[EM] RE : Ranked Preference benefits

[Juho]

I reply to myself to give a more complete answer to one of Chris  
Benham's points.

On Nov 4, 2006, at 3:03 , Juho wrote:
> On Nov 3, 2006, at 19:50 , Chris Benham wrote:
>> That at least meets  Majority Loser  and is relatively easy to
>> operate. Also in common with IRV it meets
>> Dominant Mutual Third, Majority for Solid Coalitions and  Condorcet
>> Loser.
>
> As we discussed earlier I think many criteria like Condorcet loser
> lose their original idea in some extreme cases like with strong
> cycles. For many criteria it is also ok if they are met in all the
> "usual" cases, not necessarily in 100% of the cases. Therefore I
> think it is best not to treat the criteria as boolean values (filled
> or not) but as nice exact definitions that should be supported by
> practical examples (real life failure cases) that demonstrate that
> the vulnerabilities are real, not just theoretical.

Not respecting the Condorcet loser criterion (unlike the DMC +  
preference strengths variant that Chris Benham talked about) is one  
of the properties of (the described version of) the Ranked  
Preferences Method. The reason I included this feature is however not  
related to use of the preference strengths but comes directly from  
using the basic minmax with margins to pick the winner from the  
matrix (at each cycle). If one wants to fight that problem, limiting  
the winners to the Smith set is maybe the most common approach. But I  
think electing Condorcet loser in some of the extremely cyclic cases  
may actually be the best choice available.

My usual example is this:
25:A>B>D>C
25:B>C>D>A
25:C>A>D>B
24:D

There are four parties of about equal size. D is the Condorcet loser  
but on the other hand she is two votes short of being the Condorcet  
winner. The other three candidates are badly cyclic and would each  
need 26 additional votes to become Condorcet winners. In this light D  
is not a bad winner after all. Not electing the Condorcet loser is a  
good property in 99.9% of the elections but in the remaining tricky  
cases things may look different.

If you don't buy this argumentation (that is actually minmax related,  
not ranked preference related) you probably find some slightly  
different variant of the Ranked Preferences Method better. One option  
would be to limit the selection to Smith Set only.

Juho Laatu

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