[EM] Condorcet divisor method proportional representation

[Juho Laatu]

On 3.7.2011, at 20.34, Kristofer Munsterhjelm wrote:

> Kathy Dopp wrote:
>> On Sun, Jul 3, 2011 at 2:33 AM, Kristofer Munsterhjelm
>> <km_elmet at lavabit.com> wrote:
>>> Kathy Dopp wrote:
>>>> I do not like this system and believe it is improper to call it
>>>> "Condorcet". It seems to have all the same flaws as IRV - hiding the
>>>> lower choice votes of voters, except if the voter voted for some of
>>>> the less popular candidates.  Thus, I can see there may be lots of
>>>> cases when it eliminates the Condorcet winner.
>>> Do you mean that it fails to elect the Condorcet winner in some singlewinner
>>> elections, or in multiwinner ones? If it's the latter, then there's a
>>> perfectly good reason for that.
>>> 
>>> Let me pull an old example again:
>>> 
>>> 45: Left > Center > Right
>>> 45: Right > Center > Left
>>> 10: Center > Right > Left
>>> 
>>> If there's one seat, Center is the CW; but if you want to elect two, it
>>> seems most fair to elect Left and Right. If Center is elected, the wing
>>> corresponding to the other winning candidate will have greater power.
>> I disagree. In your example, clearly 55 prefer right to left, but only
>> 45 prefer left to right.  And center is the clear winner overall.
>> Thus, if only two will be elected, it should be center and right.
> 
> That's incompatible with the Droop proportionality criterion. The DPC says that if there are k seats, and a fraction greater than 1/(k+1) of the electorate all prefer a certain set of candidates to all others, then someone in that set should be elected.
> 
> (Actually, the more general sense is that if more than p/(k+1) of the electorate all prefer a set of q candidates to all others, then min(p, q) of these candidates should win.)
> 
> You could also consider a single-candidate variant of the majority criterion: If, in a single-winner case, more than 50% vote a certain candidate top, he should win. If, in a two-winner case, more than 33% vote a certain candidate top, he should win. If in an n-winner case, more than 1/(n+1) vote a certain candidate top, he should win. Such a criterion would mean that Left and Right have to be elected, because each is supported by more than 33%.

Here's one more example that I have used to point out the difference between proportionality oriented and majority oriented elections. Party A has 55% support and two candidates, party B has 45% support and only one candidate.

55: A1>A2>B
45: B>A1>A2

A1 is the clear Condorcet winner in single winner elections.

Any proportional multi winner election that elects two representatives would elect A1 and B.

If we elect two most popular candidates, then we elect A1 and A2.

If we allow voters to elect any pair of candidates (using a single winner Condorcet method), then the candidate sets are {A1, A2}, {A1, B} and {A2, B}. Out of these three alternatives {A1, A2} would be a Condorcet winner (since the 55 A party supporters have a majority and can therefore always decide).

As Kristofer Munsterhjelm points out, proportional methods may and should sometimes not elect the (single winner) Condorcet winner. The Condorcet criterion can be applied in groups (extended) so that the best group of n candidates is does not always contain all candidates of best group of size m, where m<n (in the single winner Condorcet case m=1). In more general terms my point is also that dIfferent elections may have different needs and targets and rules.

- We could also have single winner methods that do not always elect the Condorcet winner. We could for example have a method that would elect A1 with 55% probability and B with 45% probability, and that would this way provide "statistical proportionality in time".

- A Republican government in the U.S.A. could elect only republican candidates as ambassadors and judges, maybe in the Condorcet preference order. The voters could be Republicans only, or alternatively both Republicans and Democrats, but the point is that majority would rule in both cases, until next time when the majority could be the other party.

- Also if you elect employees from a group of candidates there is maybe no need to be proportional. Just pick the best ones.

((I also note that in principle Condorcet methods need not define a full preference order of the candidates. Picking one winner is all that single winner methods need to do.))

Juho