On May 9, 2008, at 20:27 , Jobst Heitzig wrote:
Dear Juho,
you wrote:
Yes, but as I see it the reasons are different. In a typical non-
deterministic method like random ballot I think it is the intention
to give all candidates with some support also some probability of
becoming elected.
Not at all! At least in those non-deterministic methods which I design
the goal is to make it probable that the voters implement a strategic
equilibrium in which a compromise option (instead of the favourite
of a
mere majority) will be elected with (near) certainty.
Ok, there are also such methods (more complex than basic random
ballot). I interpreted the "stronger than majoritarianism" search of
a compromise candidate to be an additional requirement that
determines one subclass of (deterministic and nondeterministic)
election methods.
Juho
But for such an
equilibrium to exist in the first place, the method cannot be
majoritarian, since then the majority would have no incentive at
all to
cooperate. Instead, all voters must have some power, not only those
belonging to the majority, and therefore each voter is given control
over an equal amount of winning probability. Still, the goal is not
that they assign this amount to their favourite option but that they
"trade" it in some controlled way, in order to elect a compromise
which
makes all the cooperating voters better off than without the trading!
Since at the same time, voting shall be secret, the trading cannot be
expected to be performed by open negotiations between the voters, but
it must be facilitated by some mechanism which trades winning
probabilities automatically depending on the preference information on
the voters' ballots.
If then in certain situations it happens that not much trading
actually
takes place, so that the winning probabilities remain with the voters'
favourites, then this is only an indication that no sufficiently
attractive compromise options existed in that situation. But whenever
such an option does exist, the goal of non-deterministic methods like
DFC, D2MAC, and AMP is that voters recognize that they are better off
with the compromise than with the benchmark Random Ballot solution,
and
that they can bring about the election of the compromise by safely
indicating their willingness to trade their share of the winning
probability, without running the risk of being cheated by the other
faction(s).
D2MAC is quite good at this if only the compromise option is
sufficiently attractive, but not in a situation which is as narrow as
the one I gave at the beginning of this thread. AMP is better there,
but it is not monotonic unfortunately.
Yours, Jobst
In the deterministic methods electing some non-
popular extremist is typically an unwanted feature and a result of
the method somehow failing to elect the best winner.
*No* election or decision method should be applied without first
checking the feasibility of options with respect to certain basic
requirements. This sorting out the "constitutional" options cannot
be subject to a group decision process itself since often the
"unconstitutional" options have broad support (Hitler is only the
most extreme example for this).
In other words, without such a feasibility check *before* deciding,
also majoritarian methods can produce a very bad outcome (think of
Rwanda...).
Ok, this looks like an intermediate method where one first has one
method (phase 1) that selects a set of acceptable candidates and then
uses some other method (phase 2) (maybe non-deterministic) to elect
the winner from that set.
There is need for pure non-deterministic methods like random ballot,
and pure deterministic methods, and also combinations of different
methods may be useful.
Also in the case where the no-good candidates are first eliminated I
see the same two different philosophies on how the remaining
candidates are handled. Either all remaining candidates (with some
support) are given some probability or alternatively one always tries
to elect the best winner. The intention was thus not to say non-
deterministic methods would not work properly but that there are two
philosophies that are quite different and that may be used in
different elections depending on the nature of the election.
Due to this difference I'm interested in finding both deterministic
and non-deterministic solutions for the challenge.
Juho
Yours, Jobst
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