Abstract
Let X be a connected metric space, and let ⪰ be a weak order defined on a suitable subset of XN. We characterize when ⪰ has a Cesàro average utility representation. This means that there is a continuous real-valued function u on X such that, for all sequences x=(xn)n=1∞ and y=(yn)n=1∞ in the domain of ⪰, we have x⪰y if and only if the limit as N→∞ of the average value of u(x1),…,u(xN) is higher than limit as N→∞ of the average value of u(y1),…,u(yN). This has applications to decision theory, game theory, and intergenerational social choice.
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