[EM] A method "DNA" generator, tester, and fixer

[Kristofer Munsterhjelm]

Kevin Venzke wrote:
> Hello,
> 
> I've been working on a new method generator/tester/fixer. I did this once
> before, and my approach is still the same, but now truncation is allowed
> (instead of strict ranking). The old simulation only defined methods on
> 8 scenarios, allowing 6561 possible methods. The new simulation defines
> methods on 27 scenarios, which means 7.6 trillion methods.

Does this thing actually create new methods, as implied by the term 
"generator"? If so, what approach do you use - brute force, genetic 
programming, something different?

> Here are the criteria at the moment. I can make more, and have tried to
> come up with weakened versions of criteria to try to weed out the
> completely absurd methods from ones which may have unusual merits.

(...)

It might be possible to rigorously define these criteria in the case of 
three candidates. Say, for the sake of simplicity, that there is no 
truncation, and

variable = number of voters voting this way:

a = A>B>C
b = A>C>B
c = B>A>C
d = B>C>A
e = C>A>B
f = C>B>A

Then mono-raise failure could be specified as

there exists a,b,c,d,e,f so that:
  a >= 0, b >= 0, c >= 0, d >= 0, e >= 0, f > 0
  method(a, b, c, d, e, f) -> A wins
  ( method(a, b+1, c, d, e, f-1) -> B wins) OR
  ( method(a, b+1, c, d, e, f-1) -> C wins)

with the reasoning that any monotonicity failure can be whittled down to 
the point where a single voter changes his preference, and that if the 
candidates are randomly assigned labels A, B, and C, all such failure 
can also be reduced to the case where A is raised. That A is ranked last 
before the change instead of merely second is required to catch methods 
like antiplurality elimination.

For simple methods like weighted positional methods or elimination 
methods based on WPS, it would be possible to test the method plus 
criterion by the use of a theorem prover.