• A Liberty Classic Book Review of The Calculus of Consent: Logical Foundations of Constitutional Democracy, by James M. Buchanan and Gordon Tullock.1
First published sixty years ago this year, James Buchanan and Gordon Tullock‘s The Calculus of Consent: Logical Foundations of Constitutional Democracy is widely recognized as a seminal work in the development of the public choice school in economics and political science. The book builds some of the foundations of James Buchanan’s The Limits of Liberty published 13 years later.2 The main question raised in The Calculus of Consent, as the subtitle of their book suggests, is whether there is an individualist logic in constitutional democracy, whether rational individuals could unanimously consent to the rules that define this political system.

The authors look at politics with the lens of methodological individualism: human individuals are “the only ultimate choice-makers in determining group as well as private action.” Political theories must also rest on reasonable assumptions about individual behavior. Individuals usually follow their own interests, in political as in economic matters. Sometimes they respond to “the instincts of benevolence and sacrifice,” as Dennis Robertson wrote, but a realistic account of social matters must economize on “that scarce resource Love.”
Buchanan and Tullock further assume that “separate individuals are separate individuals and, as such, are likely to have different aims and purposes.” They observe that individuals try to maximize their respective “utility” (“utility” meaning the position of each in his own scale of preferences) through mutually beneficial exchanges. In this perspective, the state (the domain of politics) and the market are just two alternative ways of carrying out mutually beneficial exchanges, a central idea in The Calculus of Consent.

Ethics and the Organization of Human Activity

An activity will be organized collectively instead of being left in the market when it is expected to be more beneficial that way. “Beneficial” means bringing net benefits to each individual according to his own evaluation.
One reason to move an activity (say, police protection) to the collectivized or public sector would be to reduce the external costs of purely private interactions. Buchanan and Tullock adopt a wider definition of “external effects” (external costs or external benefits) than what we now call “externalities.” Their external effects include all the effects that an individual action can have on others, including purely subjective effects and effects that are mediated by markets. External costs include not only pollution but presumably also the drop in the value of somebody’s assets because of his competitors’ actions. The authors note that the cost of eliminating or reducing some external effects of private actions with government intervention may be higher than the costs of the original problem, in which case individuals will want to leave the activity in the private sector.
The problem is that a majority or a plurality of individuals may vote themselves benefits and force the rest of society to pay, or exempt themselves from taxes that the rest must pay. The majority can exploit the minority. These are a different sort of external costs that flow from government action itself.

“An equal moral value is attached to the utility of all individuals. The individualism of The Calculus of Consent is not only methodological, but also ethical.”

The exploitation of a minority raises a normative (ethical) problem if, as Buchanan and Tullock do, we adopt the ethical axiom that individuals are all equal and should benefit from equal freedom. The authors’ political economy is concerned with the organization of a “society of free men.” (It should be needless to say that “free men” means “free individuals,” not “free males” nor “men of this or that color.”) An equal moral value is attached to the utility of all individuals. The individualism of The Calculus of Consent is not only methodological, but also ethical.

