In the chapter of my dissertation on the Greek sources, I had to talk about the size of Persian armies. One of the few details about Persian armies which most Greek writers give is that they had a specific and very large number of men, and no other kind of evidence lets us estimate the size of armies in the field (the Behistun inscription lists the number of enemies killed and taken alive in various battles, and it is possible to estimate how many bow estates or temple soldiers were available in some parts of Babylonia, but neither is a reliable guide to the size of royal armies in the field). The reason why we are so determined to give the size of Achaemenid armies is that the classical tradition tells us that we should.
I side with the skeptics, such as George Cawkwell, who feel that the numbers for barbarian armies in ancient sources are not worth much, and that as they drew on similar populations and administrative systems, Achaemenid armies were probably about as big as Hellenistic and Roman ones. In a broad survey like my thesis, I had no time to propose numbers for specific cases, even if I decided that that were possible. (My master’s thesis lays out the evidence for Cunaxa as clearly as I could, although today I would add a few sentences). While arguments against vast armies are not always perfectly formed, I am not sure that the remaining believers in countless Persian hordes are really driven by the evidence (a great article by T. Cuyler Young has some suggestions about the psychology and literary forces involved). So instead of arguing back and forth about logistics and the lengths of columns, I focus on some other perspectives.