Raph Frank wrote:
On Thu, Nov 13, 2008 at 2:39 PM, Kristofer Munsterhjelm
<[EMAIL PROTECTED]> 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.)
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