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.
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