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Alternative Traditions in Public Choice

James M. Buchanan and Gordon Tullock on the Weaknesses of Majority Voting: A Triptych

James M. Buchanan and Gordon Tullock à propos des faiblesses du vote majoritaire
Julien Grandjean
p. 49-76

Résumés

Cet article opère un retour sur les démonstrations différentes mais cependant complémentaires proposées par James M. Buchanan et Gordon Tullock pour pointer les faiblesses du vote à la majorité absolue. Nous montrons que les deux auteurs ont emprunté deux voies distinctes pour aboutir à la même conclusion. Buchanan, se fondant sur sa connaissance de Knut Wicksell, a choisi d’étudier le sujet sous un angle abstrait. Tullock a de son côté proposé une démonstration pratique inspirée de ses lectures de Duncan Black et Anthony Downs. Entre 1959 et 1961 notamment Tullock a produit nombre de travaux — publiés ou non — qui forment la base de sa contribution au Calculus of Consent. Cet ouvrage, écrit par les deux auteurs, comprend un troisième type de réflexion à propos du vote à la majorité : une démonstration théorique. Cet article examine la construction du véritable triptyque formé par les travaux de Buchanan et Tullock à propos du vote à la majorité et met en lumière le rôle important, bien que négligé, de Tullock dans la formation du Calculus et dans le développement du programme de recherche du public choice en Virginie.

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  • 1 William H. Riker notes that the introduction of these two types of costs was a novelty and was intr (...)

1The public choice research program includes alternatives although it is most often associated with Buchanan and The Calculus of Consent (hereafter, Calculus) which “is one among a handful of contributions to public choice that can truly be called a classic” (Mueller, 2012b, 329). The book was indeed a cornerstone of public choice theory and attracted many major contributions to the research program such as an analysis of voting systems in terms of their decision-making and external costs,1 “one of the first rigorous analyses of logrolling” (ibid.) and “the introduction of a two-stage process for collective decision-making” (ibid.). Several authors have discussed the importance of this program (Boettke and Palagashvili, 2014; Lemieux, 2015; Medema, 2013; Mueller, 2012; Zafirowski, 2001). Buchanan is generally credited with the research framework (MacLean, 2017) with Tullock’s role in the formation of the public choice program and the writing of Calculus generally seen as secondary.

2However, Tullock played an important role and contributed his developments related to majority voting and unanimity to the book. The two types of costs involved—the analysis of logrolling, and the exploration of alternatives to majority rule—had been examined by Tullock prior to his work on Calculus in his published work (Tullock, 1959d, 1960a) and some little-known unpublished documents (Tullock, 1959b, 1959e). These latter and letters exchanged between Tullock, Buchanan and the journal editors which were lodged on the Tullock Archives at the Hoover Institution are used in this paper to propose a new narrative highlighting Tullock’s overlooked input to the critique of majority rule.

3We argue that Buchanan and Tullock had the idea of moving from majority voting separately and through different intellectual trajectories. Buchanan was inspired by Knut Wicksell and the approach in his papers on the subject published in the 1950s can be described as abstract. Tullock took a more practical approach. The two authors then decided to collaborate to expand their views by writing The Calculus of Consent (1962). Calculus was an important contribution and we show that Tullock’s influence has been overlooked. Rather than seeing Calculus as a sophisticated version of Buchanan’s views on majority voting slightly amended and decorated by Tullock’s more concrete applications, we argue that Calculus provides a genuine synthesis of the methods and views of both authors. Thus, when considered together, the contributions made by Buchanan and Tullock before publication of Calculus and contributions to Calculus stand as three distinct incarnations of the same ideas about majority voting.

  • 2 Buchanan (2012) contains a discussion of decision-making methods in relation to the chosen upstream (...)

4In a paper reflecting on the origins of the book, Buchanan (2012) emphasizes the differences and complementarities between his and Tullock’s views. Buchanan assumed the role of philosopher while Tullock was the scientist (ibid., 254). Buchanan explains that his contribution to Calculus is a continuation of his 1954 critique of Arrow.2 He describes Tullock’s input as more explanatory and as seeking specifically to apply economic tools to problems of a political nature (ibid.). The letters exchanged between the two authors concerning their respective appendices to Calculus are particularly revealing in this respect. Despite their different approaches, they show a high level of complementary, and the book is constructed around the same dynamic: the common goal of seeking a solution to certain political games and providing an “optimal set of the political rules of the game” (Buchanan letter to Tullock, June 20, 1960)—that is, a set of rules that respect individual freedoms and produce stability—so that “the whole game of politics be [a] positive sum” (Buchanan, 2004, 19).

5We show that this objective was based on Buchanan’s and Tullock’s earlier work and that Tullock’s contribution was significant in this respect. The remainder of the article is organized as follows. Section 1 deals with Buchanan’s abstract demonstration before Calculus of the weaknesses of majority voting, and sets out to show its influence on Tullock’s work. We show that Buchanan suggested that majority voting was problematic using the rationale of his knowledge of Wicksell and political philosophy. Section 2 describes how Tullock reached the same conclusion based on political and economic reasoning. The correspondence between Tullock’s practical approach and Buchanan’s abstract approach is explored in the search for other potential rules to replace majority voting. Section 3 describes the development of their ideas in Calculus, and the influence of Tullock in their elaboration in the book. The paper concludes by showing that each approach to the idea of the weaknesses of majority voting (Buchanan’s, Tullock’s and the approach in Calculus) pursues a specific goal. Thus, each approach can be compared to the part of a triptych.

1. Back to the Origins of the Triptych

6To understand Tullock’s work and its novelty, it is important to look at their intellectual context. The inter-war and the immediate post-war period are interesting in the sense that they saw the emergence of many theories of political economy proposed by political scientists and economists. Authors such as Kenneth Arrow, Robert Dahl, Anthony Downs, and Duncan Black were prominent. Certainly, Tullock’s works drew on this context but they were also influenced by Buchanan’s work.

1.1 The Intellectual Context: Confronting Markets and Voting Procedures

7Tullock was not alone in applying an economic methodology to the study of political topics.

  • 3 This was defined as a realistic or revisionist challenge to the classical interpretation of democra (...)

8In the 1940s, Joseph Aloïs Schumpeter had used the market metaphor when discussing politics. In Capitalism, Socialism and Democracy (Schumpeter, 1942), the Austrian economist questions the notion of democracy and its meaning. He disagrees with the classical definition of political regime defined by political scientists and proposes a new notion.3 Schumpeter’s definition shifts the boundary between political science and economics and brings the study of democracy into economics by conceptualizing democratic functioning as political competition and establishing a parallel with the functioning of markets. Schumpeter also puts the voting process at the center of democracy: without a vote, there is no democracy.

9Other economists drew on Schumpeter to understand democratic functioning through study of the voting process using an economic methodology. For example, Duncan Black and Kenneth Arrow both worked on voting theory as a means of achieving a collective decision.

10Black’s contribution revolves around a paper “On the Rationale of Group Decision Making” (Black, 1948) and a book, The Theory of Committees and Elections (Black, 1958). Both works describe how collective decisions are taken. In the article, Black provides an example of a number of motions proposed to a committee which must vote on only one motion. Black shows that if a committee member ranks his or her preferences, this can be represented as a curve. Black (1948, 24) explained that “there is reason to expect that, in some important practical problems, the valuations actually carried out will tend to take the form of isolated points on single-peaked curves”. Thus, these curves provide the median optimum that will be chosen by the majority and are the source of the median voter theorem. This theorem became central to political economy theory in the years that followed and was further developed by Anthony Downs in 1957. Thus, “Black developed a pioneering branch of economic analysis that studied committee decision problems as analogous to the manner in which price is fixed by demand and supply” (Amadae, 2003, 123) and one of his main results was the stability of collective decision making with single-peaked preferences.

