Instead, I'd like to present several examples of scenarios where I will argue that randomness clearly is useful and necessary, and use this to argue that, at least in these scenarios, one should abandon a fully Bayesian stance.

Sure. But, in order to check the communication channel, which of those examples do you think I (as one of the people in the previous post arguing for seeing the debate as one over word-interpretation) would disagree with either your content or your presentation? How about Eliezer?

I think I should once again push the point that the language and communication difficulties are the primary drivers of this discussion, not the mathematical difficulties: Eliezer's original post, to me*, is that there is a limited but large case of problems where randomness shouldn't help, and it's disappointing that academics in that field don't know this, and that the terminology they use lends itself to this confusion.

*I should point out I misinterpreted him in one summarization, at least, by shortening a 'kill phrase X and replace it with phrase Y" as "use phrase X as shorthand for phrase Y"