Erik Moberg ©:

A Distinction Overlooked by Buchanan and Tullock

In their analysis of the constitutional problem James Buchanan and Gordon Tullock start by considering decisions rules from the point of view of a single citizen.1 In the basic argument it is assumed that the democracy is direct rather than representative, and that the citizen himself therefore takes part in the decision-making process. When considering various decision rules the citizen takes into account decision-making costs and external costs. The former are the total of all bargaining efforts necessary for reaching a decision, the latter the sum of all disadvantages of different kinds that hit the individual as a consequence of a decision the individual is not supporting.

The two kinds of costs depend on the decision rule as indicated in the figure. The curve Ct indicates that the citizen's decision-making costs (or transaction costs) increase as the majority required for a decision increases. When the decision rule approaches unanimity the costs increase rapidly. As for the external costs it is obvious that, if unanimity is required for a decision, there can be no such costs at all. The external cost curve Ce therefore has the value 0 for the decision rule 1. Buchanan and Tullock furthermore argue that the expected external costs hitting the individual decrease monotonously as the share of citizens required for a decision increases. The sum of the decision-making costs and the expected external costs is called social interdependence costs, which are represented by the third curve Csi. For the individual citizen it is rational to minimize these costs, which means that the decision rule R is optimal. Certainly, with that rule, the individual is now and then hit by harmful effects of decisions which the individual does not support, but this drawback is compensated for by lower decision-making costs than with a larger required majority. The individual is saved from spending an unreasonable amount of time in decision making. This is Buchanan's and Tullock's answer to what they consider a fundamental problem: how come that people voluntarily accept a decision order that now and then places them in a losing minority and thereby makes them suffer from various inconveniences, or external costs?

So far we have talked only about a single individual. In order to get a constitution we must however, in some way, take a step from the individual to the totality of citizens. The constitution should be something that, on the whole, is supported by that totality, and not only by a single individual. Buchanan and Tullock take this crucial step by arguing as follows. First they make a distinction between the decisions by which the constitution is created, which we may call constitutional decisions, and the decisions which, thereafter, are taken within, and by applying, the created constitutional framework, which we may call applied decisions. They then say that it is not only desirable, but also comparatively easy, to reach a unanimous agreement about the constitutional decisions. The main reason for this is that people, at the time of the constitutional decisions, are fundamentally ignorant about their future. The constitutional decisions are therefore, to use John Rawls' well known concept, taken behind a veil of ignorance. In that predicament the individuals are unable to care about their own narrow interests, because they do not know which these interests are. They are only able to consider generally what kind of society they want to live in. And different peoples' answer to that question, formulated behind the veil of ignorance, will, according to Buchanan and Tullock, be quite similar.

For the individual the optimal decision rule can vary from one type of applied decision to another. In the example in the figure it was R, but other values are possible for other types of decisions. Since all the individuals are likely to argue in the same way behind the veil of ignorance, the implication is that they, together, will settle unanimously for a constitution requiring different qualified majorities for different types of applied decisions. This also means that the expected cost patterns, for all the individuals, and for each type of applied decision, are the same, and of the same general character as the pattern in the figure.


Buchanan's and Tullock's basic argument, as presented above, disregards, I think, a crucial distinction. Their idea about how applied decisions are taken can, in fact, be interpreted in two different ways, and the distinction is the one between these two interpretations.

In the first interpretation the population, which shall make a decision, starts as if the decision rule requires unanimity. They start perhaps by creating formations of like-minded, they certainly bargain in various ways, they might form larger and larger groups of people in agreement about a decision, and so on. In short they try to work their way from the initial unstructured situation to a final unanimous decision. Then, all of a sudden, and during the process, some outside actor, an umpire of some kind, surprises and interrupts the people and declares that the matter is settled. The umpire, by himself, may for example, without telling anybody, have made up his mind that a share R of the people should be decisive, and therefore, as soon as that share is reached, he declares that the process is over and that the agreement reached by R shall be the final decision. In the second interpretation, in contrast, people know from the beginning the decision rule which is to be applied, for example that the share R, smaller than 1, is required for the final decision.

