[EM] Re: majority rule, mutinous pirates, and voter strategy
stephane.rouillon at sympatico.ca
Thu May 26 21:43:53 PDT 2005
Pirates should, after some repetitive election,
see the wisdom of defining a mandate length before
knowing who wins...
Criterias and electoral methods hare not meant to
cope for a fractionated electorate. An electoral system
goal is to get the electorate will, whatever it is. Stability
is a further issue that should be dealt with separately,
either before by consensual agreement (over a mandate
length for example) or after with a winner's bonus when
comes time to take decisions in exchange for other
advantages to losers (as a reduction of the mandate length
for example: this is the "crutch option" proposed within SPPA).
James Green-Armytage a écrit :
> Hi Juho,
> My critique of your pro-minimax(margins) argument follows...
> >I tend to see margins as "natural" and winning votes as something that
> >deviates from the more natural margins but that might be used somewhere
> >to eliminate strategic voting. (not a very scientific description but I
> >don't have any better short explanation available :-) )
> No, that's more or less how I think of it. However, when you say that wv
> might be needed "somewhere" to reduce (not eliminate) strategic voting, I
> suggest that most public elections will fall within the region of
> "somewhere". (Please see my 3/14 post.)
> copying your pirate example for reference:
> 101: a>b>x>c
> 101: b>c>x>a
> 101: c>a>x>b
> 100: x
> >I meant that when X was the captain people wanted to change him to A, B
> >or C with a small margin of votes. But later when e.g. C became the
> >captain people wanted to change him to B with a large margin. Only a
> >minority wanted to change C to X.
> I'm with you this far.
> >But the point is that people
> >(majority of them) are now "less happy"
> ...you don't know how happy they are with any of these candidates...
> >or "more mutinous" because of
> >the problematic B>C relationship.
> Okay, let's get to the bottom of this.
> No matter who wins, 202 pirates would rather have some other candidate in
> particular. If X wins, this still holds, but 201 pirates strictly
> disagree. In the other cases, e.g. A wins, 202 pirates would rather have
> C, and only 101 pirates strictly disagree (the remaining 100 are
> Your logic is as follows: If X wins, and a group of 202 pirates who
> preferred another candidate rather than X wanted to mutiny, there would be
> 201 pirates ready to stand in their way, serving as an effective
> deterrent. However, if A wins, and the 202 C>A pirates (101: B>C>X>A, 101:
> C>A>X>B) mutiny in favor of C, there won't be sufficiently many pirates to
> fight to defend A.
> Here's what I'd like you to consider: Let's say that A is the initial
> winner, these 202 C>A pirates declare mutiny, and the 100 X pirates stay
> neutral. There may or may not be a scuffle, but anyway the 101 A>B>X>C
> pirates back down. Okay fine; C is the captain. But now the B>C pirates
> will be emboldened to mutiny against C. The process repeats, and B is the
> captain. Now it will be the A>B pirates' turn, and A will be captain once
> more. This idiotic process could go on indefinitely, so that the captain
> might shift several times in the duration of any given voyage, causing
> general irritation. Or, it could result in serious violence, and there is
> no guarantee that C will be on top when the dust settles.
> I suggest to you that this is a relatively intelligent bunch of pirates.
> (This is evidenced by the fact they are using Condorcet's method to make
> decisions.) If so, I suggest that the 202 C>A pirates will see the
> risk/futility of their mutiny ahead of time. (I'm assuming that all the
> pirates know each other's expressed ranked preferences, as would be the
> case in any real public election.) Sure, they could oust A in favor of C
> by force if the X voters sat on their hands. Maybe they could even kill
> candidate A, so as to finalize his defeat. But if they did that, a pro-B
> mutiny would be likely to follow, and perhaps this new coalition would
> murder candidate C, for good measure. Half of the C>A voters (101:
> B>C>X>A) would be all the more delighted with this second mutiny, but the
> other half (101: C>A>X>B) would rather have A than B, and they would mourn
> for C's death.