11Kenneth Arrow was also interested in analyzing collective choice using an economic methodology. In his dissertation published as a book in 1951, Social Choice and Individual Values, Arrow seeks to understand the functioning of the vote as a tool allowing social choice. His mathematical demonstration leads him to conclude that there is no means that can grant individual and social preferences without abandonment of the democratic ideal and adoption of an approach that is closer to dictatorship (Arrow, 1951). Although this conclusion is less than encouraging, Arrow’s reasoning and method remain an example for scholars.

12Arrow’s book inspired another important work from the political scientist Robert A. Dahl, A Preface to Democratic Theory which was published in 1956 and led to the body of literature on democratic theory. Dahl admitted having been influenced by Arrow’s work “in that pre-quantitative, pre-mathematical era of political science, when the almost exclusive language of political science was words” (Dahl, 1991, 298), and he presented “parts of the argument in a formal notational system”. This formalization which was inspired by Arrow allowed political science and economics to be brought together in terms of the problems that were defined and the mathematical models that were employed.

13Arrow was also the inspiration of another essential work: An Economic Theory of Democracy by Anthony Downs (1957). In this book, Downs proposed studying the determinants of voter turnout and the behavior of political parties and politicians. He developed several well known elements such as the median voter theorem (borrowed from Black) and the voting paradox. However, Downs’s other contributions are less well known. He believed in the instability of the democratic regime in the case of perfect information. But imperfect information—as used in his model—leads to voter inequality and allows the presence of lobbies. Moreover, it produces instability of the political chessboard. However, Downs believed that in reality parties were fairly stable and his positive theory is able to explain this apparent stability. His model was enriched by the stabilizing mechanism of political ideology borrowed from political science. Downs explains that if political parties and politicians want their ideology to be reliable and identifiable, they must maintain a precise position on the chessboard which allows the democratic framework to gain stability. His book, and the model he developed were to become pillars of the public choice program.

14This brief overview shows that dealing with political problems using economic tools was not completely original at the time. However, this period was marked also by the desire of some authors to question the very object of their study, namely the state. Buchanan’s works which are considered the first part of the triptych, reflect this desire to question democratic rules, specifically voting rules, something that Tullock was also to pursue.

1.2 Buchanan’s Abstract Demonstration of the Weaknesses of Majority Voting

15In the late 1940s and early 1950s, Buchanan began to work on political topics such as voting. He wanted “to recognize the potential explanatory extension made possible by the abandonment of disciplinary constraints” (Buchanan, 1992, 90). For this reason he turned to problems from other disciplines such as political science although he had already demonstrated his open mindedness. His article “Pure Theory of Government Finance” (Buchanan, 1949) is based on this work. It introduces questions about majority voting and demonstrates its weakness compared to unanimity. He returned to this topic in two papers published in 1954.

  • 4 Buchanan read Wicksell's Finanztheoretische Untersuchungen (1896) while writing his dissertation (s (...)

16This questioning was based in part on Herbert Simon and Frank Knight and was reinforced by Buchanan’s reading of Knut Wicksell’s work.4 “Stripped to its essentials, Wicksell’s message was clear, elementary, and self-evident. Economists should cease proffering policy advice … and they should look to the structure within which political decisions are made” explained Buchanan in his Nobel Prize speech (Buchanan, 1986). Thus Buchanan “called upon [his] fellow economists to postulate some model of the state, of politics, before proceeding to analyze the effects of alternative policy measures” (ibid.). His goal was “to make economic sense out of the relationship between the individual and the state before proceeding to advance policy nostrums” (ibid.).

17His Nobel lecture harked back to his 1949 paper which critiqued the analytical framework used to develop public finance theory. He indicated that even before considering finances and taxation, it was necessary to understand the nature of the state in which the agents evolve. Buchanan (1949) describes a dichotomy between two conceptions of an organic state and an individualistic state. In the first case “The State … is conceived as a single organic entity” (Buchanan, 1949, 496) while in the second it is considered “the sum of its individual members acting in a collective capacity” (ibid.). In fact, Buchanan explains that “these two approaches have not been clearly separated or distinguished in the literature of government finance” (ibid.).

  • 5 For Buchanan, before the 1940s, almost all public finance conceived the state as an organic unit. H (...)

18This distinction is fundamental. If we consider the state as organic, then we must treat it as a unit in its own right seeking to maximize its usefulness. If we consider the state as individualistic, then it does not have objectives in the sense that in this understanding the state is a tool used by individuals to realize their collective wishes (ibid., 496-498). There was a genuine desire on Buchanan’s part to go beyond the borders of economics5 to include elements of reflection borrowed from political science and philosophy.

  • 6 Buchanan refers to “comments” but provides no examples.
  • 7 Buchanan notes that Ian Little and Jerome Rothenberg were the only ones to incorporate this dimensi (...)
  • 8 Buchanan returns to the elements present in his 1949 paper.

19In 1954, Buchanan considered Arrow’s (1951) impossibility theorem. He argued that the comments6 on the book mainly referred to the formal aspects of Arrow’s demonstration. In contrast, its philosophical implications attracted little comment.7 Buchanan proposed to fill this gap employing some elements of philosophical reflection. The concept of social rationality was one such aspect. According to Buchanan, it is difficult to understand what this concept means in Arrow’s work. The term suggests that the outcome of decision-making processes should be socially rational. For Buchanan, this result could be expected only if the social group has “an organic existence apart from that of its individual components” (Buchanan, 1954a, 116).8 The question that then arises is whether the rationality of a group conceived in this way can be assessed in terms of an order of values which is not its own but is that of the individuals who compose it (ibid.). If we adopt an individualistic approach, then “the individual is the only entity possessing ends or values” (ibid.) and the very concept of social rationality makes no sense. If we adopt a holistic view, we must study the social group as an entity with its own values and ends. The difficulties related to understanding Arrow’s analysis stem from the fact that “voting and the market, as decision-making mechanisms, have evolved from, and are based upon an acceptance of, the philosophy of individualism which presumes no social entity” (ibid., 117).

20However, Arrow’s analysis is interesting as the basis for a reflection. Buchanan proposed to show that “possible inconsistency of collective choice as applied to voting is a necessary and highly useful characteristic of political democracy” (ibid., 118). He explains that in a majority voting framework, a decision that is not consensus-based may be only provisional or experimental. Indeed, majorities are themselves temporary and any decision can be overturned by a future majority; it can even be overturned by the majority that voted for it (ibid., 119). Moreover, “a majority may reject C in favor of B, and then select A over B, but still select C over A” (ibid.). The conclusion that can be drawn from this apparent paradox is simply that the majority is not able to take a definitive decision. Hence, the result is not necessarily inconsistent, and the majority rule, despite its limitations, offers flexibility and the possibility to move back and forth between different alternatives that are not a subject of consensus (ibid.). Thus, within Buchanan’s reversible representation of the social world, any alternative can be adopted, tested, modified and replaced and the paradox raised by Arrow no longer seems to be a problem. More specifically, Buchanan indicates that in the case of majority voting, a problem could arise if all members of the majority have identical preferences regarding the ranking of the various alternatives. In this case, “collective rationality or consistency is secured here only at the cost of imposing a literal ‘tyranny of the majority’. Minorities under such conditions could no longer accept majority decisions without revolt” (ibid., 120). Here, constraints should be imposed on majority voting. This was the situation that led Wicksell “to advocate the adoption of the principle of unanimity” (ibid.).

