[EM] "Guaranteed Majority criterion" on Electowiki

[Kristofer Munsterhjelm]

Kevin Venzke wrote:
> Hi Chris,
> 
> --- En date de : Mer 3.11.10, C.Benham <cbenhamau at yahoo.com.au> a écrit :
>>> The guaranteed majority criterion requires that the winning candidate 
>>> always get an absolute majority of valid votes in the last round of 
>>> voting or counting. It is satisfied by runoff voting, MCA-AR, and, if 
>>> full rankings are required, IRV. However, if there is not a pairwise 
>>> champion (aka CW), there could always be some candidate who would have 
>>> gotten a majority over the winner in a one-on-one race. Since, unlike 
>>> most criteria, this criterion can depend on both counting process and 
>>> result, there could be two systems with identical results, with only one 
>>> of them passing the guaranteed majority criterion. 
>> This is an example of what Mike Ossipoff used to rightfully excoriate as 
>> a "rules criterion".
>>
>> To me if  "two" voting systems/methods always give the same results with 
>> the same impute, then they are really 
>> just one method (which perhaps has alternative algorithms) and so they 
>> both meet and fail all the same (non-silly)
>> criteria.
> 
> Yes, I imagine criteria to be defined based on the results of the method,
> not the procedure for finding the result...
> 
> A good reason for this is that there is no objective test for what
> constitutes a "round of counting" or "getting" a vote in such a round. Or
> even what is a "valid" vote: It's not obvious that two-vote runoffs should
> satisfy the criterion. I guess in a "round of voting" the "valid votes"
> are determined based on the current (i.e. last) round but in a "round of
> counting" you use all the votes cast and not just those still being
> evaluated.

A reasonable results-only version would be a criterion that says that if 
the method is left with two candidates, the one that beats the other 
pairwise should win. But because we don't know what round of counting or 
getting a vote means, the criterion must be very weak and say that 
someone who loses pairwise to everybody else can't win (since there's no 
way that it would be the victor of a final one-on-one contest), and 
that's just Condorcet Loser.

Looking at that from another angle, we see that the "always elects the 
winner of a majority" point that IRV proponents like to wave around is 
also simply Condorcet Loser. If the method passes CL, you can construct 
a fake elimination order that leads the winning candidate to pass the 
last round - if it does not, there will be instances where you can't.