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5. Spatial Voting in Committees
- University of Michigan Press
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Chapter 5 Spatial Voting Committees • In More often than not, a committee is a relatively small subset of individuals from a larger group, charged with making some decision on behalf of that larger group. Canonical examples include representative legislatures and legislative committees, parliamentary ad hoc committees, judicial committees, and so on. And while Chapter 4 concerns the structure and implications of voting over given finite sets of alternatives, a great deal of policy-making in committee is perhaps more naturally addressed with the spatial voting model, where the set of alternatives over which an agenda is defined is typically a finite selection from a (multidimensional) continuum. In this setting, a principal problem is to account for how that selection is determined given that the final collective choice from the selection is decided by application of some voting procedure. Although there are many such procedures, we restrict attention to binary agendas, so building on the results derived in Chapter 4. As observed earlier, issue-by-issue voting is a fairly natural institution for the spatial model: there are multiple policy issues, or dimensions, each being a continuum of feasible alternatives and a reasonable way to arrive at a policy choice is to make a series of partial decisions, fixing one issue at a time, that jointly describe the final policy outcome. Indeed, a plausible (albeit somewhat coarse) description of many legislative bodies is as a collection of more-or-Iess autonomous committees with jurisdiction over particular policy issues. From this perspective, legislative policy outcomes are simply the composite of the various committee decisions within their respective jurisdictions and, as such, approximate legislative policy choice 147 148 CHAPTER 5. SPATIAL VOTING IN COMMITTEES under issue-by-issue voting. We begin, therefore, by developing the theory of issue-by-issue agenda-formation and voting for the spatial model in some detail, subsequently going on to consider agenda-formation when committee members are unconstrained to offer only single-dimensional proposal or vote over only one policy issue at a time. 5.1 Issue-by-issue voting in the spatial model Suppose that the set of feasible alternatives is given by a nonempty, compact and strictly convex set X C 3tk and that any individual i's preferences are continuous and strictly convex, Hi E Res, hence representable by continuous and strictly quasi-concave utility functions, Ui : X --+ 3t [PPTI, sect.4.3]. Thus our earlier assumption that individuals' preferences are strict on X must be relaxed. To avoid trivialities, assume X has full dimension. Although the focus of this section is on issue-by-issue agendas under majority rule in the spatial model, the analysis hinges on a more widely relevant result that does not depend on majority rule; it is with this result that we begin. Recall that for all x E X and j E K, r x (ej) is a line through x parallel to the jth axis: rAej) = {y E 3tk : y = x + tej for some t E 3t} where ej is the usual basis vector with yth coordinate one and all other coordinates zero. For each issue dimension j E K, let !J denote a simple preference aggregation rule associated with dimension j [PPTI, ch.3]. Majority preference is a simple rule but not all simple rules are majoritarian, so we admit a richer class of aggregation procedures than hitherto in this chapter (in particular, the strict collective preference relation P need not be the majority preference relation). Permitting different issues to be evaluated under different rules admits the possibility that the legislature is not neutral with respect to issues. For instance, issues dealing with constitutional change are often subject to supramajority rules, whereas issues dealing with farm subsidies are decided by simple majorities. For any x E X and j E K, let 'Yx(ej) = rx(ej) n X. Any simple rule fj is characterized by a family of decisive coalitions, £Uj) (Definition 1.3). Consequently, for all distinct alternatives y, Z E X, 5.1. ISSUE-BY-ISSUE VOTING IN THE SPATIAL MODEL 149 It follows that social preference may be strict if y and z differ in only one dimension, but y and z can be judged socially indifferent should they differ in more than one dimension. Definition 5.1 Let :F = {fj }jEK denote the family of simple rules governing changes in the k issue dimensions. An alternative x* E X is an issue-by-issue core with respect to :F if x* Ry for...