The value of information and the value of awareness

Recent literature has examined the problem facing decisionmakers with bounded awareness, who may be unaware of some states of nature. A question that naturally arises here is whether a value of awareness (VOA), analogous to VOI, can be attributed to changes in awareness.In this note it is shown, in a sense that will be made precise, that the sum VOA+VOI is constant and independent of the choice set. It follows that, the greater is VOA, the less is VOI. This point is illustrated for a simple two-state case, then proved for general classes of choice sets. The analysis is then extended to cover altenative concepts of choice under unawareness. Keywords:value of information, awareness, JEL code: D8 The value of information and the value of awareness In a modern economy, economic agents routinely make important decisions under conditions of uncertainty. Such problems have been addressed by the literature on the economics of information, beginning with the classic work of Blackwell (1951). In the standard Bayesian framework developed by Blackwell, individuals are endowed with a prior probability distribution over a set of possible states of the world. Before making a decision, they may observe information that enables them to update their prior beliefs, yielding a posterior distribution. The di¤erence between the expected return to the optimal decision based on prior beliefs and the expected return based on posterior beliefs is the value of information (VOI). Recent analysis of choice under uncertainty has challenged the assumption that individuals are aware of all possible states of the world. A growing literature has dealt with the analysis of beliefs and preferences in situations where individuals may be unaware of some possible states of the world (Grant and Quiggin 2013, Halpern and Rêgo 2008, Karni and Viero 2012).1 This raises the possibility that individuals will become aware of new possibilities and raises the question of how they should adjust their beliefs in response. A question that naturally arises here is whether a value of awareness (VOA), analogous to VOI, can be attributed to changes in awareness. In this paper, I examine VOA, represented as the improvement in expected return when a decisionmaker takes all possible states of nature into account in selecting a state-contingent income vector from a choice set. I show, in a sense that will be made precise, that the sum VOA+VOI is constant and independent of the choice set. It follows that, the greater is VOA, the less is VOI. This point is illustrated for a simple two-state case, then proved for general classes of choice sets. An alternative approach to unawareness is to suppose that individuals have access to a partial description of the world, with the result that their representation of the state space is coarser than the full state space that would be considered by an unboundedly rational decision maker (Heifetz, Meier, and Schipper 2006). The implications of this representation for VOA and VOI are also considered. 1 Illustrative example Consider a risk-neutral decisionmaker choosing over a set of state-contingent income vectors Y v R+: Assume Y is strictly convex, satis…es free out1 In the case where state-contingent outcomes are bundles of commodities or characteristics, rather than monetary values, individuals might be unaware of some possible consequences, a case considered by Karni and Viero (2012). In common with most of the literature on the value of information, however, this paper focuses on the case where outcomes are expressed in monetary terms.