21For Buchanan, if as in Arrow’s analysis individuals have an immutable ranking of social alternatives available to them, then the whole temporary majority process with its modified, kept, or reversed decisions must be reduced to a much shorter period of time, to a simple discussion (ibid., 121). The collective choice in this case can be achieved by voting only if a unanimous agreement emerges from this discussion (ibid.). Members of a minority usually know that a decision can be changed, i.e. reversed, only if the members of the majority change their minds (because their ranking of the alternatives changes over time). In this case, the members of the minority will vote for a bill even if they think it is not a good one because they think that the majority will be aware of the inefficiency of the decision and will reverse it in the future. In the polar case of an immutable ranking of preferences, members of the majority will never change their mind and a voted for decision will persist (until the majority can be changed). Knowing that, members of the minority will not vote for it. Thus, bills will pass only in the case of a unanimous decision following discussion. This is the first demonstration of the weakness of majority voting proposed by Buchanan and his first plea in favor of unanimity.

  • 9 “The individual in the market can predict with absolute certainty the direct or immediate result of (...)
  • 10 In a market context, the individual is not aware of the social repercussions of his choices (ibid., (...)
  • 11 The voter can choose to be involved or not in the decision making by voting or abstaining in which (...)
  • 12 Individuals can choose different combinations of goods and services among the multitude of choices (...)

22In the same year, Buchanan (1954b) compares the nature of the individual choices permitted by the market with those permitted by voting (Buchanan, 1954b, 334). In doing so, he again widened the scope of the political objects analyzed by means of economic reasoning. In this contribution, Buchanan examines six points: the degree of certainty that the individual can enjoy at the time of the choice,9 the degree of participation in collective decision-making,10 the degree of responsibility,11 the nature of the proposed alternatives,12 the degree of coercion, and the power relations between the individuals. The last two are the most important. The degree of coercion means that in the context of voting when a decision is made, this decision might go against the voter’s wishes but the voter must submit to the choice of the other electors: “A similar sort of coercion is never present in market choice” (ibid., 339). Again, unanimity would avoid voters being forced to accept a result they disliked. In terms of power relations, Buchanan notes that if democracy guarantees the equality of every voter at the ballot, the market will be characterized by inequality of buying power among the different individuals.

23In synthesizing this analysis, Buchanan states that if the vote is to produce a rational social choice then the individuals must agree on the goals to be achieved at the social level. Unanimity is a useful tool in this case. Otherwise, the irrationality of the vote as conceived in the previous paper, could be positive in the sense that the constraint imposed on a minority is limited by the fact that the decisions taken by the majority can be reversed.

24Buchanan claimed that the market should be privileged if “rationality in individual behavior is considered a desirable feature of a choice process” (ibid., 341). The certainty that is present in the market guarantees rational choice. It is also the preferred option when individual freedoms are valued. This conclusion triggered more work combining political and market analysis.

  • 13 Buchanan joined the University of Virginia in 1956, when he was appointed head of the Department of (...)

25Three years later, in 1957, Buchanan and his colleague Warren Nutter founded the Thomas Jefferson Center for Studies in Political Economy and Social Philosophy at the University of Virginia.13 The research center mission was to foster a “community of scholars who wish to preserve a social order based on individual liberty” (Buchanan, [1983] 2001, 39-40) capable of studying issues related to free societies (ibid.). Gordon Tullock was one of the first young scholars to join the new Center in 1958.

2. Tullock’s Contribution to the Triptych

  • 14 For further details, see Houser and Rowley (2012).
  • 15 Tullock explains how Downs and Black inspired him in letters written in 1958 addressed to Black and (...)

26Tullock’s thinking about politics was based on years of observing government firsthand.14 On joining the Thomas Jefferson Center as a post-doctoral fellow, Tullock was surrounded by scholars who like him were inspired by the works of Anthony Downs and Duncan Black,15 and prompted him to work on political topics. The “principal publication of his fellowship year was a seminal paper on the relevance of logrolling to the problem of majority voting” (Houser and Rowley, 2012, 13). This work revealed Tullock’s doubts about majority voting and his interest in designing better voting rules.

2.1 Tullock’s Practical Approach

27Black’s Theory of Committees and Elections sparked Tullock’s idea that majority voting could be questioned. In a letter to Black dated February 9, 1959, Tullock explained that “[Black’s] work demonstrates clearly that there is no necessity for there being a unique majority position on a voting process” (Tullock, 1959a). The idea that majority voting could be inefficient was developed by Tullock during 1959, and gave birth to two draft papers. One was reworked and was published in the Journal of Political Economy as “Problems of Majority Voting”(Tullock, 1959d).

  • 16 “Democratic Marginalism” is a 10-page manuscript including marginalia by James M. Buchanan. Though (...)

28The possible inefficiency of majority-rule decision-making was at the center of an undated and unpublished monograph entitled “Democratic Marginalism” (Tullock, 1959b)16 which was likely the second draft paper Tullock produced in that year. Tullock explains that in a democracy, “majority is binding on the minority” (ibid., 1), This can result in misallocation of resources and creation of external costs applied to people who receive no benefits from the decision of the vote. The fact that people are forced to accept decisions that are not their own was opposed to the political philosophy of the Thomas Jefferson Center which valued individual freedom. Tullock could not justify his opposition to what he considered to be political oppression based only on his own and the Center’s political principles. He thus attempted to translate his philosophical position into economic terms, explaining that the traditional voting system took no account of the intensity of preferences: voters with intense feelings about a measure can be prevented from making it pass by voters who have very weak feelings about it and vote against the measure to avoid the associated costs.

  • 17 The reflection developed here by Tullock—and basically his entire logic about majority rule and una (...)

29In the case of intensity preferences, logrolling—vote trading—is presented as a possible solution. Logrolling could account for intensity since it is based on reciprocity: an individual can obtain something strongly desired by promising to vote in favor of something which another individual wants. However, there remains a problem: when the decision is made and involves a cost of implementation financed by public funds and therefore through taxes, everyone including people that do not benefit from the decision is taxed. In other words, some individuals would pay “at a far higher rate than the marginal return on the benefits he receives would justify” (ibid., 3). This will lead to waste—if “the whole complex of … bills is bad for everyone, the fact that each one benefits someone a lot and hurts everyone an imperceptible amount would not save it” (ibid.).17 Further, were the total amount of expenditure and taxes to be proposed as a package to the voters, they vote against it or abstain. However, in Tullock’s model, the mass of bills is never proposed as a unit. This refers to the seriatim assumption of the model: each item is considered individually. In this context, an individual who votes against one measure will automatically attract votes against his own bills in the future. If he wants his bills to be approved, he should vote in favor of all the others. The conundrum would seem to lead to over-investment.

30In this context, each voter seeks to find a way to minimize the total amount of the bills he has to pay while maximizing the chances of the passage of his own bills. A system requiring majority voting in order to make a decision requires only a minimum 50% of positive votes rather than 100%. Thus, any voter who wants to present a bill to the voting process will have to bargain with only 50% of the electorate. Then the 50%+1 will vote in favor of the bills presented and against all the others. The winning majority could shift the cost of its bills to the other 50%-1 who would become the oppressed minority.

  • 18 This is the free riding problem proposed by Mancur Olson (1965).

