The Calculus of Consent: Logical Foundations of Constitutional Democracy

James M. Buchanan.
Buchanan, James M. and Gordon Tullock
(1919- )
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Indianapolis, IN: Liberty Fund, Inc.
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Foreword by Robert D. Tollison.
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Chapter 14The Range and Extent of Collective Action


Implications concerning the relative size of the public and the private sectors of the economy have been suggested at several points in our analysis. These implications have not been fully explored, nor have they been related to each other. In this chapter we shall try to answer the questions: What can be said about the relative size of the public sector as a result of our analysis? Does the analysis suggest that the public sector will be "too large" with respect to the private sector, given certain decision-making rules for collective choice? Or "too small"? What criteria are to be employed in judging whether or not the sphere of collective activity is "too large" or "too small"? How do these criteria and these results compare with those that have been utilized in more orthodox or standard analyses?

Majority Voting and External Costs


The analysis of Chapters 10, 11, and 12 demonstrated that the organization of collective action through simple majority voting tends to cause a relative overinvestment in the public sector if the standard Paretian criteria are accepted. Note that the effects are always in this direction under the behavioral assumptions employed in our models. This is because the majority-voting rule allows the individual in the decisive coalition to secure benefits from collective action without bearing the full marginal costs properly attributable to him. In other words, the divergence between private marginal cost and social marginal cost (the familiar Pigovian variables) is always in the same direction.*39


Recognition that the rule will result in such relative overinvestment will make the individual, at the time of constitutional choice, anticipate some net external costs as a result of the operation of majority voting. A simple extension of the majority-voting model to apply to qualified majority voting yields similar results, the only difference being that expected external costs are reduced as the voting rule becomes more inclusive.


We have shown that majority voting will tend to cause overinvestment in the public sector relative to the private sector on the basis of the orthodox or standard criterion of Pareto optimality. This is a meaningful criterion for static analysis, but it is severely limited in certain important respects. In the first place, Pareto optimality, taken alone, cannot be used to assess the effects of purely redistributive transfers of real income among persons. Moreover, as we have demonstrated in Chapter 13, almost all collective decisions embody certain redistributive elements as well as allocational elements. Redistributive action can also impose external costs, costs which the orthodox Paretian criterion cannot take into account.

The Bench-Mark Criterion


A more comprehensive criterion is provided by the bench mark or zero point used in the construction of the models of Chapter 6. With respect to any given activity, the bench mark is defined as that situation or position which would be achieved when all external costs are absent. In a sense, this represents an "ideally efficient" solution to the problem of organization. In those cases where decision-making costs can be neglected and where no restrictions are placed on the form that collective action is to take, this ideally efficient solution can be attained under the rule of unanimity and the characteristics of the solution are identical with Pareto optimality. Even this limited unanimity test fails, however, when we consider purely redistributive transfers of real income. This is because all members of the group could hardly be expected to agree on an amount of net redistribution considered "optimal" by the individual at the time of constitutional choice. Whereas majority decision-making would tend to involve redistributive "externalities" because redistribution would be extended relatively too far, the requirement of unanimity would tend to involve redistributive "externalities" because redistribution would not be extended far enough.*40 The conceptual unanimity test is helpful, therefore, only in analyzing the allocational aspects of collective action; it is not helpful in analyzing the redistributive aspects. In any case, the test is directly useful only if decision-making costs are neglected.


These costs cannot, however, be neglected. Hence our bench-mark criterion becomes a purely hypothetical standard of achievement. For all purely allocational decisions, the bench mark becomes that position which could be attained by the operation of the rule of unanimity, with compensations as appropriate, if individuals did not invest resources in strategic bargaining. The position is identical to that defined more rigorously by Paul Samuelson and R. A. Musgrave in their development of the pure theory of public expenditure.*41 For such allocational decisions, the bench-mark position may be conceptualized on the assumption that individual-preference fields are fully known at a single point in time. However, for redistributive decisions, this sort of conceptualization is not possible. A hypothetical position characterized by the absence of all external effects may be imagined, but its more precise conceptualization requires the knowledge of individual utility functions at the stage of constitutional choice as well as at the stage of operational collective decision-making.


