[EM] Juho's idea

[Juho]

On Jan 9, 2007, at 2:25 , Simmons, Forest wrote:

>> Juho wrote:
>>
>>> How about "the smallest number of ballots on which some
>>> alternative  that beats A pairwise is ranked higher than A"?
>>>
>>> Juho
>
>
>
> If I am not mistaken, this idea is equivalent to electing the  
> alternative A with the greatest number of ballots on which A is  
> ranked higher than any alternative that beats A pairwise.

Yes, seems so, if we don't care about the ties.

I'll explain a bit more my interest in this particular method. The  
vote of a voter in a way says: "I object the election of alternative  
A since voters prefer B to A (and I do so too)". We thus do not try  
to seek the alternative that beats A most (directly or in chain) (as  
typical in the Condorcet methods), but we try to count the number of  
"justifiable" objections (that may be based on losing to any of the  
other alternatives). This reasoning is mainly based on trying to  
achieve good performance with sincere votes using an alternative  
utility function. The strategic defence properties may or may not be  
there.

> Here's a variant that could be used with cardinal ratings/range  
> ballots:
>
> Elect the alternative A with the greatest number of ballots on each  
> of which A is rated above the expected rating of the alternatives  
> that beat A pairwise.

Aha, that's an interesting approach. And the same with the  
replication of names on the ballot. I'll also explain a bit more the  
thoughts I had on how this method could be developed further (to  
better or worse :-).

Instead of seeking the candidate with "the smallest number of ballots  
on which some alternative that beats A pairwise is ranked higher than  
A" one could sum up the margin comparison values (=> instead of just  
adding 1 per each vote). This would make the largest possible result  
n*n where n is the number of votes (10000 in the typical EM elections  
with 100 voters). The idea is to go closer to margin style results  
instead of the quite winning vote style results of the method where  
just the number of votes is counted. (Also (WinningVotes-LosingVotes)/ 
WinningVotes is an option.)

Juho Laatu



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