I am no longer confident in the arguments presented in two parts of this paper:
1) Section 7.1, when I argue that it is impossible to translate all of the paradox regions outside the unit simplex. As I try to visualize it, I am sure that the statement is correct, but I don't know that the method of argument is correct.
2) Section 8, where I argue that Type 1b stages must be point systems with quotas. I argue that if we think of it as a Type 1 stage augmented with Type 2 inequalities, then the Type 1 stage must always return a winner to avoid FBC violations, in accordance with the results of section 7.1. (Note that my concerns in section 8 are independent of the validity of the theorem in section 7.1. Even if the theorem is correct, I might not be applying it correctly.) Suppose that the Type 1 stage sometimes returns no winner, but only in cases where the Type 2 inequalities don't return a winner either? Then it's the non-satisfaction of the Type 2 inequalities that moves the method to the next stage, not the non-satisfaction of the Type 1 inequalities. So I have to figure out whether this is possible. I can prove that it's impossible in a restricted case, but I don't know about the general case.
It still comes in my feed, it's just well over my head. :)
ReplyDeleteAre you ever going to publish the paper? I'd suggest that if there's some hairy issue you can't resolve, instead of waiting until you triumph, you should find some way to bracket that issue and publish more-or-less as-is.
ReplyDeleteThe hairiest issue to sort out is finding the time to sit down and think this through when I have so many other projects on my plate. Whether I resolve the problem or bracket it, I have to put some time into it.
ReplyDeleteOK. Just remember: there are those who actually do care.
ReplyDelete