On rho in a Decision-Theoretic Apparatus of Dempster-Shafer Theory
  Thomas M. Strat has developed a decision-theoretic apparatus for
Dempster-Shafer theory (Decision analysis using belief functions, Intern. J.
Approx. Reason. 4(5/6), 391-417, 1990). In this apparatus, expected utility
intervals are constructed for different choices. The choice with the highest
expected utility is preferable to others. However, to find the preferred choice
when the expected utility interval of one choice is included in that of
another, it is necessary to interpolate a discerning point in the intervals.
This is done by the parameter rho, defined as the probability that the
ambiguity about the utility of every nonsingleton focal element will turn out
as favorable as possible. If there are several different decision makers, we
might sometimes be more interested in having the highest expected utility among
the decision makers rather than only trying to maximize our own expected
utility regardless of choices made by other decision makers. The preference of
each choice is then determined by the probability of yielding the highest
expected utility. This probability is equal to the maximal interval length of
rho under which an alternative is preferred. We must here take into account not
only the choices already made by other decision makers but also the rational
choices we can assume to be made by later decision makers. In Strats apparatus,
an assumption, unwarranted by the evidence at hand, has to be made about the
value of rho. We demonstrate that no such assumption is necessary. It is
sufficient to assume a uniform probability distribution for rho to be able to
discern the most preferable choice. We discuss when this approach is
justifiable.
