In the era of a polarized and stymied Congress, in which legislation is especially prone to be paralyzed by the filibuster and other supermajority devices, Melissa Schwartzberg’s new study of supermajority rules could not be more timely. In another sense, it could not be less timely: Schwartzberg generates her insights by recovering the origins of voting, majority rule, and supermajority rule in pre-modern polities. Her findings suggest that supermajority rule ought to be suspect in a polity otherwise committed to democratic principles of equal political dignity among voters.
To understand why this book is so innovative and so excellent, one needs to start elsewhere, with a peripatetic Scottish economist named Duncan Black. Active from the late 1940s through the 1970s, Black had no fixed academic post, but roamed the American academic scene in a series of visiting positions. This was a failure of the academic market to identify and reward genius. In a series of papers written around 1948 and in a book a decade later, Black laid the foundations of a branch of economics, or perhaps of political economy, known as social choice theory. Schwartzberg’s book is both a contribution to social choice theory and a corrective for its most conspicuous ills.
In its broadest sense, social choice theory is the study of collective decision-making. Given a group, and some need for a collective decision, how should the group decide what to do? In this sense, social choice has been firmly on the agenda of political theory at least since Aristotle. Black’s innovative approach was to mathematize and formalize social choice theory, both sharpening and narrowing its point. In the new world of mathematical social sciences in the postwar era, Black rediscovered the work of earlier scholars who had dabbled in formal social choice theory, such as the French polymath Condorcet and the English logician Charles Dodgson (“Lewis Carroll”). Yet it was Black’s work, and the roughly simultaneous work of Kenneth Arrow, that ignited an explosion, further fueled by major contributions from Amartya Sen and others in the 1960s and 1970s.
Social choice quickly became an enormous subfield of political economy, especially notorious for its pessimistic results and its skepticism about the possibility that democratic polities could aggregate preferences in a manner that would be both fair and coherent. Graduate students, later professors, would spin out nth-decimal mathematical refinements on Arrow’s Impossibility Theorem, which (very roughly) showed that under certain conditions collective choice rules could not be both democratic and coherent or stable; Sen’s proof of the impossibility of a Paretian Liberal, which (very roughly) showed that under certain conditions one could not be both a political liberal and a believer in the ultimate value of individual welfare, as determined by the free choices of the individuals themselves; and theorems showing that collective decision rules could not be strategy-proof—in other words, could not bar manipulation by voters willing to misrepresent their preferences. Libertarian political economists, such as William Riker, attempted to use these results to ground a sort of generalized suspicion of legislatures and other democratic institutions, which they argued were incapable of acting both coherently and democratically. Riker thus argued for a minimalist form of libertarian democracy, featuring a robust role for constitutional protections enforced by the judiciary. That attempt deflated, however, when it was pointed out that the main incoherence results of social choice theory applied just as strongly to collective voting on multi-member courts as to democratically elected bodies.
In a pattern seen wherever the social sciences become formalized, the mathematics of social choice eventually became an end in itself. Social choice theory became ever more recondite and inaccessible to the non-mathematical sectors of the university; the result was a kind of self-ghettoization, as social choice was segregated from fruitful contact with other disciplines. More seriously still, social choice cut itself off not merely from the university but also from the world. The inputs from reality, from the novel and ever-changing forms of collective decision-making used in the world’s institutions, all but dried up. The consequence was that, although social choice theorists were admired for their high IQs, signaled by their ability to manipulate theorems, the enterprise as a whole degenerated, producing a stream of essentially meaningless minor refinements. According to Jon Elster, the journal Econometrica even imposed a moratorium on social choice articles, on the ground of their patent irrelevance to real politics.
This is not to say that formal social choice theory has offered nothing new since the 1970s. In the past decade or so, a breath of new life has been felt in work that examines the aggregation not of preferences but of epistemic judgments and beliefs. The seminal result here is called the Condorcet Jury Theorem, popularized by James Surowiecki under the label “the wisdom of crowds.” In its simplest form, the Jury Theorem holds that where the group faces two choices, one of which is correct, a majority vote of the group will be more likely to identify the correct choice than will the individual voters, given a certain level of competence and independence among the voters; moreover, the accuracy of the vote increases with the size of the group. The Jury Theorem underpins a growing literature on epistemic problems and promises in democracy. The leading contributors include Christian List, a formal theorist who has found important epistemic parallels to the social choice work on aggregation of preferences, and David Estlund and Jeremy Waldron among non-formal political philosophers. Yet the mainstream of formal social choice theory remains, by and large, intellectually lifeless.
