Exchangeability and non-self-averaging

To pass from a deterministic dynamics of aggregate quantities to a probabilistic dynamics of a system of microvariables that describe the individual strategies of a population of economic agents, the route is that of Boltzmann's kinetic theory at the half of XIX century (more suitable than that of Gibbs' statistical mechanics), that is the introduction of n "elements" (molecules, agents,...), submitted to some microdynamics, wherefrom to derive the macroscopic behavior. The macrovariate is interpreted as a (time) mean of the average (on all elements) of the individual study-property at time t. The micro-derivation looks unproblematic if means and averages tend to constant values in the limit n -> ?. If this property, defined "self-averaging" in some recent papers by Aoki, holds, it would separate a deterministic result from fluctuations; consequently well defined macroeconomic deterministic relations prevail. However it is easy to show that in most cases in economy this property does not hold, due to long-range correlation existing among economic agents. If individual agents are not independent but exchangeable, also in the limit n -> ? the coefficient of variation of the macrovariable is finite, which tends to a random limit rather than a constant. Finally the term "indistinguishable agent" is criticized, and the alternative "exchangeable agent" is discussed.