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

[James Green-Armytage]

Hi, this is James G-A replying to Juho... 
>
>My assumption was that the fact that there are four parties of about 
>equal size was known. Since I at some point said that these pirates 
>would be from different countries, maybe also the exact number of 
>people in each party is known. In most elections that is not known. The 
>fact that there is a cycle and the direction and strength of it and the 
>fact that one party is not part of the cycle may or may not be known 
>(or guessed) in advance.

	I'm not talking about knowing it in advance, I'm talking about knowing it
after the votes have been cast.
	Let me clarify, for you seem to have missed my major point. I assume that
the pirates have already taken a ranked vote, the result of the vote (the
exact numbers that you printed initially (101 A>B>X>C, etc....) are made
known to all of them, and then a winner is chosen based on our choice of
Condorcet completion method. (This is obviously the most realistic
scenario, when you replace "pirate captains" with presidents, etc.) Then,
with the pirates knowing how many votes of each kind there were, and
knowing how the winner was arrived at by the voting method, the question
is how likely is a mutiny under a) minimax(margins) b) a Smith-efficient
method.
	Let's say that a Smith method chose A in this example. You argued that A
would be mutiny-prone because there is a large-margin defeat against him.
My counter argument is that the pirates can read the election result
carefully, and see that yes indeed, a C>A mutiny could succeed, but that
it would lead naturally to a B>C mutiny, and possibly later an A>B mutiny,
and so on. Hence, the C>A pirates would realize the futility/risk of their
potential mutiny, and probably they would not do it. Especially the
C>A>X>B voters, who would be especially wary of the second B>C mutiny. 
	This is what you didn't take into account when you formulated your "risk
of mutiny" principle, and this oversight is really a fatal to your theory.
You assume that voters will look exactly one mutiny ahead, but there is no
basis for this assumption. The knowledge of where further mutinies might
go should tend to stop an mutiny within the Smith set.
	However, it will not necessarily prevent a mutiny against a non-Smith
candidate, in favor of a Smith candidate, as in my RSTZ example.

>I think it is a mathematical fact that if mutiny resistance is accepted 
>by a country as the target of the election, one must elect the 
>Condorcet loser in some cases. 

	You can only say that if you totally ignore my argument.

>And MinMax (margins) is the correct 
>voting method if votes are sincere. 

	Why?
>
>Here our thinking differs. I'm thinking about the probability of the 
>first mutiny

	That's just what I'm saying! I'm saying that the first mutiny won't occur
if those who would potentially engage in it realize that it leads them
into a potentially endless cycle of mutinies, with no guarantee of a more
preferable result, and a real chance of a less preferable result. Your
failure to take this into account is frustrating.

>For Z 
>the probability of first mutiny is still the smallest. 

	Only based on your arbitrary use of defeat margin as the sole determinant
of mutiny probability. As I understand it, mutiny against Z far, far more
likely than mutiny against R, S, or T. 100 voters favor R/S/T. 71 voters
favor Z. The 100 R/S/T voters realize that they outnumber the Z voters
100-71. They realize that no matter which of the R/S/T candidates ends up
ahead, the result will be preferable to Z. I suggest that they will feel
that the method has not satisfied majority rule, and I suggest that they
will be entirely correct in feeling this. Thus, they will feel justified
in taking matters into their own hands. Since they know that they have
common cause in a mutiny, they will probably pause to decide which
candidate they would like to replace Z with. Once they figure this out,
they can happily mutiny. Z will go down, their new captain will go up, and
there will be no further mutinies.
	If R, S, or T is the initial winner, potential mutineers will be soundly
discouraged by the possibility of further mutinies, as discussed.

>This is a good argument in the pirate world if there are sequential 
>mutinies, but as I said, I'm mostly focusing on avoiding mutinies 
>altogether (and consider it a problem of the election if there is even 
>one).

	Yes, of course, that's what we're both interested in. This provides
further proof that you didn't understand my argument.
>
>Yes you did to some extent. I however still hide behind the argument 
>that the risk of first mutiny is the parameter that some election 
>organizers may want to minimize.

	"
>
>Another threatening argument in your example could be the fact that R, 
>S and T supporters could be seen as one big party. If that was the 
>case, then they would beat Z clearly 100 against 71. What would my 
>argument be against this. I think the best explanation in that case is 
>that people inside the RST party are not able to agree internally which 
>candidate is best and therefore electing Z from the other party might 
>be appropriate. 

	Voting methods should minimize the need for outside coordination.
...
	Sorry to be so harsh. It's just that I spent a lot of time and effort on
that e-mail to you, and the fact that you didn't seem to follow the main
argument is frustrating to me.

my best,
James
>