Abd ul-Rahman Lomax wrote:
At 05:03 AM 12/28/2008, Kristofer Munsterhjelm wrote:
Say that Approval distorts towards Plurality. What does Condorcet
distort towards -- Borda? "Let's bury the suckers"? If people are
strategic and do a lot of such distortion, wouldn't a runoff between
Condorcet (or CWP, if you like cardinal ballots) and something
resistant to Burial (like one of the methods by Benham, or some future
method), be better than the TTR which would be the result of
Approval-to-Plurality distortion? If people stop burying, the first
winner (of the "handle sincere votes well" method) will become more
relevant; if they don't, the latter (strategy resistant Condorcet)
will still be better than Plurality, I think.
I'm certainly open to other suggestions. However, practical suggestions
at this point should be relatively simple methods, which is why I'm
suggesting Bucklin. Bucklin distorts toward Plurality. But the
protection of the favorite is substantial enough that many voters *will*
add votes; and historically, in municipal elections, many did. Plenty
enough to impact results.
(FairVote points to a long primary election series in Alabama with only
11% of ballots using the additional ranks, but that seems to be very low
compared with the municipal elections, it's not clear what the cause
was. And my guess is that IRV would have shown quite the same phenomenon.)
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.
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.
Now, that's probably a very complex system: first you have to define
both the sincere-good and the strategy-resistant method, then you have
to set it up to handle the runoff too. But it's not obvious how to be
selfish in CWP (except burying), whereas it's rather easy in Range
(->Approval, or to semi-Plurality based on whatever possibly
inaccurate polls tell you). This, in itself, may produce an incentive
to optimize. "I can get off with it, and I know how to maximize my
vote, so why shouldn't I?"; and then you get the worsening that's
shown in Warren's BR charts (where all methods do better with sincere
votes than strategic ones). In the worst case, the result might be
SNTV-like widespread vote management.
Let's keep it simple to start! Bucklin has some interesting possible
variations: Condorcet analysis could be done on the ballots, and one
runoff trigger could be conflict between the Bucklin winner and a
Condorcet winner. Bucklin is a very simple method to canvass, just count
and add the votes. You can look at a summary of all the votes in each
position and use it. Preferential analysis is different, and requires
the matrix, but at least that can be summed!
Bucklin/Condorcet/Majority required runoff would still be simpler to
canvass than IRV.
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.
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. 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.
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.
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?
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.
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.
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.
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