31This brings us back to the original problem: the oppression of a subset of individuals. Perhaps this is not so much of a problem if the apparent equilibrium is unstable. Those individuals belonging to the minority and paying for the majority’s bills while earning nothing in return, will try to convert at least two members of the majority in order to reverse the decision: “A continuous process of trading support with each member trying to increase his own ‘take’ while maximizing the ‘outgo’ that he had to pay for it would result, and the result would be an expenditure much greater than the social optimum” (ibid., 6). Thus, any majority is fundamentally unstable. This “arises from the effort to divide revenues raised from general taxation among … groups” (ibid., 7). However as Tullock observed, if the services to be funded were indivisible, it would be impossible to pay for them by taxing rotating individuals.18 In this case, we would observe under-investment rather than the previous over-investment.

  • 19 Though the letter is undated, it seems likely that it was written between February and August 1959.
  • 20 Roads were an important topic in the economic literature of the 1950s because a major US highway bu (...)

32This first draft lays the foundations of Tullock’s thinking about majority voting and the decision-making process. The marginalia added by Buchanan were so encouraging that Tullock decided to address the issues raised in the draft more formally to try to get them published. A first version of the article, “Problems of Majority Voting”, was sent by Tullock to some of his colleagues. Buchanan responded in an undated letter19 saying that although the project was “exciting and stimulating, … it require[d] further work” (Buchanan, 1959, 1). In particular, Buchanan encouraged Tullock to develop the example of the funding of roads20 in order to illustrate his theory. Since as seen previously Buchanan’s works were mainly abstract, we can assume that this particular piece of work by Tullock would add some practical flesh to Buchanan’s own theory. Among other comments, Buchanan also developed the idea of a necessary unanimity rule when at some point, members of the minority would become aware of the fact that they were paying taxes for something that did not benefit them. In this case, unanimity might be necessary in order to pass bills (ibid.). When the paper was submitted, a journal referee suggested that either the mathematical proofs should be included or otherwise should not be referred to (Bowman, 1959, 2). Tullock opted for the latter, and the final version without mathematical formalism was published in the Journal of Political Economy in December 1959.

  • 21 This paper corresponds to “a preliminary version” (Buchanan and Tullock, [1962] 1971, 132) of chapt (...)
  • 22 In footnotes, Tullock acknowledges Anthony Downs’s and Duncan Black’s pioneering efforts 1957 and 1 (...)

33“Problems of Majority Voting”21 returned to the issues raised in “Democratic Marginalism” but this time incorporating the practical application of the example proposed by Buchanan. In this article, Tullock questions the majoritarian decision-making process and how it forces the minority to accept the will of the majority. Tullock stated that “little attention has been given to the actual process of decision-making or to the type of policy to come out of the process” (Tullock, 1959d, 571).22

  • 23 In the case of a referendum, there are too many voters so that each one “represents too small a par (...)
  • 24 These two circumstances occur in small direct democracies or in representative assemblies.
  • 25 This particular case is discussed in An Economic Theory of Democracy (Downs, 1957) where Downs show (...)
  • 26 Tullock uses Downs’s median voter theorem to explain the behavior of farmers living alongside the r (...)

34Referring directly to logrolling, Tullock explained that some cases do not allow this practice for example in a standard referendum and in the case of secret ballots.23 However, in all other cases, logrolling is permitted if the electorate is sufficiently small and voters vote openly.24 If these conditions are met, then both explicit and implicit logrolling can occur. Explicit logrolling refers to direct trading of votes; implicit logrolling refers to building a “complex mix of policies to attract support” (ibid., 572).25 Only the first type was discussed in the article which was a draft version. Tullock returned to the fact that the majority-voting process “ignores the various intensities of the desires of the voters” (ibid.). In advocating logrolling, Tullock argues this could be Pareto improving. Since some people are passionate about a measure and some are indifferent, if the former are able to impose their view on the measure and the latter are rewarded for their help, both will see an increase in satisfaction. For Tullock, “prohibiting such transactions is to prohibit a movement toward the optimum surface” (ibid.). At this point, he develops an example related to farmers and roadwork. This includes two types of farmers: the first type (referred to as Kantian in Tullock’s development) take account only of mending their threshold; the second type (Maximizers in the article) adopt a strategy of trying to get their road maintained while paying as little in taxes as possible. Maximizers form a majority capable of bending the minority by imposing the burden of the taxes on everyone despite only their own roads being maintained.26 This example leads to the same conclusions as the example developed in the first draft: a majority will bend a minority to its will, and this majority will not form a stable equilibrium since Kantian farmers will become aware of their subordination to the majority and will try to reverse the situation. Ultimately, every farmer is revealed as a maximizer and overinvestment occurs leading to a paradox where “each individual behaves rationally, but the outcome is irrational” (ibid., 575).

  • 27 Note that Tullock is aware that there could be some objections to his model. He addresses two. Firs (...)

35Tullock tried to find ways to improve upon this “unsatisfactory result” (ibid., 576).27 His first option was for “the members of a community [to] enter into an enforceable bargain under which they act according to the Kantian model” (ibid., 577); “in the more general and realistic case where governmental units deal with a continuing stream of radically different projects, no such agreed formula would be possible” (ibid.). This would “throw us back to making individual decisions with the use of logrolling” (ibid.). Another option would be to require more than a simple majority to vote for any bill but this would increase the difficulty involved in negotiating a bargain. Thus, there seems to be no simple means of improving the logrolling system that is applicable. This led Tullock to state that “the system of majority voting is not by any means an optimal method of allocating resources” (ibid., 579).

2.2 The Second Step in Tullock’s Reflection: Overtaking Simple Majority Voting

  • 28 Mary Bowman received her PhD in economics from Harvard University in 1938 and was associate profess (...)
  • 29 This monograph would constitute the sixth chapter of Calculus, “the keystone chapter of the entire (...)
  • 30 E.g. A could decide to bury his garbage in B’s garden without B’s permission. This would inflict da (...)
  • 31 Of course, permission would be given only if the decision did not inflict damage.

36In a letter to Mary Bowman28 (August 24, 1959), Tullock wrote that he decided to share his mimeographed monograph,29 “A Preliminary Investigation of the Theory of Constitutions” (Tullock, 1959e) with some of his colleagues. The first part of the monograph re-examined the theory developed in his previous article on logrolling and majority voting rule. The novelty lay in the text that deals with “possible mechanisms for compensation of the damaged parties” (Tullock, 1959e, 19) when a system forces the minority to accept the will of the majority. Tullock explained that if everyone was permitted to do whatever he wished, this would incur much damage to the others.30 The reverse of this would be the situation where before anyone took a decision, permission should be obtained from everyone else.31 This is the preferred case because it inflicts the least damage and ensures the best outcome. However, obtaining everyone’s permission would involve bargaining which is costly: it consumes time and resources “by imposing delays on various activities” (ibid., 20). Further, the cost of bargaining increases with the number of people involved. The social benefit would be maximized at the point where damages and costs were both moderate.

37In this context, government’s role is to formulate rules that facilitate bargaining. Tullock’s monograph is “concerned with the rules governing the conduct of this [government]” (ibid., 23). That is, the Constitution. This became a core element of Calculus. Tullock examined different decision-making rules, each time increasing the number of voters required for any action —from 25% of the electorate to unanimity, through simple majority or a two-thirds majority—in order to select the most satisfying solution. The voting method is also questioned, and both direct voting and election of representatives are analyzed. Tullock found that while both direct and indirect voting procedures lead to irrationality, indirect voting also leads to ignorance on the part of the voters for two reasons. First, once the representatives are elected, some might disengage from the issues to be discussed. Second, the representatives might decide to misinform their electorates (ibid., 39).

  • 32 In this case, the bargaining cost would approximate the cost of the electoral campaign and the expe (...)

