[EM] ruminations on ordinal and cardinal information

[Russ Paielli]

James Green-Armytage jarmyta-at-antioch-college.edu |EMlist| wrote:
> Hi Russ,
> 
> 	I suggest that the cardinal pairwise method provides a logical conclusion
> to some of your ruminations.
> fc.antioch.edu/~jarmyta at antioch-college.edu/cwp13.pdf
> or http://fc.antioch.edu/~james_green-armytage/cwp13.htm
> 	This method uses a continuous scale (e.g. 0-100) rather than a binary 0/1
> rating, and I am willing to argue that this extra flexibility is
> worthwhile when practical. However, there is an alternate version of the
> proposal, which I call approval-weighted pairwise, that uses an approval
> cutoff rather than a continuous scale.
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-June/013241.html
> 	The general principle of cardinal pairwise and approval-weighted pairwise
> is that the ordinal information is used to determine the direction of
> pairwise defeats, whereas the cardinal information is used to determine
> the strength of the pairwise defeats. The goal is that the weakest defeat

James,

What if the two measures disagree about who is defeated? In other words, 
what if one candidate wins the pairwise race but the other wins the 
approval race?

> in a majority rule cycle should be the one that has the lowest overall
> combination of these two factors: (1) the number of voters in agreement
> with the defeat, and (2) the relative priority of the defeat to those
> voters who agree with it. My contention is that these methods are more
> adept at solving both sincere and strategic cycles.

Your method is interesting, and it may have good properties. However, I 
don't like the idea of dropping defeats. I think dropping candidates 
based on approval scores is much easier to explain to the public and is 
perfectly legitimate. But at this point that's just my opinion.

--Russ