[EM] Condorcet vs Approval

[Forest Simmons]

Craig, thanks for the critique.

I mentioned in one posting that I owed Joe W., Bart I., and Martin H. for
certain insights that led to the need for (and certain features of) a
finer resolution dyadic system.

I also owe you for your excellent example with utilities and poll results
that showed the desirability of more resolution in Approval; a need for
some kind of move toward Condorcet, hopefully without losing good aspects
of Approval. 

And one of the key ideas (intentionally or not) came from Demorep; In one
of his cryptic messages I got the impression (right or wrong) that he was
advocating allowing voters to give weights to their preferences.  At first
I thought that would lead to voters giving maximum weight to all of their
preferences (if there were no contraint on the total of the weights) or to
insincere weights for strategic purposes (if there were a constraint on
the total of the weights).

But a little reflection showed that was not necessarily the case. If, for
example, all of the preferences between the approved and the unapproved
are given twice the weight of the preferences within each group, then a
distinction is made that does not give any voter any reason to use an
insincere preference order (as long as Condorcet ties are broken randomly,
for example, or by Approval itself).

Once you see that there might be some advantage to this distinction, it is
natural to make further distinctions of the same type within each
distinguished group, ad infinitum (especially if you like Cantor sets and
other fractals).

On Fri, 2 Mar 2001, LAYTON Craig wrote (in part):

> 
> .................the requirement to truncate your vote.  I can imagine a
> great deal of outrage from voters who look forward to the opportunity to
> put a particular party last at an election, even to the point of caring more
> about this than who they put first.

This was also pointed out by Martin Harper, and I agree.  That's why I
decided that including all the possible categories of "dyadic approval"
would be better.  In that system, the voter divides the candidates into
two groups (approved and unapproved), then divides each of those groups in
half again solely on the basis of comparisons within the group in question,
etc. 

If we wanted to be trendy we could call this method "fractal approval" .

> A compromise method
> might be the answer, if its complexity wasn't a problem.
>  

I think the complexity problem is easily solved with this dyadic approval
system.

The complexity of strategy is no problem. Just use your favorite approval
strategy within each group. That's completely adequate. 

The complexity of voting mechanics is a minor problem. Each person has the
choice of (1) rating the candidates on a scale of zero to 2^n - 1, where
the number n depends on the desired resolution (This number should be
larger than or equal to the base two logarithm of the number of
candidates, for minimal acceptable resolution.)  OR (2) listing the
candidates in order and inserting the allowable number of >>...>>> symbols
to show their preferences along with indicated strength of preference. 
Only one inequality symbol of length k is allowed between two consecutive
symbols of length greater than k. The longest symbol separates the
approved and unapproved. The shorter symbols make finer distinctions
within groups. 

Using the first method would be no more difficult than implementing CR. 
The second method might be preferable for voters that wanted to indicate
their various levels of approval and let the computer do the conversion to
ratings. 

Well, yes, any situation of voting mechanics that was too complex for both
Cardinal Ratings for Condorcet would be too complex for dyadic approval. 

But remember, we are looking for methods that can be used as theoretical
standards to help evaluate the performance of more practical methods.

Forest