[EM] Holy grail: a "condorcet compliant" cardinal method (MCA/Bucklin variant)

Jameson Quinn jameson.quinn at gmail.com
Sun Sep 5 10:10:56 PDT 2010

> 8) Others may disagree, but I think it has just the right amount of
> runoffs. Essentially (provably???), there would only be runoffs if there's
> no known honest CW; in which case, further deliberation by the voters is
> completely appropriate.

 Again I looked more deeply at an unproven claim I'd made; and again, RMCA
came out even better than I thought. Somebody pinch me; I had given up on
finding such a "perfect" system.

So, let's recap. In the first email, I claimed that "correct" strategy if
there's a known CW is to rank them alone (except for no-hopes) at their
ranking level. If there are candidates both above and below them, that would
put them in the middle rank.

This is not sufficient to guarantee one-round decisiveness. Say that more
people rank X>>CW than CW>>X + ((CW>X) / 2); then X would be RW and it would
go to a runoff.

In order for that to happen, there would have to be a number of weak CW>X
ballots. There are two kinds: CW>X>.... or ....>CW>X. If ballots of the
first kind (prefer CW and approve X) are necessary to make X a RW, those
voters - whose favorite is the CW - could easily bullet vote. By not
bullet-voting, they are saying "I am willing to consider these two
candidates again, in a runoff; because I know that if nobody changes their
mind, my candidate will win that runoff". It is entirely up to them; they
are essentially making an explicit, nonstrategic choice that a runoff could
be healthy.

The second kind of ballots are not quite so clear-cut. By voting ...>CW>X
instead of CW,...>>X, these voters are simply refusing to semi-betray their
favorite(s). However, that does say something about the strength of their
CW>X preferences, and it seems entirely reasonable to go to a runoff. If the
X>>CW voters really do care significantly more, they will turn out in higher
numbers and win; if not, and if nobody changes their mind, the CW will win.

So voter strategy if there's a known CW is:
1) Understand that a runoff will not change the ultimate result, unless
people change their minds or turnout patterns change significantly.
2) If, given that, you don't mind a runoff, vote the CW in a rank by
themselves. If the CW is your current favorite, approve only candidates
you'd like to have a second look at in a runoff.
3) If your preference for avoiding a runoff is stronger than your preference
against ranking the CW equal to your favorite, and the CW is not your least
favorite, then top-rank (prefer) the CW and approve nobody.
4) If the CW is your least favorite, then top-rank (prefer) the candidate
who you think would have the best chance of changing peoples minds (becoming
the honest CW) in a runoff, as well as everyone you like better; approve all
other candidates; and disapprove the CW.

That's pretty easy and intuitive. If people vote like this, unwanted runoffs
would be very rare.

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