[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....
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