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

[Juho Laatu]

Hello James,
 
Here is some feedback on point 1. I didn't find yet time to write a proper answer also to point 3 but I'm planning to comment also that.
 

1. Majority and Smith set

Yes, one should respect the majority opinion. My thinking however goes so that in some situations some majority opinion has to be violated.

In the ABCX example majority says that instead of X one should elect e.g. A. But if A is elected, then a larger majority says that one should elect C instead of A. And then C would be changed to B, and B to A, A to C etc.

One viewpoint to the Smith set problem is that although there is no majority that would change A (or B or C) back to X, there is a large majority that is unhappy with the situation after X has been changed to A (="from bad to worse"). If one wants to violate majority opinions as little as possible, one could consider keeping X (against the smallest majority opinion).

It is true that majority would change X to any other of the candidates. I'm having problems trying to explain why violating this type of majority opinion would be a smaller problem than violating a stronger majority opinion that would change the candidate in question only to one of the other candidates (e.g. A -> C). The mutiny example however offers one quite clear argument. If one wants the election method to produce a stable result, then electing X seems to be the correct thing to do. Condorcet is known to elect good compromise candidates. X is a compromise candidate in the same spirit => "least threat of mutiny". This "least threat of mutiny" could btw be seen as one possible ("real life") criterion that is actually so strict that it already defines the whole election method ("least threat of mutiny" = "least additional votes").

Summary: If one selects the viewpoint in an appropriate way it is possible to claim that electing X respects the majority opinion, maybe even in the best possible way.

I still violate your rule that says that one would need a majority decision loop leading back to X in order to elect X. I based my support to X only on the strength of majority opinions without considering if they form loops that include X or not. This logic corresponds to the mutiny example. The Smith set logic would maybe correspond to a real life example where the crowds would elect A and B and C in turn and never remember that also X exists (good candidate missed? or maybe just happy to leave this passive candidate in the corner? :-) ).

Btw, I think you referred to majority in the sense that "majority makes a change that no other majority will change back" while I used it more in the spirit of "majority not happy with proposed election outcome". I could claim that the majority electing one of the the Smith set candidates is just stupid since they are unable to loop back to the best option, while you could claim that majority rule would lead to the Smith set solution in any case after few rounds of fighting. Theorist vs. pragmatist?? :-)

I'm not sure if I have provided any additional viewpoints that would convince you of the merits of the non-Smith-set candidates. I hope at least some viewpoints that show that there may be some sensible threads of thought also on the other side of the fence. I.e. just trying to prove that Smith set is not as obvious requirement as often thought.

I think that there exists one natural set of real world criteria for an election method (best characterized as "least threat of mutiny"), and to this set of requirements an election method that violates the Smith set rule is the correct solution. There may be other useful single winner election methods too in principle (for other purposes than defending against mutiny) but this one looks pretty useful to me.

Based on this chain of thoughts my question to you is: what would be your favourite captain in the pirate example? Let's assume that the pirates have requested for a stable compromise captain (or a stable compromise producing voting method) because they have had lots of problems with mutinies recently. I'm just asking for a solution for one particular need. And if you say that X would be a good solution in this particular case, then you would say that there are reasonable needs for election methods that do not respect the Smith set. Remember that the life of the sailors is at your hands :-).
 
Best Regards,
Juho


James Green-Armytage <jarmyta at antioch-college.edu> wrote:

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



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