[EM] Approval reducing to Plurality

[Kristofer Munsterhjelm]

Dave Ketchum wrote:
> On Aug 30, 2010, at 4:56 AM, Raph Frank wrote:
> 
>> One of the things that the Burr dilemma assumes is that the voters are
>> split into 2 groups and each group rates their candidates as vastly
>> superior to any candidate from the other side.
> 
> When I see clones I think of them as such, and treat them alike if 
> possible.
>>
>> However, in practice, that isn't true, at least for many people.
>> Approval (and condorcet) shifts power from the extremes towards the
>> centre.
> 
> ???

Consider a one dimensional spectrum with Left, Right, and Center, and 
where most people are closer to either Left or Right than Center, so 
society is polarized. However, neither Left nor Right has a majority. 
Then you could get something like:

46: L > C > R
44: R > C > L
10: C > R = L

A majority prefers C to both L and R, so Center is the CW - but 
Plurality doesn't see past the first choice and so elects Left. In this 
particular case, as well as similar ones, Condorcet shifts power from 
the extremes (either Left or Right) to the center.

More generally speaking, that is an example of Plurality failing to 
elect the candidate closest to the median voter, and because of 
Plurality's vote-splitting problem, it usually errs towards the extremes 
as the center gets fragmented. Borda errs in the other direction.