[EM] ruminations on ordinal and cardinal information

[Russ Paielli]

Russ wrote:

>>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.

James wrote:

> 	I suppose that it would be possible to use an alternate version of
> cardinal pairwise that was based on candidate eliminations, but I suspect
> that it would be somewhat incoherent, because the logic of cardinal
> pairwise is very much grounded in the defeat-dropping principle. The idea
> is that when there is a majority cycle, and you have to overrule one of
> the defeats, you should overrule the one which voters place the lowest
> overall priority on. This is very different from eliminating the candidate
> with the lowest cardinal score, and I submit that it is much less
> vulnerable to strategic manipulation than such an approach.

James,

Let's forget about cardinal pairwise for now and focus on your approval 
pairwise proposal. Here's your proposal (cut from your EM post from June 
8, 2004, with minimal reformatting of line breaks):

Ballots:
ranked ballots with approval cutoff

Tally:
1. Pairwise tally using the ranked ballots. Elect the Condorcet winner 
if one exists.
	If there is a majority rule cycle:
2. Using the ranked ballots only, construct a map of which candidates 
beat or tie other candidates. At this point we are only determining the
direction of the defeats, not the magnitude.
3. For a given defeat A over B, the magnitude of the defeat is defined 
by the number of voters who place A above their approval cutoff and B 
below their approval cutoff.
4. Using this definition of defeat strength, you can resolve the cycle
with methods such as minimax, beatpath, or ranked pairs.

My first comment is that this proposal is significantly more complicated 
than my (or Kevin's) "Ranked Approval Voting" (RAV) proposal, which 
simply drops the least approved candidate until a CW is found.

Secondly, I find it interesting that you define the magnitude of a 
defeat in step 3 as, "the number of voters who place A above their 
approval cutoff and B below their approval cutoff." This is equivalent 
to using the difference of Approval scores for the two candidates (with 
a constant offset). If you simply used the winning approval score rather 
than the difference, I think your proposal would be equivalent to RAV.

Elsewhere you have advocated using "winning votes" rather than "margins" 
for the pairwise measure off Condorcet defeat magnitude, but here you 
seem to be advocating "margins" for the defeat magnitude when it is 
based on approval scores. Why the difference? What is the advantage of 
using "margins" in your proposal? More importantly, does the advantage, 
if there is one, justify the additional complexity of your proposal? I 
must tell you that I'll be surprised if it does. Then again, it won't be 
the first time I've been surprised.

By the way, I think the very same questions apply to your cardinal 
pairwise proposal.

--Russ