Against Tabula Rasa, Part 3: Degrees of Belief

In my first post, I argued that the judge is constrained not by possibility, but by rationality. In my second post, I argued that the judge’s starting points for a debate bear on in-round disputes because of conflicting assumptions. My next argument comes from another aspect of rationality. In this post, I set up the general framework for the argument, but the argument itself will be in the next post. 
(Note: In what follows, I may be making simple mistakes or misunderstandings. If you know a thing or two about the technical stuff below, then please correct me in a comment not only if you think I’m wrong about something important, but also if I misuse any terms or concepts.)

We don’t just believe or disbelieve propositions. We have greater or lesser degrees of belief in propositions. These degrees of belief are called credences. For example, I have greater credence in the proposition “2 + 2 = 4” than I have in “It will rain in Oxford tomorrow,” although I believe both.

We can account for degrees of belief through Bayesian statistics. Here are the technical parts:

We have degrees of belief in all well-defined propositions. We can call your initial credences your priors. For example, I just rolled a six-sided die. Before looking at it, my credence in the proposition that I rolled a four is 1/6. When you get new evidence, you update your credences into posterior degrees of belief. Your posterior credences are your degrees of belief after accounting for your evidence. So, after I observe that I rolled a four, my posterior credence in the proposition that I rolled a four is close to 1 (but not exactly 1, since my eyesight may be misleading, or something else may be going wrong). The updating process follows a rule of inference that we can ignore for now.

I understand tabula rasa to be the following view:

The judge’s priors should be as neutral, or uninformative, as possible. When a debater wins an argument for some claim, the judge’s credence in that claim increases. A perfect judge would update her credences based on the arguments in the debate as an ideal Bayesian reasoner. The judge’s posterior credence in the resolution (or in who did the better debating, who she should vote for, or whatever other question you think should determine the ballot) determines her decision. A judge’s decision is better or worse to the extent that it approximates that ideal.

I realize that no proponents of tabula rasa have actually stated their view in this way. But, to be honest, I don’t think they have stated their view precisely at all. I think the above is the best version of what they’re after. (They can’t be after “no priors allowed,” since that’s both impossible and irrational. And, as I argued in the last post, the judge needs priors to evaluate disagreements that appeal to conflicting assumptions.)

But how exactly is the judge supposed to have maximally uninformative priors? In the next post, I argue that this question raises some difficult problems for the tabula rasa view.