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

[James Green-Armytage]

Hi Juho,

	About your "least additional votes" method: Correct me if I'm wrong, but
I think that your method is equivalent to minimax (margins). Adding an
additional "vote" will decrease the margin of each of a candidates defeats
by one. So, the candidate whose widest-margin defeat is less wide than the
widest-margin defeat of all other candidates will be the one who requires
the fewest votes to be "filled up" by this process.
	By the way, I just wrote an in-depth post about the strategic instability
of margins methods
http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015125.html

>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.

	Just clarifying... When you say a larger majority, you seem to mean a
majority with a wider margin. But I would prefer to define the *size of a
majority* by the number of voters who prefer R to S (when more prefer R to
S than S to R). Hence size of the A>X majority is 202. 202 people are
pleased with the change, and 201 people are displeased. If we change the
winner from A to C, 202 people are pleased with the change, 101 people are
displeased, and 100 are indifferent.
>
>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"). 

	A large majority who is unhappy with the change? I would say that there
is a large *minority* (201 voters) that is unhappy with the change. As to
how many voters are unhappy with candidate A in general, it's hard to say,
because we only have ordinal information here, nothing about utility,
strength of preference, 'approval', etc. 
	Perhaps voters only like their first choice, and disapprove of all the
rest, perhaps because of national differences (pirates from 4 separate
countries). This means that a majority coalition will be hard to form.
Perhaps no matter who is the captain, at least 302 pirates will be
significantly unhappy. Perhaps it is just not practical for these pirates
to share a boat!

>If one wants to violate majority opinions as little as possible, one
>could consider keeping X (against the smallest majority opinion).

	Again, it might be more clear to say the 'narrowest' majority rather than
the 'smallest'.
>
>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). 

	Violating an unambiguous majority preference (e.g. A>X) is a *larger*
problem than violating a majority preference that is contradicted by
another majority preference (e.g. A>C), because the former is always
avoidable, and the latter is unavoidable in the case of a majority rule
cycle. 

>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. 

	It can only elect a compromise candidate if there is a compromise
candidate in the running. In your pirate example, there are no compromise
candidates; the pirate electorate is very badly polarized.

>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").

	= the candidate with the most narrow defeats. Okay, so if a potential
mutiny started to form around ONE particular candidate (let's say
candidate A), then it would be the closest possible fight of this nature
(201 vs. 202). But what if multiple dissatisfied groups arose at once?
Then the X supporters would be in desperate trouble (as would supporters
of any other candidate in a similar situation).
>
>I.e. just trying to prove that Smith set is not as obvious requirement as
>often thought.

	Actually, it's kind of a new thing for me to be emphasizing the Smith set
as much as I do now. It's been in my head for about six months, and I've
just begun to articulate it quite recently. I began to feel that there was
something logically inconsistent about insisting on the Condorcet winner,
but abandoning all strict majority rule requirements when no Condorcet
winner exists. It makes it seem as if the pairwise method loses its
meaning when there is no CW. I feel that insisting on the Smith set makes
for a less wishy-washy definition of majority rule, and a less wishy-washy
election system proposal. A Smith method has more logical unity than a
non-Smith Condorcet method; no matter what, it elects a Smith member,
whether the set has one member or more than one.
>
>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 :-).

	I would say none of the above candidates are a sufficient compromise
candidate. I would suggest that the pirates try a bit harder to find a
compromise captain (perhaps someone who has spent several years in each
country). Failing that, I would suggest that the four factions should go
their separate ways, finding boats that are manned by more like-minded
seafarers. 

my best,
James