Hello James,
You already know my arguments but maybe I'm able to add some more value
and/or structure to the old discussions.
On May 27, 2005, at 13:02, James Green-Armytage wrote:
I'd like to
briefly argue that minmax methods in general are very significantly
inferior to methods that pass the Smith criterion
First I'd like to check if the reason for the claimed inferiority of
minmax is 1) its insufficient strategy resistance or that 2) it would
elect a candidate that is no good (=poor utility function)? I guess
both. I think it is clarifying to separate these two concerns.
1) Strategy concerns
Yes, minmax methods have some vulnerabilities that some other methods
don't have. In many elections (e.g. in large public elections with
limited knowledge of how people are planning to vote and limited
ability to apply well planned strategies) the strategic vulnerabilities
of minmax may however be non-significant. How far one wants to go in
using methods that are capable of defending against various more or
less significant strategy threats is of course a matter of taste (or
matter of voters' interest in strategic voting, their capabilities of
doing so and the election parameters and society in general). Note that
use of strategy resistant voting methods may in some cases also mean
deviation from the choices of the intended utility function (=winner is
not the best candidate).
2) Utility
There are reasonable / easily justifiable utility functions that don't
meet some of the criteria that you listed (e.g. Smith, Condorcet loser,
mutual majority). I'm of course referring to minmax(margins) and the
fact that it is an exact implementation of "least additional votes to
become a Condorcet winner" that corresponds also to (one definition of)
resistance to mutiny/opposition. I think there may be also other useful
utility functions that may be more applicable in some other type of
elections, but minmax(margins) sure appears to be one obvious and
natural utility function. (Smith is thus a criterion that may be useful
in some elections but not necessarily in all, depending on what people
want to achieve (=utility function) with the election.)
In summary, minmax methods have some weaknesses, but I think they (at
least minmax(margins)) are useful voting methods in situations where
their properties are wanted and their weaknesses are not too bad. The
things that speak in favour of minmax(margins) are utility related.
Minmax(margins) simply implements one very natural utility function.
BR, Juho
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