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

[Jobst Heitzig]

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. 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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