[EM] Why Not Condorcet?

[Dave Ketchum]

On May 16, 2010, at 6:11 PM, Abd ul-Rahman Lomax wrote:
> At 02:16 PM 5/16/2010, Dave Ketchum wrote:
>> On May 16, 2010, at 9:24 AM, Abd ul-Rahman Lomax wrote:
>>> At 06:34 PM 5/15/2010, Dave Ketchum wrote:
>>>>> Some objections to Condorcet could be:
>>>>> 1. It is not expressive enough (compared to ratings)
>>>> Truly less expressive in some ways than ratings.
>>>>    This is balanced by not demanding ratings details.
>>>>    And more expressive by measuring differences between each pair
>>>> of candidates.

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.  I used care in  
mentioning ranking to avoid complications such as you add - and  
clearly included equal ratings and rankings.  Your extensions could be  
useful if they contributed value, but not if they just complicate.
>
>>>
>>> "Demanding" is an odd word to use for "allowing." "Condorcet"
>>> doesn't really refer to ballot form, though it is often assumed to
>>> use a full-ranking ballot. In any case, a ballot that allows full
>>> ranking, if it allows equal ranking and this causes an empty space
>>> to open up for each equal ranking, is a ratings ballot, in fact.
>>> It's Borda count converted to Range by having fixed ranks that
>>> assume equal preference strength. Then the voter assigns the
>>> candidates to the ranks. It is simply set-wise ranking, but the
>>> voter may simply rank any way the voter pleases, and full ranking is
>>> a reasonable option, just as is bullet voting or intermediate
>>> options, as fits the opinion of the voter.
>>
>> Assuming I LIKE A, B & C are almost as good, and I DISlike D:
>>
>> I can rate A=99, B=98, C=98, D=0 or rank A high, B&C each medium, and
>> D low (A>B=C>D).
>
> Dave, you are assuming that the ratings ballot has more ratings than  
> candidates. That is precisely what I did not suggest. That's why I  
> mentioned "Borda." It seems you are thinking of Range 99 as "Range,"  
> when Range is a family of methods, with the range of ratings being,  
> normally, from 1-N for Range N. With 4 candidates, the equivalent  
> Borda ballot has four ranks (1st, 2nd, and "no vote" perhaps). If  
> the ballot allows equal ranking, then, you really have a Range 3  
> ballot. So your "simple ranking" would be A>B>C>D or A>C>B>D. With  
> no equal ranking allowed, you must choose one of these, but the  
> condition of the problem is that you have no basis for this. Is that  
> hard, or what?

Since the topic is Condorcet equal ranking can be allowed, and I  
clearly indicate use of that.

After describing B and C as equally ranked I used common symbology -  
(A>B=C>D) - and am not used to the symbology you use below.
>
> Now allow equal ranking on the same ballot. Yes, you have a choice,  
> with the simplest ballot rules: You can rank them A>B=C>.>D (D  
> perhaps not being on the ballot, but I'll show the bottom rank), or  
> as A>.>B=C>D. It's a trade-off, and which one you pick depends on  
> two factors: how strongly do you want to prefer A, and how strongly  
> do you want to act against D? Strongly preferring A indicates you  
> put both middle candidates in third rank, strongly acting against C  
> indicates you might put both middle candidates in second rank. In  
> addition, there are the probabilities to consider, which may  
> outweigh the preference strength issue. Is it possible for A to win?  
> If so, indication is that you should rate B and C lower. Is it  
> possible for D to win? If so, then you might want to rate B and C  
> higher.

In ranking all I can say is to rank B&C above D and below A..

Go back to the example and see B and C each rated 98 because I DO NOT  
want them to lose to D.
>
> If the frontrunners are A and D, *it matters very little where you  
> rank B and C*

True, but ranking them below A and above D gave what insurance was  
possible.
>
> If you have trouble deciding to go for low ranking or high ranking,  
> there is an option that might be allowed in Bucklin or Range: half- 
> ranking. The way that A low-res Range 3 ballot might be shown would  
> be a list of candidates, with three options for each candidate. If  
> you mark more than one option, your vote would be, with range, half- 
> assigned to one rank and half to the other. (or a third, etc., if  
> you mark more than two, but with this particular ballot you could  
> just neglect the middle rank vote, it would end up the same). With  
> Bucklin analysis, same, except that in the counting rounds, a  
> "middle rank" would be counted after the higher rank and before the  
> lower.

Huh?
>
>
> (There are other reasons for defining what such "overvotes" mean,  
> basically to avoid discarding ballots that have an apparent meaning.)
>
> It is, in general, easier to rank candidates if the equal ranking  
> option exists. The issue, then, is how such equal ranking is to be  
> interpreted. IRV rules typically toss the vote. Not allowed. But, in  
> some small level of progress, in the U.S., the ballot simply is  
> considered exhausted at that point, the higher ranked candidate  
> still have their votes (which, if the lower ranked votes, where the  
> overvoting was, are being counted, the higher ranked candidates have  
> been eliminated. But at least the whole ballot hasn't been tossed.)

Why say this?
>
>> The example ratings of A, B,&C do the most I can to make any of them
>> win over D; the example rankings do the most I can to make A win, D
>> lose, and give B&C an equal chance.
>>
>> In Condorcet I ranked A over B and C over D but could not express the
>> magnitude of these differences.  In Score I must rate with numeric
>> values that include the differences.
>
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