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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