Ok, to move this forward, let's move past the who has read what part, which doesn't seem to be helping. Anyhow, my point is relatively subtle, I think, and getting lost in communication somehow. I get what the article is saying, but I'm not sure that everyone here is getting what I'm saying.
Let me try to elaborate. My points are:
1. The article does indeed criticize the 1/3, 1/3, 1/3 split, but not for the same reasons that I am.
2. I would prefer that the 1/3, 1/3, 1/3 split not be used as a prior at all. (Yes, I get that Bayesian priors don't matter that much if you have enough data to update them. The article, on my reading, does not offer a way to get the needed observations, so I think the priors dominate.)
3. Yes, later, the article dismisses the even split as naive but does not go far enough when suggesting a better way. You see, the "better way" still boils down to the naive assumption of counting bins: this is to say that if we have more bins, then we should have a higher expected probability. In my opinion, the "better way" is still falling into a conceptual trap: this is not a combinatorics problem. For combinatorics problems to work they have to rely on real, countable things, not arbitrary notions of how you slice and dice a problem. Yes, I get that as you add more variables to the DAG, you can certainly say that there are more possible paths through the graph. But we cannot assume that just adding more nodes in the DAG will change reality. You see, the DAG is a mental construct. We should not assume that adding more mental bins (an arbitrary way of slicing reality) will affect the distribution.
Here is an example. Francis tells Greg there are three marbles in a jar (green, red, blue) but does not reveal the distribution, so Greg cannot rightly assume a 1/3, 1/3, 1/3 distribution. But let's say Greg does anyway. Next, Francis tells Greg, "Sorry, I was oversimplifying before; really there are 4 types of marbles in a jar (forest green, lime green, red, blue)." What should Greg do? Update the prior to 1/4, 1/4, 1/4, 1/4? Well, that would be inconsistent, since 1/4 (forest green) + 1/4 (lime green) does not equal 1/3 (green). Should Greg suggest a 1/6 (forest), 1/6 (lime), 1/3 (red), 1/3 (blue) split? Nope. My point is this: down that road lies arbitrariness and contradictions.
Hopefully this helps explain what I'm talking about. I like the article, but I don't want people to get into the habit of assuming a distribution. I also don't like people counting up concepts that are arbitrary and turning that into a distribution.