As against formalized and mathematized social choice theory, there was always a submerged counter-tradition of scholarship that studied social choices embedded in history or descriptive politics—social choice as conducted by real groups in the world. Exemplars included the work of John Gilbert Heinberg on the history of majority rule, and work in many quarters on a hybrid medieval decision-principle in which the group’s choice is the view of the “sounder and larger part” (sanior et maior pars). In recent years, this counter-tradition has flourished and borne new fruit. Elster concocts a rich brew of social choice results, political theory, and history, in order to understand how institutions may filter out passions, prejudices, and other impediments to rational decision-making. Scholars such as Philippe Urfalino study social choice in collective groups of decision-making officials, such as the Food and Drug Administration and other administrative agencies; Urfalino has also identified an ancient, still ubiquitous method of decision-making called “decision-making by apparent consensus,” a method largely invisible to formal social choice theorists because it is so heavily embedded in and constituted by tacit social norms. Gerry Mackie has examined, through exhaustive case studies, the claim by disciples of Arrow and Riker that there is pervasive instability in the decisions of the U. S. Congress; Mackie finds not a single example to back up the claim, forcing its proponents to fall back on the dubious suggestion that instability is an institutional potential that always hovers unobserved in the background, like a poltergeist. Other scholars have begun to cross-fertilize the results of behavioral economics with collective decision-making, yielding “behavioral social choice”—the title of a recent book that also finds little evidence of the pervasive instability posited by the older generation.
In other words, whereas mathematical social choice became increasingly self-absorbed, cramped, and baroque, the new social choice has thrown open its doors to the fresh air of the world. Schwartzberg nicely exemplifies the trend. A political theorist who studies the institutions of collective decision-making, especially in the ancient world, Schwartzberg might resist being cast as a social choice theorist, but it is useful to describe her work as a historically inflected and institutionally sensitive version of social choice. Schwartzberg studies collective decision-making in the wild, rather than studying the theory of social choice on a blackboard. She is a field anthropologist of voting theory, although her fields of research are not usually contemporary but principally historical—ranging from Homeric assemblies to ancient Sparta, classical Athens, the medieval Church, and post-Enlightenment constitutional assemblies.
Schwartzberg’s approach gives her work a methodological unity and a distinctive flavor, apparent both here and in her earlier book on the relationship between democracy and constitutional change. But the important thing is that the historically embedded approach to collective decision-making bears fruit. The historical inflection of social choice is not only interesting in its own right, it also enables the theorist to understand the genesis, the consequences, and the political and social function of voting rules in a richer way than blackboard social choice theory can offer. Schwartzberg’s new book, whose foreground topic is supermajority rule, is an extended illustration of the returns from studying social choice in the wild.
Supermajority rules require the agreement of more than a bare majority of the group, yet less than unanimity, to reach a decision. They are ubiquitous in modern constitutional assemblies, not to mention in ordinary clubs, associations, corporations, university faculties, administrative agencies, and legislatures. The filibuster in the U.S. Senate is a supermajority rule of a special sort. Rather than allowing a minority to block a substantive enactment, it allows a minority of the Senate to prevent the majority from cutting off debate on whether to pass the substantive enactment. The result is the same, covered by a fig leaf of proceduralism that has all but fallen off by now.
Mathematically, both a majority voting rule and a supermajority rule of any particular value are just special cases of voting thresholds, which may be set anywhere along a continuum defined by the number of members in the group. (In principle, the threshold can even be less than half of the group. Some institutions use submajority rules, under which less than a majority of the group is empowered to effect some change in the status quo ante). It is true, however, that simple majority rule has unique mathematical properties. A formal result called May’s Theorem shows that where a group must choose between two options, simple majority rule is the only approach that respects equal treatment of voters (so-called anonymity) and equal treatment of the options before the group (so-called neutrality). By contrast, supermajority rule in its ordinary form violates neutrality, because it privileges one of the options—the status quo option of leaving everything as it is, an option that will become the group choice so long as a sufficient minority supports it.
