[EM] Condorcet - let's move ahead

[Kristofer Munsterhjelm]

Steve Eppley wrote:
> Hi,
> 
> On 1/18/2009 10:52 AM, Dave Ketchum wrote:
>> Your promotion of IRV discourages for, while its ballots would be valid
>> Condorcet ballots, its way of counting sometimes fails to award the
>> deserved winner (even when there is no cycle making the problem more 
>> complex).
> 
> I do not promote IRV.  IRV+Withdrawal is not IRV.  The withdrawal option 
> allows candidates to correct for IRV's tendency to undermine centrist 
> compromise.  Candidates would have the incentive to withdraw because 
> they and their supporters would prefer centrist compromises over 
> "greater evils."  See the example below.
> 
>> That the indicated winner could withdraw does not really help, for that
>> candidate does not necessarily know whether IRV has erred.
> 
> I don't see why Dave wrote about the "indicated winner" withdrawing.  
> The point of withdrawal is to allow *spoilers* to withdraw after the 
> votes are cast.
> 
> Also, it would quickly become clear whether IRV has "erred."  The votes 
> would be published soon after the election day polls close.  Then the 
> candidates would be given days after the votes are published to decide 
> whether to withdraw.  During that period of time, the candidates (and 
> other interested people) can download the published votes and privately 
> tally who will win if no one withdraws and who will win if they and/or 
> other candidates do withdraw.

Could this lead to informal coalitions? Say that IRV (deservedly) elects 
a right-of-center candidate. Could all the left-of-center candidates 
determine who's most suited among them and thus all but that one 
withdraw to cause the result to go either to that candidate, or at least 
to a candidate closer to the left?

I suppose a counter to that would be that withdrawal can only correct 
unfair vote-splitting, and inasfar as IRV is cloneproof, it shouldn't 
make a difference when the initial result was "fair" in the first place. 
I'm not sure, though. Is it possible?

>> Therefore I still wait to hear from others as to whether MAM deserves
>> backing, though it properly handled your simple cycle example.
> 
> MAM satisfies all the desirable criteria satisfied by Beatpath Winner 
> (aka Cloneproof Schwartz Sequential Dropping--CSSD for short--aka 
> Schulze's method).  It also satisfies some criteria that Beatpath Winner 
> fails: Immunity from Majority Complaints (IMC, which is satisfied only 
> by MAM), Immunity from 2nd-Place Complaints (I2C) and Local Independence 
> of Irrelevant Alternatives (LIIA).  Furthermore, simulations by several 
> people have shown that over the long run, more voters rank MAM winners 
> over Beatpath winners than vice versa, and a majority rank the MAM 
> winner over the Beatpath winner more frequently than a majority rank the 
> Beatpath winner over the MAM winner. (Those simulations suggest MAM 
> comes a little closer than Beatpath Winner to satisfying Arrow's 
> Independence of Irrelevant Alternatives criterion.)  See 
> www.alumni.caltech.edu/~seppley for more information about MAM and 
> criteria it satisfies or fails.

So voters prefer MAM winners to Beatpath winners more often than vice 
versa. What method is the best in that respect? If it is Kemeny, then 
perhaps even more Kemeny-like methods (like Short Ranked Pairs) would be 
even better. They're more complex, though.

Also, to my knowledge, River passes Independence of Pareto-Dominated 
Alternatives while MAM does not. Is River better than MAM?

> As far as I can tell, the reason some groups have adopted Beatpath 
> Winner rather than MAM is because there used to be a website co-written 
> by Mike Ossipoff in which he claimed it will be easier to explain CSSD 
> than MAM. (Mike used the name Ranked Pairs instead of MAM, but he 
> definitely meant MAM, not the pairwise margins-based voting method that 
> Nicolaus Tideman invented and named Ranked Pairs in 1987/1989.)  Mike 
> based his conclusion on a few personal anecdotes, which I think can be 
> attributed to his own greater familiarity with the Schwartz set that 
> made him more comfortable explaining in terms of subsets of candidates. 
> (I could forward emails from Mike where he acknowledges MAM is at least 
> as good as Beatpath Winner.)  As my previous message about the ease of 
> explaining MAM illustrated, Mike was mistaken about which is easier to 
> explain.  Judge for yourselves.

 From a computational and recursive point of view, Schulze (by the 
Beatpath heuristic) might be simpler to describe than MAM or its 
variants, but in general I agree, since most people don't have that 
point of view.

Rephrasing from condorcet.org (which seems to be down), you'd have a 
computational definition like this:

If X either beats or ties Y pairwise, then X has a path to Y of strength 
equal to the number of voters ranking X over Y.

If X has a path to Y of strength a, and Y has a path to Z of strength n, 
then X has a path to Z equal to the minimum of a and b (that's the 
kinda-recursion).

Of all the paths from X to Y, if the path of greatest strength from X to 
Y is stronger than the path of greatest strength from Y to X, then Y 
cannot win. The winner is the candidate who is not disqualified in this 
manner.