At 10:12 PM 5/16/2010, Dave Ketchum wrote:
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.
Dave, you apparently don't understand a good deal of what you read.
That's okay, take your time.
My point was about your use of "demanding ratings details," which is
not intrinsic to range methods. In particular, I've been pointing
out, Borda is a ranked method that is a Range method, and it becomes
full range if the method simply allows one to equal rank any two (or
more) candidates without disturbing the points given to other candidates.
The most fully expressive ballot is a Range ballot, of course, and
the higher the resolution, the higher the allowed expression.
The simplest way to understand this is through this progression:
Plurality. Vote for one, candidate with the most votes wins.
Approval. Vote for one or more, candidate with the most votes wins.
Range. Vote for one or more, fractional votes allowed, candidate with
the most votes wins.
What distinguishes Range from Ranked methods is the allowance of
fractional votes. However, once it is possible to vote fractions, and
particularly if the resolution (fractional increment) is fine enough,
a Range ballot can fully express ranking, which is a Range ballot
interfaces with a ranked ballot. Borda is a range method that is a
ranked method, and the connection is that the number of unique
ratings is equal to the number of candidates, thus a Borda ballot has
adequate resolution; however, typically, Borda ballots prohibit
assigning the same rating to more than one candidate, and all ratings
are assigned or the vote is diluted. If overvoting and empty ranks
are allowed, Borda is simply Range (N-1), where N is the number of candidates.
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.
You have not understood the "extensions," which may be because your
lack of understanding causes them to seem complex.
All this stemmed from your complaint or comment that range methods
"demand" ratings details. They don't. You can vote a Range ballot as
Borda, generally. Just spread the votes across the range. It's
trivial if the number of ratings allowed is the number of candidates.
But you seem to assume that "Range" involves some particular number
of ratings; you cited Range 99, when, quite likely, Range will be
implemented with much less than 100 ratings (0-99 in Range 99).
"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.
Yes, you did. However, you also assumed a very high resolution range,
thus creating an appearance of some difficulty. Your stated condition
can be expressed with a Range 3 ballot: A 3, B 2, C, 2, D, 0. In real
terms, if the difference between A and B=C is 99 to 98, and if D is a
viable candidate, there really is no difference at all, it is a
formal expression of preference without significant substance.
However, if D is not a viable candidate and is "Satan," then the
ratings of B=C have been disturbed by the presence of D. It's a
complex subject, in fact.
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.
Sure, you aren't. But the only difference is the existence of empty
ranks. I'd have thought that obvious. I expressed an empty rank with a "."
I wrote that it was the "same ballot." That means that the ranks are
laid out on the ballot for you to specify. You can leave a rank
empty. This is actually how Bucklin was implemented, and it is this
that made Bucklin a Range method. The empty ranks have significance.
They indicate a preference strength. The problem with pure
preferential ballots is that they show no preference strength. A>B>>C
is just A>B>C.
Now allow equal ranking on the same ballot.
I.e., a ballot with fixed ranks. IRV ballots are sometimes set up
this way, with facility for ranking all candidates (making the ballot
the same, effectively, as a Borda ballot), or for ranking a fixed
number. But preferential interpretation of that ballot means that an
empty rank is meaningless, it is simply skipped, as if it did not
exist. In Borda/Range, it has meaning.
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.
Do you understand the notation now? The first example, A>B=C>.>D
means just what you said. But you could also have ranked them
A>.>B=C>D, which would mean something a little different. Instead of
liking B and C almost as much as A, you, rather, dislike B and C
almost as much as 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.
And then I've introduced a real consideration: strategy. There is a
serious problem with assuming that ratings on a range ballot should
simply reflect relative "like" or "dislike." The fact is that we make
choices based on real possibilities, not merely on absolute
preferences. And it's necessary unless there is some way for a method
to "amplify" our preferences once irrelevant alternatives have been
removed. That is, in a way, what preferential methods do, though it
isn't normally described that way, and doing it without
discrimination means that trivial preferences are given the same
weight as strong ones. The paper from Voting Matters, latest issue,
that used a Range ballot allowed what might be called a "sincere
absolute range expression," with other data that, if I understand the
paper correctly, caused "expansion" of the voting power over a
narrower set, thus allowing the kind of vote that could be:
A:100
B:51
C:49
D:0
Where A was the Messiah, and D was the Antichrist, and B and C are
the real candidates. If I get it correctly, the voter's additional
expression would cause the B and C votes to be expressed with full or
appropriate strength. In Dhillon-Mertens Rational Utilitarianism --
which is Range voting -- the voter does this, and might vote A:100,
B:99, C:1, D:0. The absolute utilities have been modified by real
election probabilities.
