tag:blogger.com,1999:blog-3891434218564545511.post3381528026087847673..comments2024-03-28T19:56:42.305-05:00Comments on Alexander Pruss's Blog: Do Popper functions carry enough information?Alexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-3891434218564545511.post-13339434853578563532020-09-05T01:02:10.929-05:002020-09-05T01:02:10.929-05:00True. Pity.True. Pity.IanShttps://www.blogger.com/profile/00111583711680190175noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-58248149171009752462020-09-04T09:26:13.594-05:002020-09-04T09:26:13.594-05:00Ian:
Alas, that ranking is not transitive. Consid...Ian:<br /><br />Alas, that ranking is not transitive. Consider A=(1/4,1/2], B=(1/2,3/4], C=(1/4,1/2) in the uniform case on [0,1]. Then P(A-B|AΔB)=1/2, P(B-A|AΔB)=1/2, P(C-B|BΔC)=1/2, P(B-C|BΔC)=1/2, P(A-C|AΔC)=1, P(C-A|AΔC)=0. So, A≤B, B≤C, C<A.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-8085603976338777802020-07-29T03:43:28.116-05:002020-07-29T03:43:28.116-05:00This comment has been removed by the author.IanShttps://www.blogger.com/profile/00111583711680190175noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-87261835376018840712020-07-23T12:16:09.709-05:002020-07-23T12:16:09.709-05:00That's clever.That's clever.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-77265016137847714172020-07-23T04:51:39.028-05:002020-07-23T04:51:39.028-05:00Maybe you could define the probability ranking dif...Maybe you could define the probability ranking differently. Rank A and B according to the comparison of P((A-B) | (A-B) ∪ (B-A)) with P((B-A) | (A-B) ∪ (B-A)).IanShttps://www.blogger.com/profile/00111583711680190175noreply@blogger.com