At 09:28 AM 12/30/2008, Kristofer Munsterhjelm wrote:
The great majority of Condorcet methods use the Condorcet matrix to
determine the outcome. I say great majority because non-summable
Condorcet methods exist. Anyhow, the use of a matrix may seem
complex, but I think that to sum Bucklin votes, you'd also need a
matrix. The matrix would be n (number of candidates) times k (number
of rounds). The first row is the count of approval for each
candidate for first preference. The second row is the count of
approval for each candidate for second preference, and so on. To
determine the winner, you check for a majority in the first row,
then you check for a majority in the sum of the first and second
row, then the sum of the first three rows, etc.
Yes. Bucklin results were reported with such a matrix. Rows:
candidates. Columns: Totals for each rank.
Because these are simply totals of votes in voting positions, they
are easy to totalize, would work with lever machines and any system
that handles multiwinner elections already. You just assign 3
positions to each candidate. (it would work with just two, probably,
but some voters will appreciate the flexibility, and if leaving a
rank blank is allowed without spoiling the next one, it gives voters
who want it some additional "LNH" protection. *The need for this
would depend on preference strength.*)
Thus, in order to have a summable count, you'd have to use matrices
both for Bucklin and Condorcet. The matrices are different matrices
(a Condorcet matrix for Condorcet, and what one may call a weighted
positional matrix for Bucklin), but doing Condorcet analysis
shouldn't make things more complex than either alone.
Well, it depends. I don't think the Condorcet matrix can be generated
by simply summing votes from positions. Each ballot generates its own
unique votes in pairs. To get the votes from position totals, one
would need to actually have the voter vote the matrix. Too
complicated, I'd say. So Condorcet, while it is precinct summable,
isn't as simple to implement and probably couldn't, practically, use
existing equipment and software. Bucklin clearly could.
As long as the Condorcet method is a good one, I wouldn't have much
of a problem with this. If the Condorcet method is good, the
Condorcet completion winner would usually win the runoff, so nothing
lost (except the inconvenience of the second round). In that sense,
having a runoff is itself a sort of compromise option - a hedge
against the methods electing bad (undeserving) winners.
No, there is a common error here. A Condorcet winner is rigidly
defined from the pairwise elections, and does not -- except sometimes
with cycle resolution -- consider preference strengths.
The Condorcet winner, I'd predict, would generally *lose* to a Range
winner, with the same ballots in the primary used for both Range and
Condorcet analysis. I've explained why many times.
Supporters of the Condorcet winner are less likely to turn out in a
runoff than those who support the Range winner, if we assume sincere
votes. Further, with weak preferences, they are more likely to change
their minds, particularly once they are aware of the issues between
the two candidates. *The Range winner* -- if the votes have not been
badly distorted by bullet voting or the like -- is indeed the best
winner, overall.
Some Range advocates think we should just go with the Range winner.
That is actually better than simply going with the Condorcet winner,
*but* there are exceptions. A runoff will test for them!
The most common "voting strategy" would be truncation, which simply
expresses something that is probably sincere! (I.e., I prefer this
candidate strongly to all others, so strongly that I don't even
want to allow competition two ranks down!)
The method can't know whether voters are honestly truncating or are
truncating out of some game theoretical sense.
That's right. However, the division between "honesty" and "game
theoretical truncation" is very poorly defined. You don't make a game
theory move unless you have sufficient preference strength behind it!
You may say that because it can't tell the two apart, there is no
difference, but by imagining sincere preferences and then
considering adversary voter groups, we may see situations where
people could strategize just to get their candidate to win whereas
that would not otherwise be the case.
Yes, but there are severe limits on what they could do in a hybrid
Range/Condorcet method. Voting insincerely in Range, truly
insincerely, would be *very* risky, and generally useless. Maximal
strategy simply shoves votes to the extremes; with very good
knowledge of the context, this can be safe. With poor knowledge, it
can be disastrous. The sincere vote, reasonably considered, is
probably the *personally* safest vote. It doesn't aim for quite so
much benefit as an exaggerated vote, perhaps, but it does not risk
the worst outcome, either. (The worst outcome is that one's vote, had
it been different, would have avoided the election of the worst
candidate as considered by the voter.)
Burial in Condorcet is one such situation, but truncation, too, can
be gamed. For the sake of the argument, let's consider three groups.
