[EM] Truncation dilemma

[Kevin Venzke]

Hi Jameson,

--- En date de : Mer 23.6.10, Jameson Quinn <jameson.quinn at gmail.com> a écrit :
>3a. Quasi-elimination. I believe that winning-votes Condorcet methods, 
>like Schulze, are an attempt to ensure that A wins even in the face of 
>B's truncation. However, this only works if C voters truncate rather than 
>splitting evenly between CBA and CAB. Other stronger quasi-elimination 
>systems that I know of have IRV-like problems.

I would say that WV methods attempt to ensure that {A,B} wins even in
the face of B's truncation. Making A win despite truncation will often be
impossible without violating Plurality (e.g. with MMPO).

>4. Runoff. Viewed in an outcome-oriented game-theoretic vacuum, this is 
>just the same as elimination, and it suffers the same problems. However, 
>if voters have some negative utility for the runoff itself, then a system 
>can use the threat of one to motivate honest voting in the first round. 
>Since the scenario assumes that there is a clear winner with no cycles 
>under honest voting, that may be enough.

I see the use of leaving no purpose for insincerity in the second round.
For example supporters of candidate C may find it too risky to give a
second preference to one of the opposing clones, but once C has been
removed from consideration, there's no more disincentive.

It's not quite clear to me how to use a runoff to ensure sincerity in
the first round, in general.

I think I would just look at the outcomes for all important scenarios and
categorize that way: Say the candidates are C, A, B in descending order
of bloc size. C voters always truncate. A and B blocs give a second
preference to each other, or to no one.

Then you have:

A and B both truncate: Everything will elect C.
Neither A/B truncate: Almost everything will elect A. (Ignore FPP)
A truncates only: Some methods elect C, some A.
B truncates only: A B or C will win.

Without supposing anybody gets a second chance to express preferences,
there are only six possible methods, based on the last two scenarios.

CA: ?
CB: ?
CC: DSC, SPST, VFA
AA: WV, Bucklin, Approval, and many many other methods
AB: Raynaud(wv), MMPO with ties broken by FPP
AC: IRV, QR

So I guess that broadly there should only be up to four treatments or so.

Other than runoffs, another way to manipulate the ballot format in order
to encourage a different outcome is to use "votes against," so that
rather than cooperating with the fellow clone, they just incidentally 
both oppose the same frontrunner.

Kevin Venzke