Conventions and Confusing Continuity Conundrums

byPsy-Kosh10y1st May 20099 comments


The next "How Not to be Stupid" may be a bit delayed for a couple of reasons.

First, there appears to be a certain unstated continuity assumption in the material I've been working from that would probably be relevant for the next posting. As I said in the intro post, I'm working from Stephen Omhunduro's vulnerability argument, but filling in what I viewed as missing bits, generalizing one or two things, and so on. Anyways, the short of it is I thought that I was able to how to derive the relevant continuity condition, but turns out I need to think about that a bit more carefully.

If I remain stumped on that bit, I'll just post and explicitly state the assumption, pointing it out as a potential problem area that needs to be dealt with one way or another. ie, either solved somehow, or demonstrate that it actually is invalid (thus causing some issues for decision theory...)

Also, I'm going to be at Penguicon the next few days.

Actually, I think I'll right now state the continuity condition I need, let others play with it too:

Basically, I need it to be that if there's a preference ranking A > C > B, there must exist some p such that the p*A + (1-p)*B lottery ranks equal to C. (That is, that the mixing lotteries correspond to a smooth spectrum of preferences between, well, the things they are a mixing of rather than having any discontinuous jumps.)

Anyways, I hope we can put this little trouble bit behind us and resume climbing the shining path of awakening to nonstupidity. :)