Group Preference Aggregation Rules Based on Strength of Preference

In many decision problems, the consequences of an action may impact several individuals, and the decision may be based on the preferences of those who are affected. The rule for aggregating these individual preferences is called a group preference aggregation rule. In this paper we present a theory for group preference aggregation rules based on the concept of strength of preference. This concept is operationalized by asking an individual to order differences in his strength of preference between pairs of alternatives. A preference representation function that reproduces this ordering is called a measurable value function. In general we cannot expect a measurable value function and a utility function obtained from lottery questions to bear any particular relation to each other. A group preference aggregation rule based on the measurable value functions of individuals can be used under conditions of certainty without introducing lotteries into the preference assessment procedure. In addition, it facilitates the difficult problem of making interpersonal utility comparisons. We also establish several relationships between the group preference aggregation rules based on measurable value functions and previous work based on risky utility functions. These relationships allow either one of these preference aggregation rules to be transformed into the other after obtaining only a minimal amount of information from a group member. These relationships also raise several fundamental questions about the effects of the introduction of risk on the preferences of an individual and on the preferences of a group. We offer some preliminary comments and results regarding these issues.