[EM] minmax is not a good public election method

[Juho Laatu]

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