[EM] Advocacy of Kemeny's method

[Steve Eppley]

Mike R wrote:
> Steven B wrote:
>> Does this group, or anyone here, 
>> advocate Kemeny's method?
>
> I personally like it the best of all the methods 
> I've seen, except for the "NP-hard" part. I'll 
> advocate it without reservation when quantum 
> computers become available. :)

The obvious question is, why prefer Kemeny's method?
What criteria does it satisfy that other methods fail
that are more important than the criteria other methods
satisfy that Kemeny fails?

If memory serves, Kemeny is the method advocated by 
H. Peyton Young advocated in his book Equity In Theory 
And Practice.  But Young's argument was flawed, in 
my opinion.  He wrote it satisfies a criterion, 
local independence of irrelevant alternatives (LIIA),
that's a "slight weakening" of Arrow's independence 
axiom, and that is also satisfies a criterion that's 
a weakened form of the reinforcement axiom satisfied 
by the Borda method.  The problems with Young's 
argument are (1) LIIA is a huge weakening of Arrow's 
IIA, not a slight weakening, and (2) reinforcement 
is of little importance because the rules can easily 
prevent a minority from manipulating reinforcement 
failures.

It's easy to show LIIA is a huge weakening of IIA,
since LIIA + clone independence is much stronger 
than LIIA alone.  Clone independence is important 
because clone independence failures are fairly easy 
for a minority to exploit.  It's often fairly easy 
to find and nominate potential candidates that are 
very similar to candidates already under consideration.
And we wouldn't want the rules to prevent minorities 
from nominating candidates.  Under Robert's Rules, 
for instance, it takes only 2 people to propose
an alternative.

Reinforcement failures can be made moot by simply
requiring that the district boundaries remain
fixed unless a majority votes to change them.
In the simplest case, the rules can require that 
the voters not be divided at all, in other words 
a single large district.

So why not prefer a method that satisfies LIIA 
plus clone independence minus reinforcement?  

--Steve