The Uncovered Set and the Limits of Legislative Action

Abstract

We present a simulation technique for sorting out the size, shape, and location of the uncovered set to estimate the set of enactable outcomes in ''real-world'' social choice situations, such as the contemporary Congress. The uncovered set is a well-known but underexploited solution concept in the literature on spatial voting games and collective choice mechanisms. We explain this solution concept in nontechnical terms, submit some theoretical observations to improve our theoretical grasp of it, and provide a simulation technique that makes it possible to estimate this set and thus enable a series of tests of its empirical relevance.

Voting Power and Procedures

“…Nevertheless, there are also incontrovertible empirical findings from experimental committee voting games that committee voting processes do reach stopping points that are not merely random. And, when we look at real world data in situations where we can estimate the ideological location of both voters and observed outcomes, e.g., wrt to voting processes such as those in the U.S. Congress or the U.S. Supreme Court, we again find a far from random pattern of outcomes relative to the distribution of estimated legislator voter ideal points, Like Bianco et al (2004Bianco et al ( , 2006Bianco et al ( , 2008, Schofield (1993Schofield ( , 1995aSchofield ( , b, 1999 and earlier work such as Ferejohn et al (1984), we suggest that, even there is no core to the voting game, while all outcomes may be possible, some are more likely than others. In particular, as we shall see, the Shapley-Owen value, and insights derived from it about the underlying geometric structure of majority rule preferences, can aid us in identifying where outcomes of majority rule spatial voting games are most likely to be found.…”

“…In particular, as we shall see, the Shapley-Owen value, and insights derived from it about the underlying geometric structure of majority rule preferences, can aid us in identifying where outcomes of majority rule spatial voting games are most likely to be found. Bianco et al (2004Bianco et al ( , 2006Bianco et al ( , 2008 focus on the set of points in the uncovered set (Miller 1980(Miller , 1983 as the likely outcomes of majority rule voting processes over a "king of the hill" type agenda. 1 The uncovered set is the set of points such that no alternative in the set has another alternative that is both majority preferred to it and majority preferred to all point that it defeats.…”

“…Another way of defining the uncovered set is as the set of points that beat all other points either directly or at one remove. 2 Thanks to new developments in computer software (Bianco et al 2004;Godfrey 2007) it is now possible to identify the location of solution concepts such as the uncovered set even for games with large numbers of actors, even though an analytic solution for the uncovered set is known only for the three-voter case Hartley and Kilgour 1987).…”

“…9 Bianco et al (2004Bianco et al ( , 2006Bianco et al ( , 2008 note that when the uncovered set is large, the uncovered set can include most of the points in the Pareto Set, so predictions based on the uncovered set are not that specific, though they predict far better than chance. They are equally well aware that, in the unusual situations where the uncovered set is small, e.g.…”

Using Roll Call Estimates to Test Models of Politics

“…Whether preferences are defined over policy outcomes or public positions is unclear, and the meaning likely varies by application. Work focused on the representation of interests and constituents (e.g., Bartels 1991, Ansolabehere et al 2001, Bafumi & Herron 2010) typically requires only that ideal points reflect legislators' public positions, but some assume that ideal points characterize true preferences over policy outcomes (e.g., Chiou & Rothenberg 2003, Bianco et al 2004, Bianco & Sened 2005.…”