Epistemic Role of Simplicity

Over at Certain Doubts Mike Huemer started a really interesting discussion of the epistemic use of simplicity. I wanted to fill out my comments there and in a bit propose another more inchoate response than I was willing to post there.

I suggested there that

(S1) When multiple theories cover the data, the simplest is the most reasonable to believe
is a priori in the sense that it is constitutive of our concept of reasonable belief. I think this is especially clear when it comes to a deontological conception of reasonable belief for the following seems clearly true to me.

(S2) We don't have a right to posit any more (kinds or tokens of) entities than are required to cover the data.

From this it follows that

(S3) To posit more (kinds or tokens of) entities than are required to cover the data is unjustified.

I think these are basic facts about rationality.

This suggests the following account of theory simplicity.
(S4) Theory H1 is simpler than theory H2 iff H1 postulates fewer (kinds and/or tokens of) entities than H2.

I think all these principles have the positive feature of being platitudinous. I think at one time they would have been accepted as platitudes by philosophers and surely are accepted as platitudes by the innocent folk (in this case a plus in my view).

The question of whether simple theories are more objectively likely to be true is, I think, of the same status of the question of the justification of induction and therefore a very very deep and difficult problem. I think the most interesting question in the present approach concerns (S4).

(SQ1) How many new tokens are worth a new type?

(S4) is quite indeterminate w.r.t. answers to (SQ1). The main options are

(A1) It is always better to postulate more tokens than a new type.(A2) At some (vague) point, it becomes better to postulate a new type than new tokens.
Here's the sort of conflict I envision: H1 covers the data by postulating many billions of particles of a single type, whereas H2 covers the data by postulating, say, *two* token particles of two different types. (A1) strikes me as right at first, but this consideration makes me pause to reconsider (A2).