tag:blogger.com,1999:blog-3891434218564545511.post5961352156926815028..comments2024-03-28T13:23:50.623-05:00Comments on Alexander Pruss's Blog: Invariance under independently chosen random transformationsAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-3891434218564545511.post-90939926408141149012020-08-25T22:55:02.055-05:002020-08-25T22:55:02.055-05:00You can look at Randomized Invariance as a special...You can look at Randomized Invariance as a special case of conglomerability. But note that even if one rejects conglomerability in general, one can accept special, particularly plausible cases of it. I think Randomized Invariance is one such special, particularly plausible case. Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-90457100521955003432020-08-25T14:57:11.120-05:002020-08-25T14:57:11.120-05:00Non-conglomerability.
Defenders of infinitesimal ...Non-conglomerability.<br /><br />Defenders of infinitesimal probabilities must in any case reject conglomerability. So they will not be persuaded by this application of it.<br /><br />To spell out the connection, sketch the argument like this: Fix a mirror position. Say P(all Tails to the right) = ε. Conditional on any specified sequence to the left, P(Palindrome) = P(all Tails to the right) = ε. Therefore unconditionally P(Palindrome) = ε.<br /><br />On Randomized Invariance itself, I guess defenders of infinitesimal probabilities would say that if you want to randomize anything, you have to explicitly model the randomization.IanShttps://www.blogger.com/profile/00111583711680190175noreply@blogger.com