[EM] Why Not Condorcet?

[Dave Ketchum]

On May 19, 2010, at 2:32 PM, Abd ul-Rahman Lomax wrote:
> 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.

Making me think of the meaning of words mattering - such as  
"billion".  Randomly select a document with this word and the intended  
audience and when written affects the expectable meaning:
      Scientific community, or American:  1000 million , for they  
copied what the French were doing.
      British, and most of rest of world:  1,000,000 million, for they  
copied what the French were doing.

Rank ballots:
      Condorcet:  Each ballot is counted.  Matters not what the voter  
did, so long as the three possible values of candidate pairs can be  
recognized for counting.
      Bucklin:  All of the votes from all ballots, for a rank number,  
are processed together.
      Borda:  The rules defined for a particular race matter - what  
numbers are permissible , and whether larger numbers mean greater  
desirability, etc.

Point I am trying to make is that, intending to read one set of  
ballots for multiple rules, how the rules interact matters - and it  
all works only if the voters understand the combination of rules.
>
> 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.

What is missing?  I LIKE it.
>
>> 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.

What stops equal ratings?
>
>> 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.

I can imagine doing something extraneous for cycles.  That such could  
be worth the pain is suspect, since it does nothing without a cycle,  
and what might be doable for a cycle would require magic for deciding  
what actual cycle might need some doing.
>
>> 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.

Kevin had set up the subject, as ratings being more expressive - does  
not seem like two ratings could be a very expressive problem.
>
>>> 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).

Even claiming Borda is a kind of Range does nothing useful as to the  
current topic.
>
>>> 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.

All I see below is noise.
>
>
> 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.