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

[Peter Zbornik]

Hi Jameson,

I think the multiple round system (as described in my previous email
today and several others) might be a the best way to get combined
support for one single method on this list.

If we skip the issues about political support for the method, I think
a good method that everyone approves might be constructed as follows:

Precondition:
(1) We have a set of voting methods V - example: Schulze, IRV,
Majority Judgement, Score, Approval, SODA, IRV-Condorcet.
(2) Every method has a ranking based on its results in previous
elections, similar to the way tennis players have a ranking on the ATP
tour etc., for instance the ranking from best (1) to worst (7) is (1.
Schulze, 2. IRV, 3. Majority Judgement, 4. Score, 5. Approval, 6.
SODA. 7. IRV-Condorcet).

(3) Round 1: The voter casts one or more ballots and the election
winner for each method is elected.
(4) Round 2:
There are two optiond for round 2:
Option 1: The voter ranks the different winners on a ranked ballot. In
order to avoid preferring a method before an other, a
tournament-system is used, like in a tennis tournament.
The winner from the method with the highest ranking meets the winner
from the method with the lowest ranking (if sevral methods give the
same winner, then the method with the highest ranking is used). The
winner from the method with the second to highest ranking meets the
winner from the method with the second to lowest ranking.
Example: Schulze, IRV and IRV-condorcet elect candidate A. Majority
Judgement elect candidate B, Score and SODA elect C and Approval elect
D.
The rankings (high to low) of the candidates: 1. A, 2. B, 3. C, 4. D.
A meets D and B meets C in a run-off and the winners of the two
run-offs meet in a second round.
The all the winners are determined by the ranked ballot.
Option 2: The voter only elects between the first tier in the
tournament. In the example the voter votes between A vs D and B vs C.
Then the ballots are counted and a third round is held for the finals
between the two winners from the last round.
(5) After the elections the ratings of the methods are updated
according to their performance (this system has to be invented), for
instance as in Tennis or some other sport, where the tournament system
is used.

This is in some sence a unified and fair approach which helps unifying
election reformers, and at the same time allows for the testing of new
methods like SODA without potentially disastrous consequences. A new
election method is just a new player on the tour so to say.

And at the end of each election season, we would finally know which
election method won the tour :o)

Best regards
Peter Zborník

On Thu, Sep 22, 2011 at 7:34 PM, Jameson Quinn <jameson.quinn at gmail.com> wrote:
>
>
> 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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