So why don’t you just explain how Myerson’s argument works.
It is essentially the same as that of Anscombe and Aumann. Since that classic paper is available online, you can go straight to the source.
But the basic idea is straightforward and has been covered by Ramsey, Savage, von Neumann, Luce and Raiffa, and many others. The central assumptions are that preferences are transitive, together with something variously called “The sure thing principle” (Savage) or the “Axiom of Independence” (von Neumann).
So that particular method (the one in the paper you link) has, to my mind, a rather troubling flaw: it bases subjective probability on so-called physical probability. I agree with what appears to be the dominant position here that all probabilities are subjective probabilities which makes the Anscombe and Aumann proof rather less interesting—in fact it is question begging. (though it does work as a way of getting from more certain “objective” probabilities to less certain probabilities). They say that most of the other attempts have not relied on this, so I guess I’ll have to look at some of those. I’m also not sure Anscombe and Aumann have in anyway motivated agents to treat degrees of belief as probability: they’ve just defined such a agent, not shown that such conditions are necessary and sufficient for that agent to be considered rational (I suppose an extended discussion of those central assumptions might do the the trick).
It is essentially the same as that of Anscombe and Aumann. Since that classic paper is available online, you can go straight to the source.
But the basic idea is straightforward and has been covered by Ramsey, Savage, von Neumann, Luce and Raiffa, and many others. The central assumptions are that preferences are transitive, together with something variously called “The sure thing principle” (Savage) or the “Axiom of Independence” (von Neumann).
Thanks for the link.
So that particular method (the one in the paper you link) has, to my mind, a rather troubling flaw: it bases subjective probability on so-called physical probability. I agree with what appears to be the dominant position here that all probabilities are subjective probabilities which makes the Anscombe and Aumann proof rather less interesting—in fact it is question begging. (though it does work as a way of getting from more certain “objective” probabilities to less certain probabilities). They say that most of the other attempts have not relied on this, so I guess I’ll have to look at some of those. I’m also not sure Anscombe and Aumann have in anyway motivated agents to treat degrees of belief as probability: they’ve just defined such a agent, not shown that such conditions are necessary and sufficient for that agent to be considered rational (I suppose an extended discussion of those central assumptions might do the the trick).
But yes, these arguments are somewhat on topic.
Jack, you might be more interested in the paper linked to in this post.