[Election-Methods] method design challenge +new method AMP

[Juho]

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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>>
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