38An additional issue related to indirect voting raised by Tullock was the fact that a politician, elected by say 51% of the electorate in a majority voting system, would aim to be re-elected and would confine all the benefits to the majority that elected him. Attempting to please the remaining 49% would increase the taxes for the majority and be counterproductive. The circulation of voters between the two groups would appear to mimic the direct voting system: “Constitutional rules to prevent it would appear to be desirable” and “the rule that immediately springs to mind is requiring more than a simple majority in either the local election or in the voting in the legislature” (ibid., 41).32 As Buchanan predicted, in this case unanimity could be the solution. However, although unanimity might protect the minority from too much injury, it would impose severe bargaining costs.

39Since Tullock seemed to have reached a dead end, “unable to find any other rule which could be called correct” (ibid., 43), he decided to test Anthony Downs’s median voter rule. The problem is that “trying to find the exact center of the opinion distribution has the disadvantage that it would prohibit any measure which was opposed by 51% of the population, no matter how feeble their opposition or how strongly the other 49% wanted it” (ibid., 43-44). In other words, the median voter theorem fails to account for the intensity of preferences, and the first problem re-emerges. The only way to solve this would be to compare the different intensities of the voters and to achieve a new distribution, a distribution of the intensity. Unfortunately, there is no way to determine everyone’s intensity of preferences. The median intensity cannot be found, leaving the problem unresolved.

  • 33 In the case of “policies which harmed society more than they helped through concentrated injury to (...)
  • 34 Downs explains that preferences can be distributed along a line and that voters will always prefer (...)

40Of course, in the case of equal intensities for all the voters or in the case of randomly distributed intensity, “the Downs model applies” (ibid., 45), although it does not involve compensation.33 However, the Downs solution is not free of defects, and the presumed linearity of the model34 was a particular problem. Indeed, it effectively requires general agreement on the relative positions of the various proposed policies. This requires preferences to be revealed. What happens if some preferences are independent of each other? Tullock questions the transitivity adopted by Downs that “if one voter prefers A to B and B to C, then another voter who likes C best will prefer B to A” (ibid., 54). Tullock explains that a voter can prefer C yet still prefer A to B which case cannot be depicted linearly. If Charles Dodgson, Duncan Black or Kenneth Arrow had tried to work on the incompatibility of preferences, Tullock believed that this would inevitably have led to “mathematical difficulties which…. lead to the conclusion that voting can hardly provide a sensible conclusion in this case” (ibid.).

  • 35 Tullock develops this point (ibid., 58) with an example. He assumes that the electorate is composed (...)
  • 36 The Rules of Order or Robert’s Rules of Order are a body of rules of procedure for deliberative ass (...)

41Compensation also allowed another problem to be ignored. Taking the Condorcet paradox into account, if compensation were permitted—unless in the unlikely special case of equal intensity of preferences—the paradox would vanish thanks to the bargaining that would take place. This would shift society from a paradoxical situation to the selection of a policy. It should be noted however that “logrolling can itself result in paradoxes if voting is confined to a choice between two candidates” (ibid., 56)35 hence “the number of candidates for office should not be legally or institutionally limited” (ibid., 57). Therefore, the simple majority system which—following Black’s “dynamics” of election process cited by Tullock—confines elections to two parties can lead to confusion and complicates electoral campaigns. To generalize this problem, Tullock explains that all rules made to restrict choices artificially lead to “most inappropriate results” (ibid., 61). This applies to the case of “the Rules of Order36 in use in most modern democracies [which] have as their objective the reduction of all issues to a series of simple yes-no votes” (ibid.).

  • 37 Tullock (1959d, 67) notes that “problems of local government have been based on the mistaken view o (...)
  • 38 Tullock does not use the term “free rider” but the behavior he describes corresponds to Mancur Olso (...)

42From this analysis, Tullock extracts several points: The first is that rather than taxing everybody for unsolicited government actions these actions should benefit only those willing to pay for them. Two problems then arise: First, government has built a monopoly that is inefficient—permitting competition would be far better37—and consumers could act like free riders38 in relation to certain goods and services for which the profit cannot be split between payers and non-payers. This point is reminiscent of the market framework depicted by Buchanan. The second problem is illustrated by the question: who should vote on various issues? In the road maintenance example, Tullock explains that farmers should constitute small governmental units in order to facilitate the bargains. However, we need to know an appropriate unit size. Local roads are used by local people but can also be used by people coming from distant areas. Even were it possible to identify an appropriate unit size in the context of for road maintenance, would this apply to other issues requiring a vote? Let us assume that the answer is yes. The question then becomes whether the same unit will be as useful in future years. One certainty is that the size of the unit must be set in terms of “the likely spread of external costs and economies” (ibid., 67). However, these questions disappear in the context of the following reasoning.

  • 39 One of the main objectives of Calculus was to examine such possible rules.

43Tullock reasons that “if we have a good voting rule, it is relatively unimportant whether we have chosen our governmental unit wisely” (ibid., 69) but at the same time “a wise choice of government unit would make it unnecessary to spend much energy on designing the best voting rule” (ibid.). The difficulties involved make a perfect solution unlikely. Thus, a good Constitution should not provide a unique rule but rather a set of different rules applicable to different situations (ibid., 70).39 Even if “majority rule has achieved practically mystical standing in the minds of many political scientists” (ibid., 71), its replacement must be carefully considered since it could become an artificial pattern that distorts the preferences of the voters.

  • 40 Many—especially Downs and Black—remained unconvinced. Although Tullock and Downs shared some ideas (...)

44It seems that Tullock began to think that majority voting not only could but should be replaced. At the time he sent his monograph to some fellow scholars,40 he published a paper in an Italian journal—Il Politico—to provide an overview of the issue to readers unfamiliar with his new research program (Tullock, 1961b).

45Beginning with the example of road maintenance, Tullock explains directly that in order to limit external costs, people must agree about projects on which to vote. Tullock shows that increasing the number of people involved would reduce the amount of the external costs (Tullock, 1961b, 235). However, a decision would carry bargaining costs that could be split into two different types of costs: those linked to loss of desirable opportunities and those linked to the resources consumed in the bargaining process. At no point is simple majority voting considered since Tullock discovered that it “led to external costs” (ibid., 236). Tullock has one certainty: simple majority voting not only can be but must be replaced. He argues further “only by requiring unanimous agreement … could we make certain that the cost to the “decision-makers” and the real cost coincided, hence eliminating over-investment” (ibid.). Tullock excludes the simple majority voting system from his analysis and reveals his and Buchanan’s preference for working at the constitutional level of government.

3. Calculus as the Central Part of the Triptych

  • 41 In her book, Democracy in Chains, Nancy MacLean depicts Tullock as “a voluble gadfly who did nothin (...)

46Although Tullock’s contribution to Calculus is often neglected and although sometimes Tullock has been judged severely,41 his seminal works are of huge importance. As already mentioned, two of his works became chapters 6 and 10 in Calculus. Moreover, other chapters are constructed around elements of his own work. Of course, Calculus does not merely reproduce Tullock’s earlier work. It provides some new theoretical developments especially concerning unanimity rule.

3.1 A Robust Theoretical Demonstration of Tullock’s Previous Results

47Having demonstrated the limits of majority voting by the means of abstract and practical reasoning, Buchanan and Tullock combined this reasoning to produce a third type of demonstration in Calculus. Their theoretical proof, based on game theory, provides a tighter and richer argument on the weaknesses of majority voting and opens up the possibility to develop more systematically the analysis of voting rules.

  • 42 The development in this chapter can be found in a paper by Buchanan published in the Canadian Journ (...)

