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Ordinal Preferences and Uncertain Lifetimes

Peter C. Fishburn

Abstract

Axioms for an individual's preferences over time, taken from the present perspective, usually assume that the individual will live, or expects to live, throughout a given horizon span. This paper offers an axiomatization that explicitly recognizes the uncertainty of an individual's lifetime. It divides a horizon span into n periods and assumes that if death is not immediate then it will occur at the end of one of the periods. The theory is based on an unconditional preference relation over potential future consumption streams that accounts for uncertain lifetime, along with a conditional preference order that is based on the hypothesis that death will occur at the end of period i. There is a conditional order for each i from 1 to n. The utility representation involves an order-preserving utility function for each of the n conditional orders such that one potential consumption stream is unconditionally preferred to another if, and only if, the sum of the conditional utilities for the first stream exceeds the sum of the conditional utilities for the second. It is argued that the theory seems fairly reasonable only if probability of survival does not depend significantly on past consumption.