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.
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