Influence, sincerity, and pareto optimality under utility value voting

A decision procedure called utility value voting is considered in which each of several voters provides utility values for each of several candidates. These utility values from each voter are normalized by a positive linear transformation so that a largest normalized value is unity and the smallest is a preassigned nonnegative number less than unity. This number is called the “influence” for the voter. The decision is made using a probability mixture that maximizes the geometric mean of the expected utilities for the voters. It is shown that the procedure is Pareto optimal (efficient), and that the size of the effective minority increases with the influence value. Examples are included to show that insincere voting is not generally advantageous when the insincere voter has no information about the utilities and voting strategies of the other voters. The procedure and its results are illustrated by an engineering design example, where ten teams of scientists were the voters, and by a personnel selection example, where the 27 attributes of each candidate were the voters. The system can be used by a single person, as in the personnel selection example, or by an organization of any size, as in the ten-voter engineering design example.