[Election-Methods] Is the Condorcet winner always the best?

[Jonathan Lundell]

On Dec 10, 2007, at 8:00 PM, Dave Ketchum wrote:

> Since A & C are tied, you cannot do any better than B.
>
> Get far enough away, and A or C will properly win.
>
> I do not like '>>' for Condorcet.

'>>' seems like a useful shorthand to describe the "sincere  
preferences" of the voters here.

It's easy to accept that this profile:

46: A > B >> C
  5: B >> A > C
  5: B >> C > A
44: C > B >> A

...should choose B as a good compromise, with the A voters saying A is  
good, B OK, C very bad. But Diego's profile suggests to me that the A  
voters are saying something like A is good, B is bad, C is very bad.  
Not that they can express it in a normal linear ballot, just that  
we're being told a little more about their opinions.

In my example, the effect of a later-no-harm voting rule is evident.  
In Diego's, a rule (such as STV) that elects A doesn't seem  
unreasonable to me.

The problem is that with an ordinary linear ballot (no '>>'), we can't  
distinguish between the cases. Not that I'm arguing that we should  
employ '>>'; offhand, that strikes me as a complication to be avoided.

>
>
> On Mon, 10 Dec 2007 14:17:53 -0300 Diego Santos wrote:
>> Suppose this scenario:
>>
>> 46: A >> B > C
>> 5: B >> A > C
>> 5:  B >> C > A
>> 44: C >> B > A
>>
>> B beats A and C, but he is approved for only 10% of the voters.
>>
>> A possible patch is to avoid rank-only ballots and ignore candidates
>> with less than 1/2 approval (or total score, if range ballots are  
>> used)
>> of the most approved candidate. This simple rule also solves DH3  
>> pathology.
>> ________________________________
>> Diego Santos