48In chapter 1142 of Calculus in particular, Buchanan addresses the issues raised by Tullock using elementary game theory. He begins by considering majority voting in a constant sum game framework, with three and then five players.

  • 43 In a 3-player coalition, each player gets one third of the total earnings, in a 2-player coalition, (...)
  • 44 The 3 possible allocations are (1/2, 1/2, 0), (1/2, 0, 1/2), (0, 1/2, 1/2).

49First, three players set up a coalition of two or three to take a collegial decision and share the earnings among coalition members. However, it requires only a two-player coalition to make a decision since simple majority voting is used. The bigger the coalition, the less the interest in earning shares.43 Given that the players are looking to maximize their earnings and minimize the bargaining costs—which as seen earlier can be very high—Buchanan offers a set of solutions in the form of three possible allocations corresponding to three possible coalitions of two players.44 In each of these allocations, both players win half of the total earnings and the third player wins nothing.

50This allows a strategy to be decided upon. For example, if the winning coalition is the coalition composed of players 2 and 3 so that the allocation is (0, 1/2, 1/2), player 1 can offer to join player 2 and share the total earnings as follows: (1/4, 3/4, 0). Players 1 and 2 experience an improved situation. Player 3 sees his situation downgraded. So now player 3 can decide to propose to player 1 to form a different coalition with the same earnings as in the first case: (1/2, 0, 1/2). Player 2 will be excluded from any winning coalition. Knowing that such a reversal is possible, the players belonging to the first winning coalition have no interest in allying with another player. Symmetrical shares are then accepted since every player knows that if he asks for more, he can be taken out of the winning coalition and replaced by a less greedy player. Hence, the three-player game is stable. However, this stability does not hold if additional players are included.

  • 45 The 10 possible allocations are : (1/3, 1/3, 1/3, 0, 0), (1/3, 1/3, 0, 1/3, 0), (1/3, 0, 1/3, 1/3, (...)

51In the case of a five-player game, different coalitions can be formed. Coalitions of at least three players must be formed since majority voting is still used (coalitions of 4 or 5 players are possible, but non-optimal). Again, Buchanan proposes a set “F” of solutions in the form of ten possible allocations.45 In each of these allocations, the share awarded to each player is one third of the total earnings. Each possible allocation contained in the set can dominate another allocation. For example, (1/3, 1/3, 1/3, 0, 0) can dominate (0, 1/3, 1/3, 1/3, 0) and vice versa. But “as the size of the group is increased, however, the stability properties of the imputations in the set F seem to become less strong” (Buchanan and Tullock, [1962] 1971, 153). Buchanan reaches the conclusion drawn by Tullock that in an extended group, “coalitions will be formed, but any single winning coalition will be relatively unstable and impermanent” (ibid., 154).

  • 46 Buchanan implicitly assumes that individuals investing in highly productive projects show a higher (...)

52The theoretical development proposed by Buchanan is pursued though the example of a non-constant sum game. The three-players game is reused but in this case it is assumed that the shared earnings are invested in different projects. The first player invests in a very productive project, the second invests in a moderately productive project and the third player invests in an unproductive project. Thus, if the inputs correspond to the allocations (1/2, 1/2, 0), (1/2, 0, 1/2) and (0, 1/2, 1/2), the outputs differ and are now: (1, 1/2, 0), (1, 0, 1/4) and (0, 1/2, 1/4). Without vote trading, there is no indication that the socially desirable solution will be chosen. Indeed, the choice may be the first or last solution (ibid., 155-156). Buchanan explains that “these rudimentary elements of game theory” (ibid., 156) demonstrate that “If some vote-trading is not introduced, no allowance can be made for possible variations in individual intensities of preference”.46 The problem is still that logrolling has significant costs. A possible solution would be allowance of side payments—basically vote buying and selling—rather than simple vote sharing (ibid., 157). This is the only way to achieve “positions on the Pareto-optimality frontier” (ibid., 187). However, side payments are not characteristic of the modern functioning of democracy since vote buying and selling is prohibited. Since only logrolling seems possible, it must be considered an indirect way of proceeding to side payments: “individuals are unable to ‘purchase’ voter support directly with money, but they are able to exchange votes” (ibid., 158).

53The results corroborate the conclusions reached by the two authors in their previous works. However, use of game theory permits a rigorous theoretical demonstration, allowing the possibility of alternative sets of assumptions and a deeper understanding of the theoretical issues. It remains for the two authors to reconsider the unanimity rule.

  • 47 “there should be little reason to expect that constitutional rules developed in application to the (...)

54Although Buchanan and Tullock—in line with Tullock’s (1959d) conclusions—considered that adoption of a single decision rule was not necessarily desirable,47 a careful reading of Calculus reveals their inclination for the unanimity rule. Here, it turns out that using a game theory framework helped to rationalize their plea. If a player believes that his condition will be degraded by his participation in the game, he can decide to move away from it. However, in reality, it is impossible to escape the political game, and individuals who refuse to join a coalition will not only be unable to carry out their will but will also be forced to suffer losses in terms of well-being since they will have to bear external costs. The legal constraint of the state forces individuals to pay for decisions from which they do not benefit even in a case where they would prefer to leave the negotiation (ibid., 163). The unanimity rule, by making external costs disappear simultaneously allows the legal constraints to vanish. This solution can resolve the economic problem and fits Buchanan and Tullock’s vision of society.

3.2 Theoretical Developments in Calculus: Unanimity, its Benefits and Limits

55We have seen that one of the main flaws of the majority rule is that inevitably it entails external costs for the members of the minority. The authors indicate that only the unanimity rule can eliminate these costs since there is no longer a minority. Actually, they go beyond this and develop Tullock’s theory.

56In the context of external costs, it might be decided that the state should intervene in order to compel the beneficiaries to redistribute a part of their benefits to the less well-off members. However, in this case the majority who do not receive a direct transfer will use their power to make the minority pay even more for goods and services that ultimately will benefit the majority. Thus, the majority uses the money transferred to the minority for its own good. The very existence of external costs and majority voting rule questions the notion of social transfers. In fact, members of the minority will use the transfers to pay the external costs. The effect of social transfers is cancelled out, and ultimately the members of the majority are the real beneficiaries of any kind of transfer to the minority. In turn, the members of the minority are again oppressed by the majority. This is one more reason to seek to eliminate external costs and to consider unanimity as the means to achieve this.

57Note that this rule would also address another problem underlined in Tullock’s works: the existence of over-investment.

58In reality, the authors believe that some public investment should be left to the private sector. It was clear to Buchanan and Tullock that any project that benefited all individuals would be undertaken only if the majority could shift the attached costs to the minority. This would impose no limit on the adoption of projects that caused public over-investment. This is explained as follows: “If the dominant majority is able to impose the full costs of general-benefit projects on the minority, it follows that all projects yielding any benefits at all to the majority coalition members, and costing no more than the maximum taxable capacity of the minority, will be adopted without question” (ibid., 169). Once the costs of the project exceed the maximum capacity of the minority to pay, then the members of the majority must balance the benefits received if the project is adopted against the residual costs they will have to bear. If the benefits are greater, then the project will be accepted. In this case, only a very inclusive decision rule that is the unanimity rule, could avoid these costs and the waste of resources. Indeed, unanimity requires that all individuals agree on the decision to be taken, and it seems obvious that an individual who observes non-productive investment would not agree. Unanimity is impossible and the investment does not occur.

59Hence, the unanimity rule responds to the two main problems of the majority voting rule. On the one hand, unanimity makes external costs disappear. On the other hand, it avoids over-investment. However this rule is not perfect. One of its defects was demonstrated in Tullock’s 1961 Italian journal article: that is the rule imposes huge internal costs.

