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Majority Voting, Legislative Institutions, and Gordon Tullock

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Majority Voting, Legislative Institutions, and Gordon Tullock 1 Why So Much Stability?: Majority Voting, Legislative Institutions, and Gordon Tullock Kenneth A. Shepsle Barry R. Weingast March 2010 Gordon Tullock, in a memorable characterization of Arrow’s Impossibility Theorem, began an important early paper on majority rule with the observation that “a phantom has stalked the classrooms and seminars of economics and political science for nearly fifteen years.” (Tullock, 1967, 256) Majority rule, in Tullock’s view, was not nearly as badly behaved as students of social choice had come to believe; his objective in 1967 was “to exorcise the phantom…by showing that it is insubstantial.” Although Tullock misunderstood Arrow’s Theorem and the nature of equilibrium, in our view, his project was classic Tullock – neither the first nor the last word on an important idea, but a seminal one. Tullock was one of the first to extend the paper-and-pencil spatial arguments on majority rule of Duncan Black (Black, 1958; Black and Newing, 1951), mainly through simple geometric representations and carefully selected examples. The strength of Tullock’s methodology lay not in its generality or rigor but rather in its ability to capture and portray powerful intuitions – a foundation on which to build a more general appreciation of majority rule. Some might read his 1967 paper as having presciently anticipated the results of the mathematically general papers of Department of Government and Institute for Quantitative Social Science, Harvard University. Department of Political Science and Hoover Institution, Stanford University. 2 McKelvey (1976, 1979) and Schofield (1978); he certainly set the stage for these major intellectual forays. Tullock again animated scholars in 1981 with his famous paper asking, “Why so much stability?” This paper focused more carefully on one of the themes of his 1967 paper: in the presence of general theorems about cyclical preferences, why did we observe so much stability in the world? In particular, what explains the absence of voting cycles in real world legislatures and committees? Existing work provided no explanation. Tullock’s intellectual agenda-setting helped moved the field to provide an answer. In the present paper we will try to fit Tullock’s contribution into the scholarship of the time (Part I), but then go on to trace the flood of research that followed his contributions that provides answers to his fundamental question (Part II – late 1970s and early 1980s; and Part III – late 1980s through the present). Tullock failed in his stated purpose: Arrow’s Theorem has not been exorcised. But today we are the beneficiaries of a much more nuanced understanding of majority rule as well as a finer appreciation of the ways in which majority rule is embedded in institutional arrangements, in part because of Tullock’s important initiatives. 1. Social Choice and Majority Rule: The Early Years (to the mid-1970s) We can hardly do justice to the flood of social choice-theoretic analyses of majority rule of the first several decades post-Arrow, much less the last half 3 century. Early summaries of this literature are found in Murakami (1968), Sen (1970), Pattanaik (1971), and Fishburn (1973). Perusing some of these volumes, what is clear to us in this literature is that it is mainly about the possibility and consequences of aggregating weak orderings under a variety of mathematical conditions via a q-majority rule (q being the minimal cardinality of a decisive coalition). These exercises are abstract, mathematical, and ungrounded in substantive context. They are benchmark models. They fascinated the mathematically inclined for their own sake, but many social scientists, Tullock among them, were frustrated by the absence of any substantive grounding. What did these exercises in logic have to tell us about real committees, real legislatures, and real collective choice? The answer to this question awaited contributions from those that had some experience with and interest in the empirical world. A second feature of social choice theory that did not sit well with the more empirically inclined is the normative character of these analyses. Students of politics for whom the rational pursuit of objectives was the engine of analysis were decidedly less interested in desiderata claims for features of social choice processes, since such claims are simply uninformative about how individuals actually behave in social settings and what collective outcomes actually were produced there. A third feature of social choice theory, at least as initially posed, is its non- strategic nature. Individuals in Arrow’s formulation sincerely pursue their preferences in q-majority voting. Indeed, it was precisely this feature that 4 McKelvey (1976, 1979) exploited in demonstrating the capacity of a strategic agenda setter to extract all of the advantage from sincere voters in a majority-rule setting. Strategic behavior dramatically affects outcomes in many settings. Shepsle and