Rho in a Decision-Theoretic Apparatus of Dempster-Shafer Theory

摘要

In a previously developed decision-theoretic apparatus for Dempster-Shafer theory, 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, where rho is defined as the probability that the ambiguity about the utility of every non-singleton focal element will turn out as favorable as possible. An assumption, unwarranted by the evidence at hand, has to be made about the value of rho. The author demonstrates 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. He discusses when this approach is justifiable.