A Unanimous Constitution

Any self-interested and rational individual who does not know whether he will be in the minority or in the majority will want to constrain the latter. Buchanan and Tullock formalize this observation by imagining a social contract that establishes basic rules of social cooperation and limitations on the power of any majority. As a foundational beneficial exchange, the social contract must be unanimous. That such a contract has never been signed is not a valid objection, because it is only a conceptual way to say that all members of a society need to agree on the fundamental rules that will guide and constrain their interactions.
The authors reasonably claim that a unanimous agreement is more likely on general rules than on the specific social choices that will come after. There is less potential conflict in choosing the rules of the game than in the outcome of a specific match. In the stylized social contract, the individual is uncertain of his future position, as if he were under what John Rawls called a “veil of ignorance.”3 Buchanan will later say that Rawls’s analytical setting was “closely related to” that of The Calculus of Consent.4 In this  situation of uncertainty, “the individual will not find it advantageous to vote for rules that may promote sectional, class, or group interests.”
By focusing on each individual’s rational decision to adhere to a social contract that serves his interests, Buchanan and Tullock avoid the problem known as the interpersonal comparisons of utility. Such comparisons are scientifically impossible because each individual’s utility is subjective, in his own head. But, of course, an individual can decide whether he prefers one situation to another for himself.
Each and every individual knows that any government decision that will be made in ordinary politics—in “in-period politics” posterior to the social contract—risks generating for him the governmental external costs previously mentioned. The lower the proportion of voters required to approve a decision, the higher are these expected external costs. On the contrary, if a qualified majority (a supermajority) of, say, 66% is needed instead of 50%+1, the individual will have a better chance to be on the right of the majority-minority divide. As the required majority increases, his expected external costs of government action decrease.
However, the decision-making costs- the costs of persuading everybody in the required majority- will grow directly with the size of the required majority. As the qualified majority approaches unanimity, the higher the capacity and temptation become for any individual to hold for a bribe such as lower taxes or special benefits, so the cost of making a bargain with the remaining opponents increases more and more.
Any rational individual will want a constitutional rule that minimizes the sum of decision-making and governmental external costs. The individual will want a proportion of voters closer to unanimity in future political decisions that are likely to affect his previously determined property rights, but a smaller majority or plurality for activities “most characteristically undertaken by governments,” such as education and police protection. Buchanan and Tullock do believe that government intervention—political exchange—is beneficial in many activities.
In this view, a democratic government is “us” but we have to mistrust its power.
Rational individuals establishing constitutional rules will want to impose other limits to majority power, such as a bicameral assembly. Buchanan and Tullock demonstrate that this device greatly limits the capacity to form exploiting coalitions: it can be equivalent to a unanimity requirement in a single house.
Government decentralization whereby individuals can vote with their feet introduces competition and “marketlike alternatives into the political process,” allowing individuals with different preferences to have them catered to by different jurisdictions. This suggests that “where possible, collective activity should be organized in small rather than large political units.” We may wonder if this idea doesn’t underestimate the potential for tribal-like majorities who can better exploit their own minorities, like, say, the Whites with respect to the Blacks in the old South.
For Buchanan and Tullock, at any rate, it is clear that the ideal remains unanimity. Lower voting proportions are just “practical expedients” necessary to take into account the cost of decision-making in day-to-day politics. Only unanimity has a special status and normative significance. The problem of democratic societies is that “majority rule has been elevated to the status which the unanimity rule should occupy.” Ultimately, in the social contract itself, unanimity gives a veto to each and every individual. Unanimity is ultimately the only conceivable test of a right political choice. At the social-contract level, it buttresses the economic concept of Pareto improvement, which means that, from a given starting point, at least some individuals benefit and none are harmed.
Another implication of the unanimity rule is that any individual has the “right of revolution,” which must be the right to secede individually from the contract and not, of course, the right to force others to do the same. If an individual opts-out of the social contract, however, he is likely to lose its protection. The Calculus of Consent is often coherently radical.

Logrolling and Special Interests

Majority voting does not take into account the intensity of preferences: “Even those voters who are completely indifferent on a given issue will find their preferences given as much weight as those of the most concerned individuals.” Although it is forbidden in every democracy, trading votes would at least partly offset this problem. If Mary could sell her vote to John, who values it more, the latter could express the intensity of his preferences (and the former would gain too).
Informal vote-trading is possible through the intermediation of political parties and political entrepreneurs. For example (my own example), if I attach a high value to the Second Amendment but only have a mild preference for federal subsidies to education, I can vote for a candidate or political party that defends my intense opinion even if he strongly opposes the issue about which I care less. It is just as if I had traded my vote with somebody who cares a lot about stopping federal subsidies to education but is lukewarm on the Second Amendment: he gives me his vote on the Second Amendment in return for mine on education subsidies. This indirect trading of votes is called “logrolling.” It is most effectively practiced among elected representatives in smaller legislative assemblies, where one supports pork for  another representative’s constituents in exchange for the latter returning the favor.
One problem of logrolling is that it tends to produce an overextension of the public sector. It is inseparable from democracy, but, as Buchanan and Tullock recognize, the extended exploitation of vote-trading by special interests undermines the democratic regime.
Pressure groups who defend the special interests of their members, such as trade unions (or, for that matter, the special interests of corporations for protection against competition), can impose high external costs on other citizens. The more there is to extract from the government, the more incentives for special interests to enter the political fray. When the segmentation of society into special interests enters a spiral of more and more “differential or discriminatory legislation,” constitutional change becomes necessary to save constitutional democracy. Contrary to what Buchanan and Tullock hoped, however, there is still no sign of a large demand for such a reform.

