The Shapley–Owen Value and the Strength of Small Winsets: Predicting Central Tendencies and Degree of Dispersion in the Outcomes of Majority Rule Decision-Making

Drawing on insights about the geometric structure of majority rule spatial voting games with Euclidean preferences derived from the Shapley–Owen value (Shapley and Owen, Int J Game Theory 18:339–356, 1989), we seek to explain why the outcomes of experimental committee majority rule spatial voting games are overwhelmingly located within the uncovered set (Bianco et al., J Polit 68:837–50, 2006; Polit Anal 16:115-37, 2008). We suggest that it is not membership in the uncovered set, per se, that leads to some alternatives being much more likely to become final outcomes of majority decision-making than others, but the fact that alternatives differ in the size of their winsets. We show how winset size for any alternative is a function of its squared distance from the point with minimal win set, and how this point, referred to by Shapley and Owen (Int J Game Theory 18:339–356, 1989) as the strong point, is determined as a weighted average of voter ideal points weighted by their Shapley–Owen values. We show that, in experimental voting games, alternatives with small winsets are more likely to be proposed, more likely to beat a status quo, and are more likely to be accepted as the final outcome than alternatives with larger winsets.