This paper proposes and axiomatizes a recursive version of the vector expected utility (VEU) decision model (Siniscalchi, 2009). Recursive VEU preferences are dynamically consistent and ``consequentialist.'' Dynamic consistency implies standard Bayesian updating of the baseline (reference) prior in the VEU representation, but imposes no constraint on the adjustment functions and one-step-ahead adjustment factors. This delivers both tractability and flexibility.
Recursive VEU preferences are also consistent with a dynamic, i.e. intertemporal extension of atemporal VEU preferences. Dynamic consistency is characterized by a time-separability property of adjustments---the VEU counterpart of Epstein and Schneider (2003)'s rectangularity for multiple priors.
A simple exchangeability axiom ensures that the baseline prior admits a representation \`a la de Finetti, as an integral of i.i.d. product measures with respect to a unique probability $\mu$. Jointly with dynamic consistency, the same axiom also implies that $\mu$ is updated via Bayes' Rule to provide an analogous representation of baseline posteriors.
Finally, an application to a dynamic economy a la Lucas (1978) is sketched.