are also rare.)
	Sincere cycles may be rare (there is debate over this point, but I tend
to agree, at least when there is not a huge number of candidates), but the
frequency of strategically created cycles may depend on the method in use,
i.e. whether it gives incentives to create false cycles.

all my best,
James