Efficient Algorithm & Smith Criterion

[Mike Ositoff]

The efficient algorithms, such as the one proposed by Norm,
and Goldfish are of interest because, being more computable
than SD or Schulze when there are many candidates, and if they're
briefly defined, then they avoid those problems while meeting
at least some desired criteria. As always, though, it might be
that the easy computability requires complication of the rule,
or the loss of a criterion.

Say {A,B,C} and {D,E,F} are clone sets, and 
{A,B,C} beats {D,E,F} with 1 vote against.

A>B 5
B>C 6
C>A 7

D>E 2
E>F 3
F>D 4

{A,B,C} is the Smith set.

That more computationally efficient algorithm, since nothing
is unbeaten and everything beats something, starts by dropping
the strength 1 defeats. During that process, nothing becomes
unbeaten or unbeating. Then D>E 2 gets dropped, and E wins.

***

I'm not saying that's likely, but it could be criticized by
academics--the mere fact that it's possible. I don't consider
the Smith criterion to be really important, which is why I
like plain Condorcet. And its violation by the method in
the preceding example would seem an unusual occurrance.

To the trade-off between criteria & simplicity, we may have
to add easy computability, making the trade-off choice even
more complicated.

For me the really essential criteria are Condorcet &
GMC (either version).

So the practical results of Norm's efficient algorithm would
be fine, as far as I'm concerned. 

Maybe it would be good if someone devised a formula to calculate
the best trade-off with respect to simplicity, criteria, &
easy computability. Maybe it's just a matter of asking people
to find out how simple it has to be, and finding out which
methods (all of them?) can do a 20-candidate election in a
reasonable amount of time, and then, among the uneliminated methods,
proposing the one that does best by criteria.

***

I'd be interested in a posting of algorithms for Schulze & SD.
Can one be written whose computation time doesn't increase
roughly with the factorial of the number of candidates?

***

I still don't know Goldfish's properties, because it does something
quite different. But what it does is plausible, and maybe will
turn out to be helpful, results-wise.

***

Mike