Increasing Downside or Outer Risk? The Challenge of Measuring Competitive Imbalance in Closed and Open Leagues

In two seminal articles, Menezes, Geiss, and Tressler (1980) and Menezes and Wang (2005) have defined the concepts of increases in downside and in outer risk. Such notions are useful to give intrinsic characterizations of the notions of prudence and temperance. In this article, we explore a new application about higher-order risk preferences: the measurement of competitive imbalance in sports leagues. We show that desirable properties for the measurement of imbalance are the inclination to any increase in downside risk in the context of closed leagues, and the aversion to any increase in outer risk in the context of open leagues.