On 6/9/05, Chris Benham <[EMAIL PROTECTED]> wrote:
These are interesting questions, and I'll try to take a look at them in the future. I'm going to have to give you a rain check for now, for reasons that will be apparent below.
Quite simply, I was wrong. Daniel Bishop & Araucaria Araucana tried to help me understand this, but I was stubborn & it took a couple of days for the message to sink in. I apologize to them for that.
The primary objective to me is to maximize protection from candidate dropping effects (I avoid use of the term IIA because of its multiple meanings--it's also a constraint against possible election methods). The examples we discussed before show that in some small subset of profiles at least, symmetry maintenance & candidate dropping protection are incompatible. In these cases, symmetry must be broken to obtain our goal.
So, CIBR appears to be less than ideal, which stems from the fact that the weakest candidate isn't necessarily eliminated first. I've managed to work out a fix, which is relatively straightforward & maintains all of CIBR's desirable qualities and apparently meets CC. (I haven't been able to find a failure, but I have no proof.)
I'll post the revised method in the near future.
Thanks!
-Ken
Ken,
Does CIBR (like plain Borda) meet Participation? (a tall order).
If not, does it meet Mono-raise (i.e. is it monotonic)?
These are interesting questions, and I'll try to take a look at them in the future. I'm going to have to give you a rain check for now, for reasons that will be apparent below.
And a more general question: why do you think its better or more
important to meet Symmetry than the Condorcet criterion?
Quite simply, I was wrong. Daniel Bishop & Araucaria Araucana tried to help me understand this, but I was stubborn & it took a couple of days for the message to sink in. I apologize to them for that.
The primary objective to me is to maximize protection from candidate dropping effects (I avoid use of the term IIA because of its multiple meanings--it's also a constraint against possible election methods). The examples we discussed before show that in some small subset of profiles at least, symmetry maintenance & candidate dropping protection are incompatible. In these cases, symmetry must be broken to obtain our goal.
So, CIBR appears to be less than ideal, which stems from the fact that the weakest candidate isn't necessarily eliminated first. I've managed to work out a fix, which is relatively straightforward & maintains all of CIBR's desirable qualities and apparently meets CC. (I haven't been able to find a failure, but I have no proof.)
I'll post the revised method in the near future.
Thanks!
-Ken
---- Election-methods mailing list - see http://electorama.com/em for list info