Unless one, for example, thinks of D as a frontrunner, in which case
one might well vote A:100, B:99, C:98, D:0.
Bucklin with runoff can handle this case reasonably well.
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.
Yes. And that's what I described. But you made the decision more
complex by imagining a high-resolution Range method. If D is not a
realistic outcome, you then may have over-rated B and C. Essentially,
you rated A, B, and C all the same, for most practical purposes.
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.
Depends on the canvassing method. Bucklin is cool because you can
express any significant first preference with very little harm, yet
still vote maximum strength for your second or third choices.
Bucklin/Runoff even allows you to postpone the lower choice decisions
to a runoff, unless you see a danger of your least favorite winning
in the primary.
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?
Yes, you don't understand. It's been explained before, you either
didn't read it (which is fine) or you didn't understand then, either.
Take a three-rank Bucklin ballot. Suppose a voter votes for a
candidate in both second and third rank. When is the vote counted?
The only law I've seen that considered this specified that the vote
was counted in the higher rank. That's arbitrary, but better than
tossing the vote. It could have been that it would be counted at the
lower rank. The problem with Bucklin and voting machines was that
both the votes would be counted, unless the ballot was arranged
properly so that such overvotes would be impossible. This requires
that the ballot be arranged so that each candidate is, as it were, an
independent race, vote-for-one-rank-only.
But with hand counting or more sophisticated machine counting, the
vote could be counted as if it were in rank 2.5. That would mean that
it is not counted in the second round, but before the normal third
round. This would allow finer ranking. Otherwise the possible
information is discarded. Which is better? In any case, the voters
should know how such a vote will be counted.
This interpretation of such overvotes could turn a three-rank Bucklin
ballot into a five-rank one, with no fuss or extra ballot space taken
up. Indeed, it would convert a two-rank ballot to a three-rank one.
And I don't think it would be at all difficult to understand.
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?
Why not?
How overvotes are handled is an important topic. It's the "equal
ranking" topic, really, which certainly is relevant to Condorcet
counting methods.
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.
You are showing, Dave, that you have completely missed the point.
Again, you use "must." No, a Range ballot can simply be a list of
ranks. On a real ballot, you would not enter numbers at all, but the
voting positions might have numbers attached. With low-res Range,
they might have names. I've described a Bucklin ballot that is a true
and complete Range 4 ballot, it would have names like
Favorite(s)
Preferred
Acceptable
Less than Acceptable
Rejected
Sort the candidates into these five categories. The top three
categories are approval votes if you place the candidate there. The
lower two categories are disapproved categories and are used for
Condorcet analysis and runoff determination, probably.
The magnitude of preference between two candidates is expressed on
this ballot by the rank distance. On this ballot, the rating step
between ranks can be expressed as 0.25.
Bucklin is a method which steps down what can easily be seen as a
Range ballot, adding in approvals when the sliding down of Approval
cutoff reaches candidates. Classic Bucklin had only three ranks, and
was equivalent to a Range 4 ballot with the ratings of 0 and 1
combined (into 0). Any approved candidate was rated at or above
midrange (which sets midrange as the average expected election value,
classic approval voting strategy).
The theory can get somewhat complex, but the actual voting was very
simple. I'm suggesting tweaks for the use of Bucklin in runoff
voting; these tweaks would make it Condorcet compliant, or so close
to compliant that the difference would be merely theoretical and very
unlikely to show up in actual elections. (Depends on the runoff
rules, but I've suggested that any Condorcet winner should be
included in a runoff, and the ballot contains good data for the
determination of that.)
The above ballot, with an explicit Rejected rating (which would also
be assumed, I'd prefer, for any non-rated candidate), can become even
finer in expression of the "overvoting" scheme is followed. By using
multiple rank expression, the five single ratings become nine
possible ratings. My opinion is that this is more than adequate. But
the voter does not need to pay attention to these complications
unless the voter needs the flexibility.
...
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