[EM] Weak Condorcet winners [was: FairVote are not the friendliest]

[Jameson Quinn]

2011/9/22 James Gilmour <jgilmour at globalnet.co.uk>

> Jameson Quinn  > Sent: Thursday, September 22, 2011 2:00 AM
> > If I'm right, the claim is that voters, and especially
> > politicians, are intuitively concerned with the possibility
> > of someone winning with broad but shallow support. In
> > Approval, Condorcet, Majority Judgment, or Range, a
> > relatively-unknown centrist could theoretically win a contest
> > against two high-profile ideologically-opposed candidates.
> > The theory is that the electorate would be so polarized that
> > everyone would explicitly prefer the centrist to the other
> > extreme, but because the voters don't really expect the
> > low-profile centrist to win, they might miss some important
> > flaw in the centrist which actually makes her a poor winner.
>
> I cannot comment on the quoted remark (cut) that prompted your post and I
> know nothing at all about the activities of anyone at
> FairVote, but you have hit on a real problem in practical politics in your
> comment above  -  the problem of the weak Condorcet
> winner.  This is a very real political problem, in terms of selling the
> voting system to partisan politicians (who are opposed to
> any reform) and to a sceptical public.
>

Yes. I think that your term "weak Condorcet winner" is clearer than my terms
"mushy centrist" or "unknown centrist". And I think that a lot of IRV
supporters talk about LNH, is actually about this problem.



>
> For example, with 3 candidates and 100 voters (ignoring irritant
> preferences) we could have:
>        35 A>C
>        34 B>C
>        31 C
> "C" is the Condorcet winner.  Despite the inevitable howls from FPTP
> supporters, I think we could sell such an outcome to the
> electors.
>
> But suppose the votes had been (again ignoring irrelevant preferences):
>        48 A>C
>        47 B>C
>         5 C
> "C" is still the Condorcet winner - no question about that.  But I doubt
> whether anyone could successfully sell such a result to the
> electorate, at least, not here in the UK.
>
> And I have severe doubts about how effective such a winner could be in
> office. Quite apart from the sceptical electorate, the
> politicians of Party A and of Party B would be hounding such an
> office-holder daily.  And the media would be no help  -  they would
> just pour fuel on the flames.  The result would be political chaos and
> totally ineffective government.
>
> The flaw in IRV is that it can, sometimes, fail to elect the Condorcet
> winner.  But IRV avoids the "political" problem of the weak
> Condorcet winner.  I suspect that's why IRV has been accepted for many
> public and semi-public elections despite the Condorcet flaw.
>

I agree. Let's look how susceptible the good systems are to this flaw:

Approval: Theoretically susceptible. Depends on whether the typical voter
will approve a candidate who is in between the two frontrunners. I
personally am skeptical that this would be a practical problem, but can cite
no direct evidence of that.

Condorcet: Susceptible, especially in margins-based versions. Probably the
least susceptible version is Condorcet-Approval(implicit); which, along with
its simplicity, is the reason I favor this version.

MJ: Theoretically susceptible, but there is evidence to believe that it is
not in practice. If B+L's empirically-based simulations rerunning the 2007
French presidential elections are to be credited, MJ is the least
centrist-biased of the good systems (but also less extremist-biased than IRV
or Plurality).

Range: Theoretically susceptible, even to the extent of violating the
majority criterion. The fact that this is unlikely to be a practical problem
is, in my opinion, not going to be enough to assuage voter fears about what
can be portrayed as a serious flaw.

SODA: Uniquely unsusceptible among good systems (susceptibility roughly on
par with IRV). This is a primary reason I see SODA as the proposal with the
best chance of practical implementation over the long term.

Jameson
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