[EM] Why Not Condorcet?

[Abd ul-Rahman Lomax]

At 09:50 AM 5/16/2010, Kristofer Munsterhjelm wrote:
>Abd ul-Rahman Lomax wrote:
>
>>"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.
>
>If the range is too narrow or too wide, the equivalence fails.

If you read what I wrote carefully, you can see that I was describing 
a ranked ballot, which assumes full ranking and no other ranks. That 
is a Borda ballot (if fully voted). The question is what happens then 
if you equal rank.

I.e., if you have A>B>C>D, and you decide to equal rank, say, A and 
B, is you vote

A=B>C>D, or is it

A=B>.>C>D

which maintains the four ranks? (Or it could also be A=B>C>.>D, the same).

As to practical expression on a ballot, this is actually easier than 
simply expressing two ranks instead of three, and the two possible 
A=B>C votes I showed have different implications for the utility of C.

There are two ways:

                 A       B       C       D
1st rank:       O       O       O       O
2nd rank:       O       O       O       O
3rd rank:       O       O       O       O

or

rank:           1       2       3
A:              O       O       O
B:              O       O       O
C:              O       O       O
D:              O       O       O

In either case there are 12 voting positions. But the second form 
looks more like a Range ballot.

If you add more candidates, of course, you either have to add more 
ranks or allow equal ranking. The stupidity of the RCV ballots is 
that they didn't allow equal ranking. If they did, four ranks (three 
expressed plus one default of no-vote) could handle a lot more 
candidates; one Bucklin election had a huge number of candidates, I 
remember there being ninety.

Note that RCV with equal ranking allowed would actually be an 
Approval method, I have no doubt that it would be either the same as 
IRV or better. With 23 candidates, like some of the San Francisco 
elections, definitely better! But it would then expose the center 
squeeze problem of IRV, and people would then dump elimination and 
make it Bucklin....

DYK that San Francisco used Bucklin for at least two elections, in 
1919 and 1921? Maybe 1917, it's not clear. It was not dropped because 
it was not popular, it was dropped because the Election Commission 
decided to use a few voting machines (not for everyone, just a few of 
them!) and a law had just been passed that read that, if voting 
machines were used, the election would default to the general state 
method. I.e., FPTP. It would be fascinating to know if the voters, 
approving what looked like a minor tweak to the election code, 
realized that they'd be dumping a voting method that they had 
recently approved by a large margin.... I suspect that this involved 
some very clever political manipulation.... or maybe it wasn't. Maybe 
it was just a coincidence.