In typical modern episodes of constitutional design, this status quo bias is defended as necessary to protect minorities from economic exploitation or the deprivation of rights. In perhaps the most famous version of this justification, James Buchanan and Gordon Tullock argued that citizens choosing a constitution behind a veil of uncertainty would balance the benefits of protecting minorities from exploitation, which favors supermajority rule, against the higher costs of assembling a coalition for change, favoring majority rule. Yet the issues are more complex than Buchanan and Tullock understood, because supermajority rule can harm minorities as well as protect them. Critics such as Anthony McGann have pointed out that supermajority rules also make it harder for minorities to form coalitions to overturn deprivations that are currently in place. If the status quo is already oppressive for a given minority, then the lower the threshold needed to change it, the better. More broadly, there are a myriad of different potential minorities and majorities, in different potential coalitions. There is no single effect of supermajority rule; everything depends upon who “the minority” is or will be, with respect to a given decision, and what the status quo is, at the time of voting.
Whatever the ultimate conclusions, however, the work on majority rule and supermajority rule in formal social choice theory is so vast that one might spend a lifetime reading it, and then be farther behind than when one started. Schwartzberg has gotten around or behind all this work by studying the historical origins of vote-counting, majority rule, and supermajority rule. What she finds is illuminating. One cannot understand majority or supermajority rule, or the choice between them, until one understands the logically antecedent choice: should there be counted votes at all, or instead alternative methods of expressing judgments or preferences? In the ancient world, and well into the modern one, perhaps the principal method of collective decision-making was not voting but acclamation—the shouts of the assembled crowd, populus or demos. Social choice theorists have said essentially nothing until very recently about acclamation, yet—Schwartzberg argues—the choice between acclamation and vote-counting carries with it certain political and theoretical commitments that should also inform the logically subsequent choice between majority and supermajority thresholds for voting.
Right from the beginning, the counted vote was saturated with political symbolism and significance. With close studies of councils, juries, quasi-judicial bodies, and legislative assemblies in Sparta, Athens, and Rome, Schwartzberg shows that vote-counting emerged not principally on instrumental grounds but as a means of recognizing the dignity of the voters’ political judgment, and the political equality of those whose votes counted. There are historical complications here: the Athenian assembly, for example, often voted by means of raised hands, with the count being estimated rather than explicitly enumerated. But the main contrast is between counting of any kind and acclamation. The mass character of acclamation submerges the individual in a sea of noise. By contrast, the mutual visibility and common knowledge to which vote-counting gives rise—all we voters can see that the others among us can see that our votes are counted, and so forth—implies equal political dignity, among those whose judgment is sufficiently respectable to be counted at all. This sort of consideration is non-intuitive, instantly plausible when Schwartzberg identifies it, deeply human and political, and yet sufficiently slippery that it is resistant to inclusion in a formalized treatment of collective choice.
Resistance to formalization is true obviously for acclamation itself, and for related practices such as the ancient practice of thorubos, or crowd noise, ranging from outcry to murmuring, that were used as methods of indicating the views of the assembled people. Schwartzberg is at her most arresting and novel when she documents and explains the use of such non-formal methods of social choice; the contrast with the blackboard theorems can be no sharper. The need for mathematical tractability in a formal theory, it turns out, is itself not neutral as to subject matter. It biases the theorist’s attention toward certain methods of collective decision-making—those that are quantified, explicit, and aggregative—and away from others that are tacit, protean, and thoroughly social rather than individualistic.
Having shown that the question of voting thresholds is logically dependent upon a prior decision to count votes at all, Schwartzberg moves on to discuss the choice between counted supermajority thresholds and other thresholds. Here a striking case study involves voting over the choice of popes in the medieval church. Schwartzberg shows that supermajority rule, usually thought of by modern constitutional designers as an alternative to majority rule, emerged principally as an alternative to unanimity. The church hoped and expected that the true Pope would be recognized by all, with the guidance of the Holy Spirit. Yet it was eventually recognized that the fallibility of fallen man implied that some might fail to recognize the true Pope and insist upon their error, blocking unanimity in the group of selectors. Supermajority thresholds thus emerged as a means of coping with human fallibility, in contrast to their typical modern justification as a means of protecting rights.
