[EM] Why Not Condorcet?

[Abd ul-Rahman Lomax]

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.
>>
>>"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?

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.

If the frontrunners are A and D, *it matters very little where you 
rank B and C*

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.

(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.)

>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.

The "numeric values" are assigned to the voting positions on the 
ballot. On a Borda ballot, your expression is limited to values where 
the range of values is the number of candidates. If you don't know 
how Borda is counted, you should read http://en.wikipedia.org/wiki/Borda_count

>I do not understand "empty spaces" above.  B&C being equally liked got
>equal rating and equal ranking - exactly the same as one of them would
>have earned with the other omitted.

That's right. Here is a Borda ballot, equal ranking not allowed. I'll 
assume that you ranked B over C, you don't have the choice of equal 
ranking them on a ballot with no equal ranking allowed (which would 
include some preferential ballots, not others).

Borda points may be figured from rank by subtracting the rank from 
the number of candidates. (There are other ways that amount to the same thing.)

You would vote in ranks
1 A; 3 points
2 B; 2 points
3 C; 1 point
4 D; 0 points.

Now, suppose you equal rank B and C. Would you vote like the following:

1 A; 3 points
2 B=C; 2 points
3 D; 1 point.

If so, you just tossed away a third of your voting power. So you 
would want to leave D at zero points. That opens up an empty rank, 
either 2nd rank or 3rd rank.

And allowing equal ranking, with empty ranks allowed, turns the Borda 
ballot into a Range ballot, with the same strategy and ordinary 
rules. If you decided that defeating D was relatively important, you might vote

1 A
2 B=C
3 .
4 D

So you have placed in each election pair a vote strength:
A>B, 1/3 vote
A>C, 1/3 vote
A>D, 1 full vote
B>C, 0 vote (no preference)
B>D, 2/3 vote
C.D, 2/3 vote.

In a full positionally weighted voting system, you are voting for, 
not candidates as such, but *groups* of candidates, a group being all 
candidates you position as the same. If there are enough positions, 
you can fully rank. But you might decide to do otherwise.

Borda is a decent system with sincere votes, as long as there aren't 
some weird preference patterns, and if you rank all the candidates, 
and it looks right to you, *this would be your sincere Range ballot.*

Now if you are presented with a Range ballot with a maximum of 100 (I 
dislike 99, it's not how people think), sure, it may seem not so 
easy. But you can simply strew the candidates across the spectrum, 
and then modify it if you need to. 4 candidates, you would rate them, 
in order of decreasing preference, 100, 66, 33, 0 or something like 
that. But I don't expect to see Range 100 ballots any time soon in 
public elections. Range 4, yes, very simple and very desirable. 
(Bucklin ballot, with or without rating 1 present.)

I have read no accounts of it being difficult to vote in Bucklin. 
Partisan voters who strongly dislike the idea that they might end up 
abstaining in the contest between their favorite and a possible final 
contender (i.e, without their vote it is a tie, or fails to become a 
tie) can simply bullet vote, which indicates strong preference, which 
is the condition I just described! It's sincere.

An elimination method like IRV takes the voters' lower preference 
votes, which generally represent lower preference strength, and 
"magnify them," turning them into full strength votes. Bucklin turns 
all the votes into full strength votes, without eliminations so, 
while it does involve a (partial) abstention, it also provides 
additional opportunity for a candidate who would otherwise be 
eliminated to gain votes from other voters.

The first Bucklin election elected a candidate who was in third place 
until the ranks were collapsed. And this was clearly a majority 
preference, from the votes. The first-round leader wasn't even in 
second place after the smoke cleared. Bucklin worked, and that is 
exactly, my opinion, what killed it. The first-round leader was a 
Republican. The winner was a Socialist. This was 1909, in Grand 
Junction, Colorado. You can imagine the arguments against the method, 
and you might be right.

There was an attempt in Oklahome to implement a range-like versin of 
Bucklin. The positional weightings were not equal, i.e., 1 new vote 
added with each rank. Rather, second rank was a half-vote, third rank 
was a one-third vote, as I recall. (Or was it one-fourth?).

I think they got it wrong, it should have been, for decent Range, 1 
vote for first position, 3/4 vote for second rank, and 1/2 vote for 
third position. That method wasn't actually used, because, in a 
bright idea to try to find majority winners, they mandated additional 
ranking. That wasn't going to fly in the U.S., it was predictable 
that the law would be tossed. But the interesting thing to me is that 
the Supreme Court of Oklahome did not simply invalidate the mandatory 
voting requirement. They tossed the whole law. I strongly suspect 
that this is really what they wanted.... they found a handy excuse. 
And the Bucklin movement faded rapidly, and I have been unable to 
find clear reasons, it had been very popoular where it was used.

There is no substance to the FairVote "history" on this. People liked 
Bucklin; the Minnesota Supreme Court, noting the popularity and the 
majority of legal opinion at the time that it was lawful, basically 
said, "Too bad! We are the Supreme Court. It is unconstitutional in 
Minnesota because we say so, and if you don't like it, change the 
constitution!" Which they knew would be impossible at that point. The 
two major parties did not want to see an improved voting system 
unless it was going to favor them.