Example 6-8 number of Outperforming Portfolios

[Joseph-L-Morgan]

First of all thank you for writing this book. It's been an informative read and the examples are fun and challenging.

That being said I believe there is a typo in Example 6-8:
312 outperforming portfolios must mean there are 430.5 honest members of congress. It is quite funny to say that there is a half-honest politician, but 313 outperforming portfolios does result in a whole number of honest and dishonest members of congress who add up to 538. So it makes more sense if the number of outperforming portfolios is 313.

[Joseph-L-Morgan]

In the likely event that I am incorrect here is how I reached that conclusion.

Total members of congress = 538
op = number of outperforming porfolios = 312
hc = honest chance = 50% or 0.5
dc = dishonest chance = 90% or 0.9
hm + dm = 538 or honest members + dishonest members = 538
(honest members * honest chance) + (dishonest members * dishonest chance) = 312

(honest members * honest chance) + (dishonest members * dishonest chance) + 226 = 538
(hm * hc) + (dm * dc) + 226 = hm + dm
(hm * hc) + [(538 - hm) * dc] + 226 = (538 - hm) + hm
(hm * 0.5) + [0.9(538 - hm)] + 226 = 538
0.5hm + 484.2 - 0.9hm = 312
-0.4hm = -172.2
hm = 430.5

[AllenDowney]

I'm not positive I understand the question, but it sounds like you are bothered by the fact that the mean of the posterior distribution is not an integer. I think that's normal. Like the average value if you roll a six-sided die is 3.5. But maybe I'm missing your point.