[EM] Three rounds

[Kristofer Munsterhjelm]

Raph Frank wrote:
> On Thu, Nov 13, 2008 at 2:39 PM, Kristofer Munsterhjelm
> <km-elmet at broadpark.no> wrote:
>> For honesty, then, we have to know which are the two best candidates. This
>> sounds like a proportional representation problem with a "council" of two;
>> however, such methods cannot be invulnerable to cloning, since the Droop
>> proportionality criterion and clone independence contradict each other (by
>> http://www.mcdougall.org.uk/VM/ISSUE3/P5.HTM , "clone-no-harm").
> 
> I disagree, a PR method is not what you want here.  If the best
> candidate is cloned, then both clones should be picked as the top-2.
> 
> This will not happen with PR.  In the linear policy case, the best
> candidate is at the 50% mark.  PR will likely elect candidates at the
> 33% and 67% marks.  Neither of those candidates is optimal.
> 
> In fact, I think that picking one of the 2 would be give roughly the
> same result as the plurality system.

I might have been too vague. What I meant was that it sounds like a 
proportional representation problem at first, but then (as I show 
afterwards), turns out not to be so, since we can't satisfy the DPC 
(which PR methods should have) and the various good single-winner 
criteria at the same time.

It might seem like a PR problem since one would intuitively think that 
the runoff candidates should in concert cover as much of the opinion 
space as possible.

>> Also, if we want to retain the properties of the first-round election
>> system, and that election system is Condorcet, then one of the candidates in
>> the runoff must be the CW (when it exists). I would go further and say that
>> there's no need for a runoff if there's a CW, but others may disagree.
> 
> In a condorcet election, the top 2 candidates would be at the 50% mark
> in the 1d policy space.
> 
> The runoff would held the voters decide from 2 pretty good candidates.

This does mean that a party can crowd out its competitors by running two 
candidates of the exact same position. On the other hand, that may be 
what you want, since one could reason that this brings a competition of 
quality to the center position, where the two best centrists would be 
picked for the runoff. That doesn't give the people much to discuss 
between the first and second rounds, though, since the candidates' 
position would be identical.

In any case, if that's what you want, then picking the candidates for a 
runoff should be easy. First round, use a method like Schulze to get a 
social ordering. Pick the first and second place candidates on that 
social ordering for the second round.

>> The former
>> destroys any chance of passing the DPC, since Droop proportionality is
>> incompatible with Condorcet (by example given in the Voting Matters article
>> linked to above).
> 
> I don't see why you want them picked by a PR method, the idea
> shouldn't be to pick 2 candidates who each represent half of the
> community, it should be to pick 2 that represent the whole community,

It's a reasonable first guess to imagine using a PR method, but it 
doesn't work. See above.

>> Call the candidate that's retained from the first round to pass criteria,
>> the retained candidate. Perhaps we could then say that if the retained
>> candidate is off-center in n-space, then the right thing would be to pick
>> the viable candidate closest to its antipode (reversed coordinates) as the
>> other candidate. But what's a viable candidate?
> 
> You could deweight the votes that voted for the first winner.  This
> would shift the winning point away from the centre.

That's what D'Hondt without lists does; or rather, it deweights those 
preferences that are lower than the winner of the first round, since the 
voters already "got what they wanted" on a higher preference. (Of 
course, I would use Sainte-Laguë instead of D'Hondt, but that's an 
implementation detail.)