You might want to look at Dempster-Shafer theory, which is a generalisation of Bayesian reasoning that distinguishes belief from probability. It is possible to have a belief of 0 in heads, 0 in tails, and 1 in {heads,tails}.
It may be that, when looked at properly, DS theory turns out to be Bayesian reasoning in disguise, but a brief google didn’t turn up anything definitive. Is anyone here more informed on the matter?
After looking at the reasoning in that article I was about to credit myself with being unintentionally deep, but I’m pretty sure that when I posed the question I was assuming a fair coin for the sake of the problem. Doh. Thanks for the interesting link.
(It’s really kind of embarrassing asking questions about simple probability amongst all the decision theories and Dutch books and priors and posteriors and inconceivably huge numbers. Only way to become less wrong, I suppose.)
You might want to look at Dempster-Shafer theory, which is a generalisation of Bayesian reasoning that distinguishes belief from probability. It is possible to have a belief of 0 in heads, 0 in tails, and 1 in {heads,tails}.
It may be that, when looked at properly, DS theory turns out to be Bayesian reasoning in disguise, but a brief google didn’t turn up anything definitive. Is anyone here more informed on the matter?
After looking at the reasoning in that article I was about to credit myself with being unintentionally deep, but I’m pretty sure that when I posed the question I was assuming a fair coin for the sake of the problem. Doh. Thanks for the interesting link.
(It’s really kind of embarrassing asking questions about simple probability amongst all the decision theories and Dutch books and priors and posteriors and inconceivably huge numbers. Only way to become less wrong, I suppose.)