The first group knows the votes of the other groups. This is not
necessary, but I'm making these simplifying assumptions so
constructing the puzzle is easier.
Just so it's clear, this assumption can drastically take our example
away from reality. Whenever any group knows the votes of the other
groups, it can then arrange its own vote for maximum effect from
their point of view. It is practically a tautology. The group can be
as small as one voter, the only difference between that and a large
coherent group is that the possibility of being able to affect the
outcome is larger, and if knowledge is certain, it is either moot or
a certainty.
10: C > B > A
10: A > B > C
5: B > C > A
1: C > A > B
In Bucklin, after the first round, there is no majority. After the
second, B wins (20 out of 26 > 13). But say that the C-voting group
knows all the (sincere) preferences. Since they've put C > B > A,
they want C to win. Is there any way they can force that by truncating?
Now, right off, I don't find election examples meaningful if we don't
understand the preference strengths. Strategy that makes sense with
one set of such strengths may make no sense with another.
There is no first round majority. These voters, let's assume, really
want C to win, they have a significant preference for C over the
others, even over B. If the preference strength for C over B were
small, truncation might not make sense -- and it would be difficult
for a group to gain coherence from its members. But strong preference
in a three candidate election, could be common.
So what would I predict, right off? They know that C and B are frontrunners.
Standard approval strategy: vote for one. Supporters of frontrunners
have no motivation to add a preference for the runner-up.
They will truncate, under the large preference assumption, bullet
voting. Your point?
10: C
10: A > B > C
5: B > C > A
1: C > A > B
First round, there's no majority (A has 10, C 11, B 5). Second
round: 16 C, 15 B, 11 A). So truncation paid off.
Yes. Same as with Approval and range. But suppose the C>B preference
is weak. In real elections, only some of the C supporters will
truncate, others will vote for B in second rank. B will win.
Look, want to understand these examples, start with *sincere Range
votes*. Want to understand what would happen in a runoff, start with
absolute utilities! don't normalize at first, only normalize when
converting them to votes, and exclude the voters who have low
*intrinsic* preference strength -- i.e., absolute utility difference
between the candidates. (Most simulations I know of assume that all
voters have the same overall possible utility range. That is a *very*
poor assumption, inaccurate. Some voters aren't going to vote unless
you stick them with a cattle prod.)
Note that I've made no mention of the strength of the C-supporter's
support of C, just that their sincere preference is C > B > A. By
truncating, they got C to win.
In Condorcet, tricks like this can result in game-of-chicken
dynamics (if each faction has sufficient knowledge of the others'
preferences for the previous round). There's nothing special about
truncation that makes it resistant to strategy.
The game of chicken, if practiced, causes majority failure. *This is
why runoffs are needed.* The "game of chicken" actually shows strong
preference, it doesn't happen with weak preference.
That there is a runoff would probably encourage more truncation;
however, supporters of truly minor candidates can make their minor
candidate statement and prevent compromise failure in the primary.
They will continue to add additional preference votes, and it is
this that will generally prevent Center Squeeze.
True, the runoff would soften the impact of truncation. On one hand,
that's good because it reduces the destructive outcome if all
strategize (the metaphorical car crash when nobody veers). On the
other, it may encourage voters to strategize more because less is on the line.
"Strategizing more" isn't a bad thing. That it is has been an
assumption that has poisoned our consideration of these issues a long
time. Excessive strategization -- which in an Open Voting system is
severely restricted -- simply leads to majority failure. If the
voters would rather see a runoff than abandon their strong vote,
*that is their choice.*
"Strategy" is how voters express preference strength in a vote or
no-vote method. I have some doubt whether or not, in full,
hi-resolution Range, we can even consider approval-style votes to be
"dishonest." They are vNM utilities, which are, indeed,
game-theoretic, in the very natural sense that we all employ
instinctive game theory.
Bucklin *allows* voters to do something other than "strategize." A
plurality primary *only* allows strategy. Voters can and will add
additional preferences, and these will find *some* majorities that
would not be found with a plurality primary. My very rough estimate
is that about half the otherwise-necessary runoffs will be avoided,
which is pretty good for a practically no-cost system. (Even
hand-counted, remember, only up to a third or so of voters will add
additional preferences, sometimes considerably less, and with
hand-counting, it is only the additional votes which create
additional counting labor needed.)
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