I also wonder what kind of bias is introduced by zappers learning about posters. 

This is a KBC, after all. If quality is consistently high, but not increasing, I’d expect zaps to increase, which will look like the writer learning to make better posts.

Thinking through it, I believe that anything which is predictable and/or a function of effort needs to go into the first regression (zaps on quality), because the point is to measure how much "surprise" there was in previous zaps.  So to the extent that user FE captures known factors, including the users' own typical effort levels, it would go into the first regression.

Thanks for asking the question, it was clarifying for me to type that out.

SimpleStacker

How do you want to think about poster fixed effects? Other things equal, some  posters receive more zaps than others.