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

[Juho Laatu]

Hello Stephane,

Yes. Electoral methods should aim at electing the candidate that is 
best for the planned period (based on the will of the electors as 
expressed in the ballots). Repetitive mutinies are thus something one 
need not normally prepare for.

If the community can agree what the "utility function" (that sets the 
criteria and determines which candidate is best) is, then the 
calculating the election results is quite straight forward (((although 
maybe computationally complex))). There is of course one important 
thing to take into account when agreeing the utility function (or 
electoral method). The electoral method should be sufficiently strategy 
resistant (= the reason why often only ranking based methods are 
considered, and why also between these there is lots of discussion 
about the smaller granularity strategy questions).

BR, Juho



On May 27, 2005, at 07:43, Stephane Rouillon wrote:

>  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).
>
>  Steph.
>
>  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
>  indifferent).
>          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:
>
>          Preferences:
>  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
>  qualification.
>  >
>  >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
>  rule.
>
>  all my best,
>  James
>  http://fc.antioch.edu/~james_green-armytage/voting.htm
>
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