ntoronto@cs.byu.edu writes:
This is almost precisely the Borda protocol:
No, it is not. The Borda rule requires a linear order, whereas this is a partial order, and complete indifference is possible.
Why? The agents are voting a kind of utility, not a preference. With the addition or removal of a function, the sum of votes for any other function will not change.
And this utilitarian rule has its own big problems. For one, you could argue that it violates the Arrow condition of non-dictatorship because *somebody* has to choose the weights. In particular, weighting the number of levels by one doesn't make a lot of sense: some developers prefer a shallow style with an abstract class and a lot of concrete derivatives, others prefer a hierarchy of abstract classes with several levels before arriving at the concrete implementations. I think it would be a bad thing if devotees of the latter style were discouraged because their users found the convenience of automatic dispatch more important than the (usually invisible) internal type hierarchy. Also, my intuition doesn't rule out the possibility that self *should* be a dictator if it "expresses a preference" -- the Arrow condition of non-dictatorship might not even be appropriate.
I imagine that making next-method calls behave is a nightmare, though. The more I read about multiple dispatch, the less I like it.
It's a hard problem.