  As a means for testing for the presence of influence across individuals, we
discuss the concept of a stochastic choice function for a group of agents which
allows observation of correlation structure (correlated choice rule). We ask
when choice behavior is consistent with an underlying unobserved (latent)
variable or signal which jointly governs preferences: this hypothesis
represents absence of influence. Key is the property of marginality, which
demands the independence of any given agents' budgetary choices from the
budgets faced by the remaining agents. Marginality permits the construction of
well-defined marginal stochastic choice functions. Marginality and
non-negativity of an analogue of the Block-Marshack polynomials are equivalent
to joint stochastic rationality for small environments. For larger
environments, we offer an example of a correlated choice function establishing
that each of the marginal stochastic choice functions may be stochastically
rational while the correlated choice function is not. Thus, the detection of
influence can be aided by studying correlated choice data.
