On May 9, 2010, at 2:34 AM, [email protected] wrote:
Here are some more late comments (I was busy with some other
activities for a while).
Juho,
Thanks for your interest and input.
Having an approval cutoff to rank just like the candidates is a good
idea. On ballots where the cutoff is
ignored (i.e. truncated) then all ranked candidates are ranked above
the cutoff.
In general, I don't think that voters will truncate a decent
Condorcet candidate, since voters will tend to rank
the lesser evil last and truncate the greater evil when they think
no really good candidate has a decent
chance of winning.
I was thinking about situations where both left and right wing have a
good compromise candidate. Let's say that both wings have one extreme
and one moderate candidate (XL, ML, MR, XR) and the extreme ones have
more support within their wing.
Let's first assume that left wing voters will not rank (nor explicitly
approve) the right wing candidates and vice versa (but most of them
rank candidates of their own wing).
As a result one of the extreme candidates (let's say XL) will probably
have greatest approval, and XL will pairwise beat ML.
- If left wing has majority then XL will win
- If right wing has majority then XL is probably covered by both right
wing candidates and XR will win
Conclusion: We need more approvals and/or rankings across the border
line between the two wings if we want to elect good compromise
candidates in this set-up. Voters must use the implicit approval
cutoff so that they "approve" also candidates that they may strongly
dislike and that are the strongest competitors of their own favourite
candidates. The supporters of the extreme candidates may need to rank
both their first compromise candidate and also the compromise
candidate of the other wing (if there are not many enough supporters
of the moderate candidate to do the job).
(One could also generalize this so that any Condorcet method that
encourages truncation to separate one's favourites and those that are
not carries a risk of making the sincere Condorcet winner lose.)
Let's then assume that sufficient number of left wing voters will rank
the moderate right wing candidate and vice versa so that the moderate
candidates will pairwise beat the extreme candidates of their own wing
(ML>XL, MR>XR). In this case we will probably have a Condorcet winner
(ML or MR).
Then let's try to see what will happen when there is a top cycle (and
the approvals may influence the outcome of the election). Let's say we
have a third wing with candidates MT and XT. We also assume that
voters will rank the moderate candidates of the other wings
sufficiently so that they will both beat and cover the extreme
candidates. The winner must be one of the moderate candidates then.
The moderate candidates are looped, so none of them cover any of the
others.
In this situation any approval that a voter gives to the moderate
candidate of some other wing increases the probability that the winner
will be that candidate and decreases the probability that the moderate
candidate of one's own wing will win. It seems that a good strategy
(with explicit approval cutoff) could be to approve some of the
expected frontrunners (that might become looped) (not all of them, not
none of them). If one wants to use an implicit cutoff, then maybe
something like "approve all but the last ranked candidate(s)" could
work. Or maybe "approve all but the last two ranked candidates" since
the size of the cycle is at least three and this might often enough
lead to a bullet approval vote to one's favourite among the three
frontrunners. If voters know that there is such an approval cutoff
they might also give fuller rankings (good!) since they would now
happily rank also the compromise candidates of the other wings as
"ranked but not really approved" (and ranking one of the favourites
just above the truncated / tied last candidates would carry a flavour
of not approving them).
(Another psychological trick would be to use ballots that have a
"green" section to rank the nicest candidates and a "red" section to
rank the less liked candidates. It would feel natural to fill also the
"red" section. Also here I try to get full rankings of all the
potential winners.)
(And yet one more and more complex approach would be to have also a
third neutral section that could be used in Bucklin style to find the
most approved candidate when there are too few "green" approvals.)
Now, changing the subject slightly, remember DMC? In that method
if the second place approval candidate
beat the approval winner pairwise, then that was enough to keep the
approval winner from being elected. In
MEA tha's not enough, but if the second place approval candidate
covers the approval winner, that is enough
to keep the approval winner from being elected. So MEA takes
approval somewhat more seriously than
DMC.
Both DMC and MEA are based on a serial process. What do you think of
comparing directly the uncovered candidates and their approval levels?
Does the serial process that is used in MEA improve the results when
compared to jumping directly to the uncovered candidates?
My proposals on explicit cutoffs are problematic in the sense that in
real life elections most decisions would probably be done based on
rankings only, and therefore the approval cutoffs are just extra work
to the voters in most elections. Maybe explicit cutoffs would provide
at least some interesting statistical data. And they might encourage
voters to rank also other candidates than their favourites.
Juho
Forest
From: Juho
To: EM Methods
Subject: Re: [EM] Proposal: Majority Enhanced Approval (MEA)
Message-ID:
Content-Type: text/plain; charset=WINDOWS-1252; format=flowed;
delsp=yes
You seem to use implicit approval cutoff at the end of the
ranked
candidates (since you say "based on ranked ballots with
truncations
allowed"). How about using explicit cutoff? Would that take away
something essential? I'd like the left wing voters rank also the
right
wing candidates and vice versa. Otherwise we might easily lose a
sincere Condorcet winner.
Juho
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