Assuming answers to complex integrals
The basic problem with a lot of discussion of economic methodology is that many people (e.g. [1], [2]) assume they know the answer to this:
$$
\text{(1)}\;\;\; \int dE \;\;\; \left( \hat{O} | H. \;\; economicus \right) \stackrel{?}{=} \int dE \;\;\; \left( \hat{O} | H. \;\; sapiens \right)
$$
where $E$ is an economy and $\hat{O}$ is some observable operator. The integral is just a notational way of representing an aggregation problem using a given agent model. But we don't know the answer. No one does. Anyone who claims an answer is probably just assuming an answer.
On this blog, I make a case that most of the time
$$ \text{(2)}\;\;\; \int dE \;\;\; \left( \hat{O} | H. \;\; atomicus \right) \simeq \int dE \;\;\; \left( \hat{O} | H. \;\; sapiens \right) $$
where $H. \;\; atomicus$ is an even simpler creature that has no brain whatsoever and simply randomly walks into an office, receives money, and then bumps into products and buys them.
And whenever
$$ \text{(3)}\;\;\; \int dE \;\;\; \left( \hat{O} | H. \;\; atomicus \right) \neq \int dE \;\;\; \left( \hat{O} | H. \;\; sapiens \right) $$
it is generally bad news.
I did show that under certain conditions:
$$ \text{(4)}\;\;\; \int dE \;\;\; \left( \hat{O} | H. \;\; atomicus \right) \simeq \int dE \;\;\; \left( \hat{O} | H. \;\; economicus \right) $$
But at the end of the day there is no answer to equation (1).