Functions of Government

What then should be the role of the state? Buchanan and Tullock’s answers may disappoint libertarians and many classical liberals: they view a potentially wide role in reducing the “external costs” of private action, which can be whatever an individual does not like others doing, and in producing whatever good or service the state can produce at a lower cost. The problem is of course tempered by constitutional constraints based on superseding rules that are theoretically unanimous. The state does not enforce a vacuous or ad hoc “public interest.” The “public interest” does not exist except “in terms of the operation of the rules for decision-making, and these rules can be evaluated only over a long and continuing series of separate issues.” This formulation suggests an interface with Friedrich Hayek’s theory of the rule of law.
The rational individual, Buchanan and Tullock argue, will want the constitution to allow some form of “income insurance” because he does not know where he will end up in the distribution of income. The individual is assumed to have diminishing utility of income, which means that one dollar lost is worth more in utility than one dollar gained for him. Such income insurance must be constrained, the authors admit, lest a majority just decides to transfer to itself income from minority’s members, or special interests transfer income from the poor to the rich. The authors of Calculus of Consent point out that this is what framers of political constitutions do in practice: they allow for redistribution but not pure, unconstrained redistribution.
Buchanan and Tullock cited the great Swedish economist Knut Wicksell (whose writings have much influenced Buchanan): improving distribution would be better done through the definition of property rights than through the fiscal system. Although no example is given, one might think that Georgist land taxes for the benefit of the landless would fit the bill; or perhaps stopping the drift of “intellectual property” laws.
Another interesting implication of the constitutional theory developed in The Calculus of Consent is that a more homogeneous community will face lower external costs of governmental decisions, presumably because similar individuals will impose what everybody wants to do anyway. It follows that the members of this community will more readily accept less restrictive rules on majority power. On the contrary, in a more heterogeneous community, individuals will want more restrictive rules against the majority. “Many activities that may be quite rationally collectivized in Sweden, a country with a relatively homogeneous population, should be privately organized in India, Switzerland, or the United States.” But this may underestimate the possibility of parochial oppression, as I suggested above.

The Good Society

Buchanan and Tullock’s “Good Society” remains one in which the power of the government is constitutionally limited. The Enlightenment gave rise to a system where “constitutional democracy in its modern sense was born a twin of the market economy.” In his Appendix on political philosophy, Buchanan emphasizes David Hume’s claim that the purpose of constitutional checks and controls is to make it “in the interest of even bad men to act for the public good.” Recall that, in The Calculus of Consent, the public good is defined as what all individuals would agree on.
Given the drift to differential or discriminatory legislation, Buchanan and Tullock argue for constitutional change. In their opinion, this would mean a shift toward more inclusive voting rules (more requirements of qualified majority) and more restrictive limits on the range of collective activity, although they admit that this is “an explicit value judgment” on their part. They were optimistic that such constitutional change was coming, but didn’t deny that the change could also go the other way. We may also ask how unanimous constitutional change could possibly happen in today’s polarized America or what good change could possibly come out of the process.
The revolutionary character of Buchanan and Tullock’s constitutional doctrine shows clearly in a remark by Tullock in his own Appendix on the book’s theoretical forerunners: “The State should have enough power to ‘keep the peace’ but not enough to provide temptation to ambitious men. The State should never be given enough power to prevent genuinely popular uprisings against it.” Beware of Leviathan!
The Calculus of Consent contains many unanswered questions, which is not surprising for a pioneering book, or any book for that matter. What is the contour of the “group” or “community” of individuals who adhere to a social contract? Doesn’t the growth of the state and the resulting polarization contradict the idea of politics as compromise? If the book provides, as the author claims, “some conceptual rationalization for the type of political complex represented by American constitutional democracy,” hasn’t something very wrong happened in America? Does the state represent politics as exchange or is it more a Leviathan?

For more on these topics, see “A Conversation with James M. Buchanan”, a 2-part video interview at Econlib recorded in 2001; and “Lessons and Challenges in The Limits of Liberty, by Pierre Lemieux, Library of Economics and Liberty, November 5, 2018. See also the EconTalk podcast episode Michael Munger on Constitutions; and Public Choice, by William F. Shughart II in the Concise Encyclopedia of Economics.

Buchanan himself seems to have later become less optimistic.5 He explained how the strict contractarianism of The Calculus of Consent had “a natural tendency to neglect the problems that arise in controlling the self-perpetuating and self-enhancing arms of the collectivity itself,”6 that is, in controlling the state. He seems to have become more fearful of the state conceived as “us.”7
These are crucial issues on which the future of individual liberty, if not of civilization, may depend. And there is no doubt that The Calculus of Consent was a milestone on the road to understanding the social and political world.


[1] James M. Buchanan and Gordon Tullock, The Calculus of Consent: Logical Foundations of Constitutional Democracy (1962) (Liberty Fund, 1999).
[2] James M. Buchanan, The Limits of Liberty: Between Anarchy and Leviathan (1975) (Liberty Fund, 2000).
[3] John Rawls, A Theory of Justice (Belknap Press, 1971).
[4] Buchanan, The Limits of Liberty, p. 10.
[5] Buchanan, The Limits of Liberty, pp. 10-12. See also “Afraid to Be Free: Dependency as Desideratum,” Public Choice 124 (2005), pp. 19-31.
[6] Buchanan, The Limits of Liberty, p. 12.
[7] See also Pierre Lemieux, “Lessons and Challenges in The Limits of Liberty,” Liberty Classics at Econlib.org, November 5, 2018.

*Pierre Lemieux is an economist affiliated with the Department of Management Sciences of the Université du Québec en Outaouais. He blogs on EconLog. He lives in Maine. E-mail: PL@pierrelemieux.com.
For more articles by Pierre Lemieux, see the Archive.