Weingast (1984a), for example, showed that, in majority decision- making contexts in which all agents are strategic, an agenda setter continued to enjoy disproportionate advantage, but not nearly as extreme as that documented by McKelvey. Sincere preference revelation may roughly obtain in large-n elections, where the probability of any individual being pivotal is infinitesimal, but this is mooted by the empirical fact that most large-n elections do not entail pairwise comparisons as its procedural practice. (And, when there are more than two candidates in a plurality-rule, large-n contest for a single office, most votes are collected by the top two vote-getters, as supporters of less advantaged candidates desert their first choices and vote strategically for the “lesser of evils.” See Riker 1982, Palfrey 1989) In committees and legislatures, on the other hand, where pairwise voting is the norm, strategic motion-making and voting must be part of the story. Duncan Black (1958) made the most important political innovation in the early years.. He demonstrated (later generalized with his colleague R.A. Newing – see revised edition of 1998) that there is something special about decision contexts that “scale.” If the set of alternatives on offer can be arrayed along a single dimension in a manner that induces single-peaked preferences among the agents, then majority rule yields an equilibrium outcome at the ideal point of the 5 median voter. For spatial models of greater dimensionality, however, only knife- edge conditions yield a majority rule equilibrium (Plott, 1967). So, Arrow’s phantom is harmless in some specialized domains, but still haunts universal domains. 2. Why So Much Stability? Initial answers (Late 1970s through early 1980s) Several milestones occurred next. Tullock’s (1981) asking, “why so much stability?” framed the principal question of this middle period. Following up his 1967 work, this paper squarely faced the obvious discrepancy between the set of results from the social choice era emphasizing preference cycles and instability with the obvious stability shown by most legislatures. Contra Arrow, McKelvey, et.al., legislatures did not appear to generate endless voting cycles, even in the presence of preference cycles. The answer came in the form of two key ideas – universalism and structure- induced equilibrium. The two of us, individually (Shepsle, 1979, 1986; Weingast, 1979) and collectively (Shepsle and Weingast 1981a,b, 1982, 1984a,b; 1987), and others (Denzau and MacKay 1983, Kramer 1972) began a project of embedding social-choice and game-theoretic ideas into the analysis of real (multidimensional) legislative settings. These works demonstrated a new logic of stability. Weingast’s 1979 insight about universalism was inspired by the fact that constant-sum majority-rule games have an empty core. For any division of the spoils – as in the classic game of distributive politics – there are other divisions 6 preferred by decisive coalitions. Any such play results in an arbitrary outcome, dependent on idiosyncratic factors like a time limit, or random recognition to make proposals, or rules on amendments (e.g., closed rule). Consider an n- person legislature, where the n agents are symmetric in their endowments and authority. Each has a program worth b to her district and which costs c, b>c. The total cost for all funded projects is borne equally by all districts (whether receiving a project or not). An idea prevailing at the time was that minimal winning coalitions (MWC) would form to pass their projects and programs (Buchanan and Tullock 1962, Riker 1962), and only theirs. That is, a bare majority of legislators would form a coalition, excluding all others. For members in the MWC, the payoff as n grows large is approximately b – c/2 (each member captures all of the benefits from his or her project and pays 1/n of the costs of the (n+1)/2 projects being built). Of course, no member could be assured of being in the MWC that forms. Assuming each MWC is equally likely, the expected payoffs to member i converges to (b-c)/2 as n grows large. Weingast reasoned that intelligent agents would seek out ex ante arrangements to improve on this. In doing so, he produced a rational basis for the observance of a norm – namely, to agree ex ante to divide things up evenly instead of playing out the coalitional in-fighting. A norm of universalism – building a project for all members – yielded higher expected payoffs than playing the minimum winning coalition game with its uncertainty. The payoffs under universalism are b-c to each legislator, which exceeds the expected payoffs under minimum winning coalitions, (b-c)/2. (See also Noiu and Ordeshook 1985 7 and Shepsle and Weingast, 1981b.) The commitment to rationality-based norms is one answer to the Tullock challenge – Arrow’s phantom is still alive and well, but rational agents can respond institutionally to the unstable social choice processes it implies. Shepsle’s approach (Shepsle 1979, extended in Shepsle and Weingast 1981a) incorporated not only norms, but also all manner of other institutional features and arrangements.
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