tag:blogger.com,1999:blog-3891434218564545511.post6064679586833834063..comments2021-05-13T12:47:57.847-05:00Comments on Alexander Pruss's Blog: Dutch Books and update rationalityAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3891434218564545511.post-63800181823712892992019-08-29T10:29:35.230-05:002019-08-29T10:29:35.230-05:00OK, I've convinced myself that that if the boo...OK, I've convinced myself that that if the bookie can read Carl's mind, they still can't Dutch Book him. The reason is this: One will always do better against a particular sequence of offers if one's credences are strictly closer to the truth. The bookie can't Dutch Book Alice. But no matter how the two random events come out, double-heads-coin and heads-toss, there is a chance that Carl's credences are either the same as Alice's or closer to the truth. So any algorithm--even one based on reading Carl's mind--for generating sequences of bets that would be a Dutch Book for Carl no matter how his random credence generator comes out would be an algorithm generating sequences of bets that would be a Dutch Book for Alice.<br /><br />Again, none of this really matters much. The post is really just a parenthetical note.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-82725319202306969222019-08-28T13:07:18.157-05:002019-08-28T13:07:18.157-05:00I was thinking that the book covers the eventualit...I was thinking that the book covers the eventualities. Here's the first bet to be offered. (Since there is no data there, that's just fixed.) Then, if the coin toss is heads, here's the second bet to be offered. If the coin toss is tails, instead, here's the bet to be offered.<br /><br />On reflection, though, the proof in my post doesn't work if the Dutch bookie can read Carl's mind and offer a bet dependent on Carl's credence. I don't know right now if it can be fixed.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-73000840383524684662019-08-28T12:16:18.964-05:002019-08-28T12:16:18.964-05:00Is there a requirement that the book be decided on...Is there a requirement that the book be decided on before the first bet? I always pictured it as a Dutch bookie sitting next to the coin-flippers, offering them losing bets opportunistically.<br /><br />Anyway, this all became clearer to me when I figured out that ordinary binary logic has a notion of consistency, and once you start using the range between 0..1 you still need an analogous notion. The Dutch book is a way to make that concept of "probabilistic consistency" concrete, not a practical danger of losing money. Heath Whitehttps://www.blogger.com/profile/13535886546816778688noreply@blogger.com