[EM] Why Not Condorcet?

[Abd ul-Rahman Lomax]

On May 16, 2010, at 9:50 AM, Kristofer Munsterhjelm <km-elmet at broadpark.no 
 > wrote:

> Abd ul-Rahman Lomax wrote:
>
>> "Demanding" is an odd word to use for "allowing." "Condorcet"  
>> doesn't really refer to ballot form, though it is often assumed to  
>> use a full-ranking ballot. In any case, a ballot that allows full  
>> ranking, if it allows equal ranking and this causes an empty space  
>> to open up for each equal ranking, is a ratings ballot, in fact.  
>> It's Borda count converted to Range by having fixed ranks that  
>> assume equal preference strength. Then the voter assigns the  
>> candidates to the ranks. It is simply set-wise ranking, but the  
>> voter may simply rank any way the voter pleases, and full ranking  
>> is a reasonable option, just as is bullet voting or intermediate  
>> options, as fits the opinion of the voter.
>
> If the range is too narrow or too wide, the equivalence fails.
>
> For an example of the former, there's no way to express all possible  
> Range-4 ballots with a ranked ballot with three candidates, even if  
> you permit equal rank.

Of course not. The equivalent Range ballot is Range 2, not Range 4.

> To do so, you would have to be able to vote for "Nothing", e.g.
> A > B >> C, which is A > B > {} > C, which is A gets 4 pts, B gets  
> 3, C gets 1.
>
> It works the other way as well: if you have five candidates, ranked  
> ballots expressing a full preference ordering cannot be converted to  
> Range-4.

Incorrect. To allow full ranking, for N possible candidates, you need  
Range(N-1). Number of ratings = number of ranks. With 5 candidates,  
the Range ballot needed for full ranking is indeed Range 4. If the  
voter does not equal rank, the ballot is a Borda ballot. Borda works  
as a method to the extent that preference strength between adjacent  
ranks is equal, or averages to equal. Borda breaks down when this  
assumption breaks down. True clones with pure Borda cause ratings to  
fall for all lower-rated (ranked) candidates, whereas with Range  
(Borda with equal ranking and thus empty ranked allowed) ratings are  
independent.

Borda is a Range method with a peculiar restriction. That restriction  
made sense when it was assumed that the only relevant information was  
rank order. It is really the same error as vote-for-one, which works  
fine when a majority is required....