Hi,
Although Jobst may not have intended this assumption, I will continue to
make the assumption that the B minority's preference intensity for the
compromise C over A is much greater than the A majority's preference
intensity for A over C. (I am NOT saying there is a way to measure or
compare sincere preference intensities or utilities suitable for input
into a good vote tallying algorithm.) Without an assumption like this,
we would have no reason to believe C is better than A for the society.
There would be little motivation to take up Jobst's challenge to find a
voting method that will elect C instead of A. In other words, I believe
we should confine ourselves to solving the Tyranny of the Nearly
Indifferent Majority but not try to solve the Tyranny of the
Passionate Majority.
In the real world, it is much easier to elect a compromise than Mr.
Lomax seems to be saying below, because in the real world the set of
alternatives is not fixed to {A,B,C} by nature (nor by Jobst). Most
procedures allow a very small minority to add an alternative to the set
being voted on. (Under Robert's Rules of Order, for instance, only two
people are required: one to propose alternative D and the other to
second the proposal.)
Suppose D is an alternative that is very similar to the compromise C,
except D includes something extra that at least 11 of the A faction
will like enough to prefer D over A. Assume the extra in D is not so
bad for the B faction that the B faction prefer A over D. Then at least
56 (45 + 11) have an incentive to add D to the set of alternatives.
The preferences in the 6 pairings of {A,B,C,D} would be as follows:
AC 55
AB 55
CB 55
DA 56+ (45 plus at least 11)
DB 55
C?D ?
The C versus D pairing is unspecified. If D entails some transfer from
the B faction to members of the A faction, then presumably all of the B
faction prefer C over D. We don't have enough information to say
whether more than 11 of the A faction will prefer D over C. However, we
do know that the DA majority will be the largest or second largest
majority, so A would not be expected to win given a good Condorcetian
method (such as MAM).
In some circumstances, the extra that amends C to D might be a vote
trade: a promise by some members of the B faction to vote later in a way
the 11 members of the A faction will need later. Assuming this
electorate will vote on many issues (or expect to have other important
dealings with each other) and that it will not be kept secret how each
person votes, the individuals will have an incentive to keep their
promises. In the case of a secret ballot, which undermines the
incentive to keep one's promises about voting, the extra would need to
be explicitly included in D to be credible.
The elections of greatest interest to me--and to most members of this
maillist, I believe--are the election of people to public offices.
Candidates and potential candidates are relatively free to advocate
whatever set of policies they believe will maximize their chances of
winning, especially if they've consistently advocated those policies or
similar ones. Given a competition-promoting majoritarian voting method
such as MAM, why would candidates who want to win advocate a collection
of policies A, when there exists a collection of policies D preferred by
a sizable majority of the voters? They would expect A to be a losing
position, since potential candidates can enter the race at positions like D.
--Steve
---
Abd ul-Rahman Lomax wrote:
At 03:32 PM 8/22/2007, [EMAIL PROTECTED] wrote:
The problem is not well-posed, since the sincere ratings are not expressed
in units, which means it's unclear whether C has the most utility for
society.
However, assuming the intensity difference between the A faction's 100 and
80 is much less than the intensity difference between the B faction's 80
and 0, here's another way to elect C: The 45 can pay 6 of the A faction to
vote for C. (Not necessarily a payment of money.) We can expect members
of the A faction to be willing to sell their votes fairly cheaply since
they like C nearly as much as they like A, and we can expect members of
the B faction to be willing to pay that price, since they like C much more
than they like A and they can share the cost.
(From an economics standpoint, transfers of wealth are not inefficient,
all else being equal.)
That's correct. It is doable. It might also be illegal, here. But
there could be ways to do it legally, as mentioned, it would not
necessarily be a payment of money. But for these factions to trust
each other could be a problem. If C is elected, what is to keep the B
voters from simply not paying?
Nevertheless, that kind of proposal is similar to what I mentioned
about systems that would encourage voters to vote true utilities. In
this case, the B supporters shift the utilities of