> So I ask you, would the B>C>X>A voters participate in the first mutiny
> against A? I suggest that they would not, because they would realize that
> a victory for C so reached would be unlikely to last. In short, you
> neglected to assign foresight to your imaginary pirates, and foresight
> would prevent a mutiny against a Smith set member. Would foresight prevent
> a mutiny against a non-Smith member, in favor of a Smith member? Not
> necessarily! Example:
> 35: R>S>T>Z
> 33: S>T>R>Z
> 32: T>R>S>Z
> 71: Z>R=S=T
> Pairwise comparisons:
> R>S 67-33
> S>T 68-32
> T>R 65-35
> R>Z 100-71
> S>Z 100-71
> T>Z 100-71
> Candidate Z is the minimax(margins) winner. However, he is in no wise the
> most mutiny-proof candidate. If Z is the initial winner, then all 100 of
> the R/S/T faction will have a common cause in ousting him. Perhaps if they
> change the winner to R, there could conceivably be further mutiny, but no
> matter what, such further mutiny will not lead to another result that the
> R/S/T pirates like less than Z. (Hence they can happily mutiny against Z
> without worrying that it will hurt them in the long run.) More likely,
> however, there will be no further mutiny. The R/S/T faction would do well
> to first choose whom they prefer among themselves (let's say that they
> settle on R), and to then march over to the Z faction and announce the
> change of leadership. The odds are running heavily in favor of the R/S/T
> faction if a fight breaks out.
> Again, once Captain R (as in "ARRR!") takes over, any potential mutiny
> coalition has to face the prospect of subsequent mutinies that cause a
> result that they like less than Captain R. So I argue that Captain R would
> suffer less risk of mutiny than Captain Z.
> I hope that I have disrupted your assumptions concerning the "risk of
> mutiny" concept.
> >I think all the majorities are unambiguous (because that is what the
> >voters told us). A>X could be called "loopless", if we want to describe
> >how it is different from the others. Both electing X and electing A
> >violate a majority opinion. One can avoid violating A>X by not electing
> >X (= select one of the Smith candidates). But one can also avoid
> >violating e.g. A>B by not electing B. All of the individual preferences
> >are thus avoidable. And all the Smith loop violations can be avoided by
> >electing X.
> If there is a majority rule cycle, then one cannot avoid ignoring at
> least one majority preference. However, one can always avoid ignoring a
> majority preference that is not contradicted by another majority
> preference (via a cycle).
> >> In your pirate example, there are no compromise
> >> candidates; the pirate electorate is very badly polarized.
> >I agree. The basic setting is four parties of about equal size. I think
> >this situation is quite normal.
> Four parties of equal size. Okay, that's not very common, but there's no
> particular reason why it couldn't happen. What I'm calling your attention
> to is not the relative size of the parties, but the intensity of the
> polarization between them. We have intense political polarization in
> countries that have voting systems that encourage polarization. In
> Condorcet systems, we should not assume that this polarization will
> remain; rather, it seems logical that compromise candidates will emerge,
> which they haven't done in your example.
> >I claim that
> >"mutiny" is one well defined criterion that is useful is some
> >situations and directly points out the correct voting method (MinMax
> >with margins).
> Please read and consider my recent post about strategic vulnerability in
> "margins" methods before you state so unequivocally that it is "the
> correct voting method". Actually, even then you might want to be careful
> about calling anything "the correct voting method" without some sort of
> >Mutiny of everyone against one is one candidate for another real life
> >criterion. I think mutiny to replace one with one is however the most
> >useful and typical case (both in the ship and in politics). This
> >"mutiny for anyone else" would also give support to sticking to the
> >Smith set when electing the winner.
> If your second criterion is to select the candidate who is not the first
> choice of the fewest voters, this is equivalent to selecting the candidate
> with the most first choice votes, a.k.a. plurality.
> >That is not allowed :-). We had an election with four candidates. And
> >elections are not supposed to cause countries to break into separate
> >smaller countries. The best single winner election method must be
> >capable of electing one (the best) of these candidates.
> Sure, but if all of the candidates are highly divisive (as they are in
> your example), you can't blame the method for choosing a divisive
> candidate. Based on the information available, A, B, and C are equally
> good choices, which is to say that they are equally bad choices. X is a
> slightly worse choice, because choosing X unnecessarily violates majority
> all my best,
> Election-methods mailing list - see http://electorama.com/em for list info
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