I still include minmax(margins) in the set of good Condorcet methods,
also for practical elections. AWP style defeat strength measuring is a
very interesting addition to the Condorcet family. It may be a bit
tedious to the voters but in principle very interesting as said. Also
variants of the AWP preference strength rule would be interesting.
In minmax(margins) I'm not very worried about those criteria that it
violates and some other popular Condorcet methods meet since those
situations are typically rare and often one may also argue that in
those cases one actually should violate those rules. I won't cover the
numerous details in this mail. I note also that different elections
may have different needs on what kind of properties the winner should
have, so different methods may be used for different needs. In
addition minmax(margins) is simple, easy to understand, implements one
very natural utility function (least additional votes to win all
others) and the results can be shown nicely e.g. as histograms that
clearly show how close each candidate is to winning the race at any
point during the calculation process or when the results are final.
I do have some worries about minmax(margins). Some of the properties
that are commonly mentioned as the key problems may sometimes be even
like requirements to me (e.g. ability to elect sometimes outside the
Smith set may well be a requirement in some elections). The problem
that I refer to here (and that is usually not covered anywhere) is the
possibility to artificially create a cycle or strengthen a cycle e.g.
so that all candidates in the Smith set are strongly looped. As a
result a candidate outside the Smith set may (strategically) win in
minmax. I guess also this is not a major vulnerability in practical
elections (requires too much coordination), but at least this is an
additional vulnerability of minmax that most other common Condorcet
methods do not have.
I like the minmax style of comparing the winning candidate to other
potential winners (to measure in some (not perfect) way "the strength
of opposition against the winner" after the election). The path based
methods have some clone related properties that people may want but
the philosophy of chained pairwise victories do not make as much sense
to me (as a target) as direct (one step) comparison of candidates.
(As I recently wrote I also don't like heuristics that try to force
the group opinions into some linear ordering (often called "breaking
of the cycles"). Group opinions may be cyclic and there is no "right"
non-cyclic preference order that would be more correct than the
original cyclic opinion. We should learn to live with the idea that
the group opinions are sometimes cyclic and we need to understand
which candidate would be the best winner in that situation (not
necessarily one of the top cycle candidates, as you can guess :-).)
In addition to listing the theoretical vulnerabilities of different
election methods I put a lot of weight on real life like examples of
the vulnerabilities. It is not easy to construct examples that would
demonstrate obvious vulnerabilities in typical (large, public etc.)
real life elections. All typical Condorcet methods are actually pretty
good in typical real life elections. Many criteria are also
incompatible with each others, and in these situations the real life
like examples offer a reasonable basis to estimate which rule should
be violated (to get the best winner with sincere votes or to defend
against the most plausible strategy).
If A wins and then another ballot with A ranked unique first is
added to the count, A still wins.
This criterion seems to be a close relative of the "the candidate that
needs least additional votes to win all others wins" rule (that
defines minmax(margins)). The "additional votes" should be ones where
that candidate is "ranked unique first".
Here's one example for minmax(wv).
1: A>B
2: B
2: C>A
A wins. Then we add one ballot with A ranked unique first.
1: A>C
A and C are tied. A doesn't necessarily win any more. Was the weak
version intended to cover both minmax(margins) and minmax(wv)?
Knowing that Beatpath satisfies the weaker version but not the weak
version may be an inducement for voters to bullet vote candidate A
to make sure that they avoid the no show paradox. But MinMax is
free of this temptation; they wouldn't have to truncate the other
candidates.
Condorcet methods give good results only with good input. One should
try to keep the level of bullet voting and truncation low (except if
the voter really feels that the remaining candidates are practically
equal (maybe equally unknown)). Minmax(wv) has some truncation
incentives. I however do believe that in real life elections most of
the truncation does not emerge because of the technical properties of
the used method but for some more generic reasons like laziness to
rank all candidates or (mainly irrational) fear that ranking a
competitor of one's own favourite would somehow generally support that
candidate and help him/her beat one's favourite candidate. The true
properties of the method could be used in propaganda to encourage
truncation, but as seen in real life the real life, propaganda is
often not very rational. Quite as well the truncation arguments could
be irrational and the (even marginally) rational arguments could be
ignored :-). So, in real elections one should just try to make the
voters feel comfortable with the idea that with the used (Condorcet)
method it is wise to just sincerely rank numerous candidates and not
truncate (and not try any stupid strategies that might hurt more than
help).
Juho
On Apr 22, 2010, at 12:36 AM, [email protected] wrote:
I don't know if Juho is still cheering for MinMax as a public
proposal. I used to be against it because of its clone dependence,
but now that I realize that measuring defeat strength by AWP
(Approval Weighted Pairwise) solves that problem, I'm starting to
warm up more to the idea.
MinMax elects the candidate that suffers no defeats if there is one,
else it elects the one whose maximum strength defeat is minimal.
There are various ways of measuring defeat strength. James Green
Armytage has advocated one called AWP as making Condorcet methods
less vulnerable to strategic manipulation.
If all ranked candidates on a ballot are considered approved, then
the AWP strength of a defeat of B by A is the number of ballots on
which A is ranked but B is not.
Then more recently I was reading a paper by Joaquin Pérez in which
he shows that MinMax is the only commonly known Condorcet method
that satisfies the following weak form of Participation:
If A wins and then another ballot with A ranked unique first is
added to the count, A still wins.
Beatpath, River, Ranked Pairs, etc. fail this weak participation
criterion, but they do satisfy this even weaker version:
If A wins and then another ballot with only A ranked is added to the
count, then A still wins.
Proof: First add a ballot in which no candidate is ranked. The
above mentioned methods allow this, and it doesn't affect their
outcome since no mention of absolute majority is made in any of
them. Then raise A while leaving the other candidates unranked.
This cannot hurt A since all of the above mentioned methods are
monotone.
Knowing that Beatpath satisfies the weaker version but not the weak
version may be an inducement for voters to bullet vote candidate A
to make sure that they avoid the no show paradox. But MinMax is
free of this temptation; they wouldn't have to truncate the other
candidates.
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