Comparing these two interpretations it is easily seen that the first is in a sense mystical. The people, who starts as if a unanimous agreement is needed, are suddenly interrupted from outside by an unknown umpire who applies the decision rule that really, and without the people knowing it, holds. In contrast to this the second interpretation, not relying on any unknown umpire, is perfectly realistic.

A second, important difference between the two interpretations concerns the social interdependence costs. Let us first consider these costs in the process implied in the first interpretation. There, when people move along the way to the intended unanimous decision the accumulated decision-making costs will get higher and higher as in the figure above. It is also reasonable to think that the remaining external costs will become lower and lower, again as in the figure. The people who already are attached to the formation that ultimately will include everybody suffers no external costs at all, because otherwise they would not be attached. The people outside that formation would however probably suffer some external costs if the deal, which at the moment is considered by the people inside the formation, would be declared the final decision. These external costs are however, so to speak, only accidental. They appear only because the people suffering them have so far not been able to make an agreement with the main formation. The costs are only a kind of accidental remnants from the initial unstructured situation. This, of course, is also the reason why the external costs, as in the figure, become less and less as the bargaining process continues.

The process implied by the second interpretation is, in this respect, fundamentally different. To be more specific, and this is the really interesting difference between the two interpretations, the external costs hit the outsiders in other ways, and for other reasons, than in the first interpretation, whereas the analysis of the decision-making costs is rather similar. That the mechanisms which determine the external costs are quite different is easy to see. When the people start negotiating, knowing that it is only necessary to enroll the share R, it is quite possible to have an idea from the beginning about which people shall be left outside (the share 1 - R), and therefore to use these people in different ways. One way, of course, is to exploit them outright for the benefit of the people in the share R. The outsiders may however also be used in other painful, but perhaps less repugnant, ways, as for example as payers of side payments. If for example two groups, potentially belonging to the decision making coalition, find it difficult to agree because one favors a certain decision whereas the other does not, they may simply plan to tax the people potentially outside the coalition and give the money as a compensation to the group which first disliked the proposed decision. In that way it is obviously much easier for the people in the potentially decision making coalition to reach an agreement than if they had to iron out all their different opinions by using side payments only between themselves, and without access to the people potentially outside the decision making coalition. In fact, when the people outside the decision making coalition are available, it becomes possible for the coalition to reach agreements about many things which would be impossible without those people.

The conclusions concerning the second interpretation are thus the following. First the external costs hitting the people outside the decision making coalition are not, as in the first interpretation, accidental remnants from the situation before the decision making process. They are rather deliberately inflicted upon the outsiders, and they may quite possibly become so large as to constitute real exploitation. It is quite clear that external costs governed by mechanisms like this cannot be captured by a simple formalism such as the curve in the figure. Something more complicated is required, such as for example some kind of game theoretical formalism. The decision-making costs, on the contrary, can probably be represented by an increasing curve of the same kind as in the first interpretation. Since the negotiations are easier in the second interpretation the costs are, however, lower. The curve will therefore be placed under the curve in the first interpretation.

Buchanan and Tullock obviously did not make any distinction between two interpretations and the problem therefore is how their position shall be interpreted. If we choose the first interpretation their formalism, as shown in the figure, is valid, but the situation it represents is quite mystical. If, on the other hand, we choose the second interpretation the formalism is no longer valid, but the reality we are talking about becomes concrete and comprehensible. The reasonable choice, I think, is to settle for the second interpretation.

The implication of this is that we must reject part of Buchanan's and Tullock's argument, and part of their formalism. Some of the essentials remain however. Decision-making costs and external costs are still important concepts in the analysis of decision rules and decision making processes, and our view of the decision-making costs and their determinants is also basically the same as Buchanan's and Tullock's. The important differences are that the mechanisms governing the external costs become much more complicated, that the external costs in many relevant situations become considerably higher, and that the decision-making costs become lower.


1The analysis described here was originally given by J M Buchanan & G Tullock, The Calculus of Consent, Logical Foundations of Constitutional Democracy (Ann Arbor: The University of Michigan Press, 1962). A condensed version of the analysis is presented in D C Mueller, Public choice II, A revised edition of Public choice (Cambridge: Cambridge University Press, 1989), p 52 ff. In Swedish the analysis is also described in E. Moberg, Offentliga beslut.