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 �crit :
>
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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