60The unanimity rule requires the agreement of every individual involved in the decision. It takes only one individual to disagree to make it impossible to vote for the measure. Therefore if there is a will for agreement undecided or opposing voters must be persuaded of its merits. It can take time and effort to achieve the agreement of every voter which raises decision-making costs. In this context, each individual has monopoly power over a resource that is essential for the decision-making, that is his or her consent. This power complicates matters considerably and can cause overly high negotiation costs.

61Thus, although the unanimity rule is the only one allowing a Pareto-optimal decision, its costs can be such that “even the most rationally constructed constitution will allow some decisions to be made that are ‘nonoptimal’ in the Pareto sense” (ibid., 95). In other words, it is rational for some decisions to use rules that do not require unanimity. The rational individual will internalize all the costs inherent in the different rules when choosing the constitutional rules to govern collective decision-making.

62The difficulty identified by Tullock concerning unanimity and negotiation costs is thus resolved by allowing the individual to choose the rule rather than by imposing one or another rule.

4. Conclusion

63Buchanan and Tullock constructed a substantial demonstration of the inefficiency of simple majority-rule voting. The overall argument in Calculus combines arguments and views taken from each author’s previous contributions to the subject, and adds new intuitions, specific developments, and rationales facilitated by use of a game theoretic framework.

64The first argument is the abstract notion held by Buchanan in the late 1940s and early-1950s based on his reading of Wicksell. The gist of the argument is to emphasize a methodologically individualistic view of society and to defend individual freedom though the application of a unanimity voting rule. Were this to improve social decision-making, we would suggest that Buchanan’s reflection was not designed to change anyone’s mind. It was rather a means for uncovering new questions although he had already decided about the problems related to majority voting.

65The second argument consists of Tullock’s practical demonstration of the weaknesses of the majority voting rule. First, Tullock questioned the majority-rule principle based on his reading of Black’s work. After much wrangling, Tullock concluded that this decision-making rule could be replaced. Second, his study of alternative voting rules led him to think that not only could it be replaced but that it ought to be replaced. Finally, Tullock became convinced that the unanimity rule although not perfect was a better way of taking social decisions. Tullock’s use of simple concrete devices to model voting situations was meant to convince people that he and Buchanan were right.

66The third step in the building of a meaningful normative theory of voting rules was provided in Calculus. A robust theoretical proof of the superiority of the unanimity rule over majority voting was still lacking, and Buchanan and Tullock did provide it within a game theoretic framework. We have seen that both economists subscribed to a certain underlying political and philosophical ideology aimed at preserving individual freedoms when alternatives to market coordination were at stake. The use of mathematical models and game theory allowed them to express their views through standard modeling practices and to take those views as the basis for a research program. Although their book received mixed reactions (Buchanan, 2012, 254), their work aroused the interest of many colleagues such as James Meade, John Rawls and William Riker. As such, the theory of majority voting in Calculus combines Buchanan and Tullock’s previous ideas and innovates in various ways along the lines of Tullock’s intuitions much more than is usually acknowledged.

The author would like to thank the Hoover Institution, Samuel Ferey and Sarah Patton for the help provided in finding documents, Marianne Johnson for her proofreading and the reviewers for their helpful comments.

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Notes

1 William H. Riker notes that the introduction of these two types of costs was a novelty and was introduced to answer the main question posed by its authors: “On what basis does a rational man, situated in a society created by unanimous agreement, consent to the transfer of a particular activity from private to collective decision-making?” (Riker, 1962, 409).

2 Buchanan (2012) contains a discussion of decision-making methods in relation to the chosen upstream epistemological positioning (see section 1).

3 This was defined as a realistic or revisionist challenge to the classical interpretation of democracy (Cunningham, 2002, 9).

4 Buchanan read Wicksell's Finanztheoretische Untersuchungen (1896) while writing his dissertation (see Johnson, 2014) and started to translate it in 1951 (see Marciano 2020). Buchanan's translation was published in Musgrave and Peackock’s (1959) Classics in Public Finance. In this text, Wicksell states that “voting by the unanimity rule allows members of a parliament to choose the public services and their tax prices with an allocation similar to that in the market exchanges.” (ibid.)

5 For Buchanan, before the 1940s, almost all public finance conceived the state as an organic unit. He sought to push economics in the direction of an individualistic state.

6 Buchanan refers to “comments” but provides no examples.

7 Buchanan notes that Ian Little and Jerome Rothenberg were the only ones to incorporate this dimension in their comments.

8 Buchanan returns to the elements present in his 1949 paper.

9 “The individual in the market can predict with absolute certainty the direct or immediate result of his action” (Buchanan, 1954b, 335) whereas in the voting process, “he can never predict the behavior of other voters” (ibid.) and then the result of the vote. Buchanan states that the voter’s behavior can only be understood through a theory that assumes uncertainty. This is what Downs tackled in 1957.

10 In a market context, the individual is not aware of the social repercussions of his choices (ibid., 335-336). In an election, the individual “recognizes that his vote is influential in determining the final collective choice” (ibid., 336), he is aware of the fact that his choice is social. Buchanan states that awareness of the individual who participates in a vote can lead him to change his choice and make a decision that would be different were he choosing only for himself. By contrast, Tullock postulated egoism on the part of voters who vote only according to their own objectives (see below).

11 The voter can choose to be involved or not in the decision making by voting or abstaining in which latter case the choice of the action is left to other individuals. In a market framework, the individual cannot abstain (ibid., 337) but has more knowledge about the benefits and costs inherent in his actions than in the case of voting.

12 Individuals can choose different combinations of goods and services among the multitude of choices offered in the market. The electoral framework severely restricts this possibility, the different alternatives are usually exclusive: voting in favor of a particular alternative prevents the voter from voting for another alternative.

13 Buchanan joined the University of Virginia in 1956, when he was appointed head of the Department of Economics (Boettke and Marciano, 2015, 55).

14 For further details, see Houser and Rowley (2012).

15 Tullock explains how Downs and Black inspired him in letters written in 1958 addressed to Black and to Friedrich Hayek (Tullock, 1958a,b).

16 “Democratic Marginalism” is a 10-page manuscript including marginalia by James M. Buchanan. Though the draft is undated, based on Tullock’s correspondence with editors and with Buchanan it would seem to have been written in late 1958 or early 1959.

17 The reflection developed here by Tullock—and basically his entire logic about majority rule and unanimity—is very “Wicksellian”. In 1896, Knut Wicksell wrote a public finance treatise in which he explained that simple majority rule could not guarantee the allocation of benefits to everyone at the individual level but that unanimity would guarantee such an allocation. See Johnson (2016) on this point.

18 This is the free riding problem proposed by Mancur Olson (1965).

19 Though the letter is undated, it seems likely that it was written between February and August 1959.

20 Roads were an important topic in the economic literature of the 1950s because a major US highway building program had just been launched. Buchanan was very interested in road maintenance. For more details, see Marciano (2018).

21 This paper corresponds to “a preliminary version” (Buchanan and Tullock, [1962] 1971, 132) of chapter 10 of the Calculus of Consent.

22 In footnotes, Tullock acknowledges Anthony Downs’s and Duncan Black’s pioneering efforts 1957 and 1958.

23 In the case of a referendum, there are too many voters so that each one “represents too small a part of the total electorate for [the bargain] to be worth the effort involved” (Tullock, 1959c, 571). In the case of a secret ballot, it is “impossible to tell whether voting promises are carried out” (ibid.).

