MBS 93-28
Joint Receipt and Certainty Equivalents
R. Duncan Luce
Several rules have been proposed for calculating the utility of the
joint receipt of two amounts of money in terms of their individual utilities
and/or the utility of their sum. this paper explores how the rules can
be generalized to gambles. A concept of a structure of gambles with a joint
receipt operation & and a certainty equivalence (CE) mapping is described
(Definition 1). Monotonicity of & relative to preference permits simple
generalizations of the rules to gambles (Theorem 1), and general properties
of the utility function are related to general properties of CE (Theorem
2). the latter establishes that several apparently plausible properties
are inconsistent, which raises empirical questions. A homogeneous scaling
property is introduced that leads to a class of joint receipt operations
that have not yet received attention (Theorem 3). Finally, for the restrictive
case of lotteries (random variables), it is shown that if the convolution
operation is monotonic in preference, then the CE mapping is onto addition
(Theorem 4). It is argued that gamblers, at least, must fail monotonicity
of convolution.