[EM] [CES #4445] Re: Looking at Condorcet

[Juho Laatu]

On 4.2.2012, at 19.14, robert bristow-johnson wrote:

> so, i have a few questions for everyone here:
> 
>    1.  do we all agree that every voter's franchise is precisely equal?
>    2.  if each voter's franchise is equal, should we expect any voter
>        that has an opinion regarding the candidates/choices to
>        voluntarily dilute the weight or effectiveness of their vote,
>        even if their preference is weak?
>    3.  so, based on the answers to 1 and 2, if there is an election or
>        choice between only two alternatives (yes/no) or two candidates,
>        that this election be decided any differently than, as we
>        were told in elementary school, the "simple majority" with
>        "one person, one vote"?

My generic answer is that there is no single answer to how single-winner decisions should be made. Different elections may have different targets.

In some elections / decision making processes people may voluntary dilute their vote. This approach typically means that the election is non-competitive.

The properties of the environment, like competitiveness set some limits to what election methods can be used. Another criterion to what election method to use is how well each election method implements the targets of the election. The choice of the election method and collected information in the ballots thus depend on the targets and the environment. (Strategies could be seen to depend on the properties of the envionment and on how well a method can implement the targets in this environment.)

I'll expand the pizza example a bit to demonstrate that there is a rich set of possible targets and ballot information. When a group of friends decides on which pizza to take or where to eat they quite often (unconciously) use a model where the range of opinions is not from 0 to max, but from minus infility to plus infinity. The scale has some fixed points that are linked to natual language. Such points can be "excellent", "not my favourite" and "pretty much unacceptable". Vote -inf means "impossible". Vote +inf means "the only possible alternative". With these values the outcome of the election / decision making process may be undecided (if two alternatives get +inf, or if some alternative gets both -inf and +inf, or if all alternatives get -inf).

My answer thus is that in all three questions there can be different options. If someone asks me what single-winner method should be used, I'll probably ask what the targets and the environment are. A good definition of the targets should be detailed enough to allow also e.g. understanding what relevant information one expects the voters to have and express. The targets should also tell what alternative would be a good choice. With information like this it should be (in principle) a quite mechanical process to check all relevant available methods against the targets and environment description, and then pick the best method (and ballot format) (and guidance to the voters on how to vote).

Juho