In the final chapters, Schwartzberg consolidates her arguments and offers a critique of supermajority rule. In light of her findings about the genesis of vote-counting and of supermajority thresholds, she offers some key principles for social choice in democratic polities—especially equal dignity of political judgments, and the recognition of fallibility—and leverages them into an argument in favor of majority rule and against supermajority rule. Generally speaking, majority rule is the most straightforward way to recognize the equal dignity of political judgments in the voting group. And we know that we have that commitment to equal political dignity in the first place when, and because, we are counting votes in the first place—perhaps Schwartzberg’s most illuminating observation. Conditional on that commitment to the equal dignity of all participants and their judgments, majority rule is the natural follow-on, as May’s Theorem and the Jury Theorem confirm from different angles.
To be sure, there is a bloodless sense in which supermajority rule respects equality, in advance of the decision. In theory, anyone in the voting group has an equal right to make up part of the minority that prevails when a supermajority threshold is decisive. It is even true that counting is not logically and necessarily tied to equal political dignity at all. John Stuart Mill favored a scheme for giving multiple votes—explicitly counted votes—to highly educated elites much like himself, a scheme that one rarely hears about from Mill’s many celebrants. So if one possesses a particularly robust self-confidence, it is possible to count votes explicitly without respecting the political equality of one’s fellow citizens.
Yet this is the sort of abstraction, the sort of quest for necessary and sufficient conditions, as opposed to contingent embedded arguments, in which Schwartzberg resolutely refuses to deal. Given the track record of abstract social choice theory, it is hard to fault her. In real-world settings, it is usually clear which group or interest will be empowered by supermajority rule, and in real-world settings, it is often those advantaged by the status quo ante who desire the most constraints on majority rule. To say that anyone can take advantage of supermajority rule is, in reality, often akin to saying that the rich and the poor have an equal right to sleep under the bridges of Paris.
Moreover, the interaction between counting and supermajority rule makes the latter especially problematic. When a majority votes for X, a minority votes for -X, and the minority prevails by virtue of the supermajority rule, the result is that the rule has created what Schwartzberg calls an “enumerated minority,” possessing superior power. That is a form of inequality after the fact, and it is a blatant form of inequality, thrust into the majority’s face. Why exactly should the smaller number, who are otherwise of equal dignity and political status, prevail over the larger number? Faced with the division—this majority of citizens to one side and that minority to another—our second-order justifications for supermajority rule start to seem remote and excessively precious. Viewed in a dynamic perspective, taking into account not just this vote but a series of interactions, repeated exercise of supermajority rule threatens to undermine goodwill and the sense of a common venture among fellow citizens. It is plausible, although unprovable, that the Senate filibuster has had exactly this effect.
Schwartzberg is not an absolutist; implicit cost-benefit balancing tempers her conclusions throughout the prescriptive sections of her book. While her principles suggest a kind of institutional presumption in favor of majority rule, she admits the important qualification that supermajority rule will be indispensable in some settings in which there is a genuine need to bias choices against a certain outcome, as when juries are allowed to convict only by a supermajority or even unanimity in order to give extra protection to the innocent. Yet there are also important cases in which the protection afforded by supermajority rule—assuming it exists—can be secured by other institutional devices that inflict less harm on our principled democratic commitments. Whatever level of supermajoritarian effect is desirable may often be obtained through indirect constraints on majoritarianism, such as a constitutional scheme of checks and balances. Those constraints are not less transparent—children are taught in school that checks and balances make it harder to enact legislation—but they have the virtue of avoiding the sort of deliberate and flagrant offense to equal political dignity that supermajority rule creates.
The merits of Schwartzberg’s arguments, although formidable, are not the main thing. The main thing is the sense her work conveys that collective decision-making is a living subject, with which people of good faith in many lands and times have struggled, and that it is deeply interwoven with social norms, the status of individuals, and the self-understanding of groups. (It is impossible to understand medieval voting practices without an appreciation of Christian thought.) Considerations of this sort are not especially tractable, but they are the heart of the matter.
Adrian Vermeule is John H. Watson Professor of Law at Harvard Law School and the author, most recently, of The Constitution of Risk (Cambridge).