[EM] Why Not Condorcet?

[Abd ul-Rahman Lomax]

At 10:37 PM 5/18/2010, Dave Ketchum wrote:

>I had written promoting Condorcet.
>
>Kevin Venzke offered some objections, #1 is above, indicating that
>ratings have the value of being more expressive.  I responded to his
>thoughts, also above.
>
>Abd ul, who often writes usefully, wrote a book here, wandering into
>various topics such as Bucklin.

My condolences. You were not forced to read it.

The upshot of my writing has been to note that there is no conflict 
between Range ballot and Condorcet method, because a Range ballot can 
be used to rank candidates and thus as a basis for condorcet analysis.

Bucklin is a method which, I've been noting, effectively uses a range 
ballot to drive an Approval election, repeating this with lowering 
approval cutoff. If Bucklin finds a majority, but not two majorities, 
the Bucklin winner must be the Condorcet winner.

With a finer resolution Bucklin ballot, multiple majorities will 
become less likely. Condorcet failure when a majority of the 
electorate has approved the Condorcet winner, but approved another in 
greater numbers, represents a small loss of utility, ordinarily, and 
this is a classic solution where two propositions are considered for 
Yes/No vote simultaneously, they conflict, and both pass.

>>>The base topic is Condorcet.  It would take a book to respond to all
>>>your extensions such as IRV.  Likewise I see no benefit in adding
>>>Borda - Range/score is an adequate source for ratings.
>
> From Wikipedia:
>Condorcet:  For each ballot, compare the ranking of each candidate on
>the ballot to every other candidate, one pair at a time (pairwise),
>and tally a "win" for the higher-ranked candidate.

You should know that the "opinion" of Wikipedia is not necessarily 
any better than my opinion -- indeed, in some cases, it is my opinion 
and I put it there --, and these articles swing with the wind.

The definition is badly written. It's not a definition, actually, 
it's an algorithm, with missing pieces.

>Range voting uses a ratings ballot; that is, each voter rates each
>candidate with a number within a specified range, such as 0 to 99 or 1
>to 5.

Or ranks the candidates, assuming that enough ratings are available 
to do this fully.

>In Condorcet the counting is of pairs of candidates so the
>possibilities for A vs B cannot be other than A>B , A=B, or A<B - no
>way to have a skipped rank.

But don't confuse Condorcet analysis with Condorcet method and 
Condorcet ballot.

A Condorcet ballot can have skipped ranks. A Condorcet method does 
not use them. Condorcet analysis of a Range ballot would assign no 
meaning to the skipped ranks. Unless it was designed to do so: it 
could do so, for example, to resolve condorcet cycles. Some Condorcet 
methods, in effect, do this, with the "skipped ranks" being ranks 
occupied by candidates not involved in the pair.

>In Range the limits can be other than 0-99, but those are suitable for
>the discussion.

Not if you are complaining about Range "forcing" you to make refined 
decisions. Do remember, Approval is a Range method, with only two 
ratings. 0 and 1, or No and Yes.


>>Dave, you apparently don't understand a good deal of what you read.
>>That's okay, take your time.
>>
>>My point was about your use of "demanding ratings details," which is
>>not intrinsic to range methods. In particular, I've been pointing
>>out, Borda is a ranked method that is a Range method, and it becomes
>>full range if the method simply allows one to equal rank any two (or
>>more) candidates without disturbing the points given to other
>>candidates.
>
>The topic is "ratings" and, Range being adequate for the cause, there
>is no need to wander into other methods.

The point is that Borda is not an "other method," it is Range with a 
peculiar restriction: no equal ranking allowed, and incomplete 
ranking dilutes the ballot (with some rules).

>>You are showing, Dave, that you have completely missed the point.
>>Again, you use "must." No, a Range ballot can simply be a list of
>>ranks.
>
>Such a list might be - but numbers would make more sense with limits
>such as 99.

That would be a list of ranks, from 0 to 99. A Range ballot allowing 
this would allow complete ranking for up to 100 candidates. Don't 
want the sweat of deciding exactly where to rank each candidate? 
Easy, just spread them roughly across the range. You are then voting 
a Borda-like ballot, and you are fully ranking.

Frontrunner is in the middle? Okay, if you want to cast an effective 
ballot, push the rating up -- and all rated above this candidate -- 
or push it down, and all rated below. It would be easier if you rate 
frontrunners first, you can then spread remaining candidates through the range.

I do not recommend such high resolution Range. I'd be happy to see 
Range 4, used as a ballot to feed a Bucklin set of rounds, with a 
runof if a majority is not found. Very easy to vote, and a powerful 
technique, much more flexible than straight Approval.