24 These two circumstances occur in small direct democracies or in representative assemblies.

25 This particular case is discussed in An Economic Theory of Democracy (Downs, 1957) where Downs shows that in order to attract voters, political parties or candidates will try to offer programs that please a maximum of voters through the deployment of a wide political ideology. We do not know whether Tullock was inspired directly by Downs in this line of thinking since he is not referenced in the paper. Previous references to Downs reveal that Tullock did read his book.

26 Tullock uses Downs’s median voter theorem to explain the behavior of farmers living alongside the roads to be maintained.

27 Note that Tullock is aware that there could be some objections to his model. He addresses two. First, maximizers could face an ethical issue that would prevent them from following their strategy. However, Tullock explains that the American system does not include an ethics that would bar logrolling. Second, it is possible that the farmers might realize that adopting a maximizing position would lead all other farmers to adopt the same position. This would result in a maximizing equilibrium that would be worse than a Kantian equilibrium. Thus, “on the basis of cold selfish calculation, [farmers would] follow the Kantian system” (ibid.). But farmers will not act in this way since unless it is possible to prevent every farmer from becoming a maximizer there will always be one person who will act this way and will attract followers.

28 Mary Bowman received her PhD in economics from Harvard University in 1938 and was associate professor of economics at the University of Chicago in the late 1950s.

29 This monograph would constitute the sixth chapter of Calculus, “the keystone chapter of the entire book” (Houser and Rowley, 2012, 14).

30 E.g. A could decide to bury his garbage in B’s garden without B’s permission. This would inflict damage on B.

31 Of course, permission would be given only if the decision did not inflict damage.

32 In this case, the bargaining cost would approximate the cost of the electoral campaign and the expense of running the legislature (Tullock, 1959d, 42). Note that Tullock reminds the reader that the conclusions drawn in this paper are correct only if the “minority on a given project feel more strongly than the majority, that there are a number of such projects, and that the majorities and minorities are not identical in each case” (ibid.).

33 In the case of “policies which harmed society more than they helped through concentrated injury to the minority, the compensation principle not only insures a more equitable distribution of the benefits of various measures, it also rules out a number of undesirable policies which would be adopted if compensation were not required” (Tullock, 1959d, 47). By compensation, Tullock means a system that rewards voters that are hurt by the bills or policies decided in order to compensate for the damage. This compensation could be a monetary compensation or a promise to vote for another policy or some other kind of gift.

34 Downs explains that preferences can be distributed along a line and that voters will always prefer a policy close to his own position on the line to a policy that is more distant on the same line.

35 Tullock develops this point (ibid., 58) with an example. He assumes that the electorate is composed of 7 voters, that the majority voting system is used and that there are 2 candidates A and B. If A offers benefits for voters 1 to 4 and B offers benefits for voters 4 to 7, then voter 4 will be indifferent between A and B. The result of the election is thus undetermined. If B decides to give benefits only to 4, 4 will vote for B as will voters 5 to 7 since they will have nothing in common with A. However, giving benefits only to voter 4 will be less costly in terms of taxes. B should win the election. But if B is the first to reveal his strategy, A has plenty of possibilities to defeat B. A can decide to promise benefits to every voter but 4 or to no voters or to voters 1 to 3 and to voter 5, etc.

36 The Rules of Order or Robert’s Rules of Order are a body of rules of procedure for deliberative assemblies. They constitute the rules necessary for the proper running of an assembly.

37 Tullock (1959d, 67) notes that “problems of local government have been based on the mistaken view of government as a producing agent rather than the collection of consumers which it in fact is” adding in footnotes that “this particular point is one where [his] indebtedness to Dr. James Buchanan is most obvious”.

38 Tullock does not use the term “free rider” but the behavior he describes corresponds to Mancur Olson’s free rider behavior, developed in his (1965) The Logic of Collective Action.

39 One of the main objectives of Calculus was to examine such possible rules.

40 Many—especially Downs and Black—remained unconvinced. Although Tullock and Downs shared some ideas and thoughts privately, Downs told Tullock that he was actually “preparing a reply to … ‘Problems of Majority Voting’” (Tullock, 1960a), although he had already proposed some modifications to the article prior to its publication. Downs published his response in two different papers: “Why the Government Budget is Too Small in a Democracy” (1960) and “Problems of Majority Voting: In Defense of Majority Voting” (1961). Tullock responded in turn in “Problems of Majority Voting: Reply to a Traditionalist” (1961a) in which he continued to express his reluctance about majority voting.

Meanwhile Black responded in a series of unpublished documents gathered in Brady and Tullock (1996). Black’s response was basically an objection to the use of logrolling. “Black held the view that a morally correct man would not actually act in this way” (Brady and Tullock, 1996, 127). Hence Black brought ethical considerations into the debate. To support his conviction, he relied on Albert Venn Dicey, an English jurist and theorist who once said that logrolling was “an admitted evil” (ibid., 196) permitting “the voice of fanatics” to defeat “the common sense of the nation” (ibid.). Going further, Black explained that “a good democrat will want the proposal adopted to be genuine majority choice” (ibid., 150), this fact being the “essence of the democracy” (ibid.). Thus, logrolling, involving “deception and lying … is an evil and repulsive behavior” (ibid.) that “weakens mutual confidence within a chamber and between the chamber and the outside world” (ibid.).

41 In her book, Democracy in Chains, Nancy MacLean depicts Tullock as “a voluble gadfly who did nothing in a conventional way” (MacLean, 2017, 189), who never seem to be working, with a desk “as bare as his trademark smirk” (ibid., 190).

42 The development in this chapter can be found in a paper by Buchanan published in the Canadian Journal of Economics and Political Science in 1961 entitled “Simple Majority Voting, Game Theory and Resource Use”.

43 In a 3-player coalition, each player gets one third of the total earnings, in a 2-player coalition, each player gets half of the total earnings.

44 The 3 possible allocations are (1/2, 1/2, 0), (1/2, 0, 1/2), (0, 1/2, 1/2).

45 The 10 possible allocations are : (1/3, 1/3, 1/3, 0, 0), (1/3, 1/3, 0, 1/3, 0), (1/3, 0, 1/3, 1/3, 0), (0, 1/3, 1/3, 1/3, 0), (1/3, 1/3, 0, 0, 1/3), (1/3, 0, 0, 1/3, 1/3), (0, 0, 1/3, 1/3, 1/3), (0, 1/3, 0, 1/3, 1/3), (0, 1/3, 1/3, 0, 1/3) and (1/3, 0, 1/3, 0, 1/3).

46 Buchanan implicitly assumes that individuals investing in highly productive projects show a higher intensity of preference for a specific solution, the one permitting their investment.

47 “there should be little reason to expect that constitutional rules developed in application to the passage of general legislation would provide an appropriate framework for the enactment of legislation that has differential or discriminatory impact on separate groups of citizens” (ibid., 22)

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Julien Grandjean, « James M. Buchanan and Gordon Tullock on the Weaknesses of Majority Voting: A Triptych »Œconomia, 11-1 | 2021, 49-76.

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Julien Grandjean, « James M. Buchanan and Gordon Tullock on the Weaknesses of Majority Voting: A Triptych »Œconomia [En ligne], 11-1 | 2021, mis en ligne le 01 mars 2021, consulté le 24 juillet 2021. URL : http://journals.openedition.org/oeconomia/10780 ; DOI : https://doi.org/10.4000/oeconomia.10780

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Julien Grandjean

Ecole Nationale d’Administration

Université de Lorraine, Université de Strasbourg, CNRS, BETA, 54000 Nancy France, julien.grandjean@ena.fr

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