Axiom 1 - the population whose behaviour was modeled should be sufficiently large.
Axion 2 - the population should remain in ignorance of the results of the application of psychohistorical analyses.
From the Wikipedia entry on Seldon:
Paul Krugman
At the 67th science-fiction world convention in Montreal, Paul Krugman, the Nobel Laureate in Economics, mentioned Hari Seldon. According to Krugman, his interest in economics began with Asimov’s Foundation novels, in which the social scientists of the future use ‘Psychohistory’ to attempt to save civilization. Since ‘Psychohistory’ in Asimov’s sense of the word does not exist, Krugman turned to economics, which he considered the next best thing.
http://en.wikipedia.org/wiki/Hari_Seldon