[EM] Arrow's Theorem

[Kristofer Munsterhjelm]

Dave Ketchum wrote:
>>
>> Well, Fairvote would like to make us believe that some cases, if the 
>> Condorcet winner had won, we'd all be saying "but wait! He didn't have 
>> enough core support! Boo!".
> 
> But, we chose ranking rather than Approval to let voters approve, but 
> with unequal liking.  Bush haters could want to vote both Gore and Nader 
> as better, but not as equally liked - with whoever they ranked second 
> still seen as better than Bush.

True. If you have a binary level, Approval is the obvious method to use. 
If you have rank, then Approval will be problematic because you can't 
designate relative strength within those you do approve. Condorcet still 
respects relative rank, but it seems they argue it doesn't respect 
relative rank *enough*, particularly when the rank is relative to first 
place.

>> (Presumably we should also be saying, if the Plurality winner won, 
>> "but wait! Lots of people second-ranked someone else! Boo!". One might 
>> wonder how much "core support" is enough.)
> 
> But, if the Plurality winner won without a runoff, all three methods 
> would agree as to winner.

I was a bit unclear here. What I meant was that if the method had been 
"Ranked Plurality" (everybody submits rank-ballots and whoever is listed 
first on most ballots win), then they would say that this is bad because 
it doesn't take lesser preferences into account. So this shoehorning of 
Plurality is too bad in one direction, and Approval is too bad in the 
other. Why, then, is Condorcet also too bad in the other? How much "core 
support" is too much, and why?