This difficulty in conceiving the existence of a bench-mark situation is actually helpful to us instead of providing a barrier to our understanding. This is because one of the main points to be emphasized is the fact that an independent criterion for determining the appropriate allocation of resources between the public sector and the private sector does not exist. Even if all external effects could be eliminated, the costs of agreement required might be so large that the costs-minimizing organization of the activity in question would require the presence of some positive external costs. If this is the case, there must be an overextension of the activity, that is, too many resources utilized relative to that organization presented by the hypothetical ideal. However, these external costs, which measure the distortions caused by the relative overextension, may be more than offset by the reduction in decision-making costs below the level that full unanimity might entail. All of these points were made in Chapter 6; they are repeated here in order to show their relevance in answering the questions posed at the beginning of this chapter.


In one sense, therefore, we can quite properly say that all decision-making rules embodying less than full consensus will tend to cause relatively too many resources to be devoted to the public sector—too many relative to that idealized allocation of resources that the omniscient observer, knowing all utility functions over time, might be able to describe. In another sense, however, if we leave such omniscience out of account, no such conclusion can be reached. The alternative organization of activity—either a removal from the public sector or a change in the collective decision-making rules—might increase rather than decrease the necessary interdependence costs of the activity in question. At this more meaningful level of discussion, when we consider realizable organizational alternatives, no normative judgment can be formed concerning the extent of the public sector from a simple comparison of an existing organization with the bench-mark or ideal solution. Such meaningful judgments can be made only on the basis of a comparison with realizable and relevant alternatives. To say, for example, that majority rule tends to overextend the public sector relative to some idealized and unattainable bench-mark allocation of resources is descriptively meaningful, but the statement is useless in answering the only important question that must confront the individual in framing constitutional decisions. The only meaningful overextension of the public sector must refer to realizable alternatives, and unless interdependence costs can be shown to be reduced under these alternatives, normative statements cannot be made. As Frank Knight has often remarked, "To call a situation hopeless is equivalent to calling it ideal."


The organization of an activity can be classified as "ideal," even though it will be overextended relative to some hypothetical ideal, only if the appropriate constitutional decisions have been made. If the organization is not that which effectively minimizes the interdependence costs, realizable alternatives are possible and normative judgments can be made. If, for those activities that have been shifted to the public sector, the costs-minimization decision-making rule has not been chosen, normative statements can be made about certain changes in organization. External costs imposed on individuals through the operation of the activity may be higher than they need be, and these costs can be reduced only by a change in the decision-making rules.


The "overextension" of collective activities relative to the hypothetical ideal is precisely equivalent in normative content to the existence of externalities resulting from individual behavior in activities appropriately organized in the private sector. As we pointed out in Chapter 5, the existence of such external effects provides neither a necessary nor a sufficient condition for a change in institutional organization.

The Range and Extent of Collective Action


When we discuss the allocation of economic resources between the public or collective sector and the private sector of the economy, it is essential to distinguish between the range of activities that may be collectivized and the extent to which collectivized activities may be pushed. This important distinction is often overlooked. We may clarify the distinction by a single example. Water-resource development and the provision of telephone services are two separate "activities," either of which may be organized privately or collectively. Let us assume that, as in the United States, the first is largely collectivized while the second is primarily organized in the private sector. In the terminology above, the range of collective action will include the activity of water-resource development but not that of telephone service.


What our analysis of the decision-making rules has shown is that, with less-than-unanimity rules, water-resource development, as a single activity, will tend to be "overextended" relative to the hypothetical bench mark. Relatively "too many" resources may be devoted to the development of water-resource projects, even though it may be "ideally" organized in a more meaningful sense. The main point is that our analysis of the operation of decision-making rules says nothing about the range of collectivization. This may or may not be "overextended" relative to the bench-mark criterion. This range of activities will depend on the constitutional decision that has been made concerning the organization of the activities in question.


Such constitutional decisions may or may not be appropriately made. If these decisions are made correctly, the range of collective action will be the "ideal" one, and within this range the separate activities will be organized by the costs-minimizing decision-making rules. External effects will normally be present, which is the same as saying that these activities will be "overextended" relative to some hypothetical ideal, but this sort of inefficiency will be necessary to achieve an organization which will minimize over-all interdependence costs. However, if constitutional decisions are not appropriately made, either the range or the extent of collective action, or both, may be modified in the direction of improved social organization. The set of activities organized through the public sector may be either unduly restricted or unduly expanded, while the extension of the separate activities collectivized may fall short of or exceed that which would be present under more efficient costs-minimizing decision-making rules.


Figure 17.  Click to open in new window.
Figure 17

Several of these points may be illustrated clearly with reference to Figure 17, which is similar to Figure 6 employed earlier. The figure depicts expected costs for a single activity—external costs plus decision-making costs. For this activity collective organization is indicated. If 0A represents the expected external costs from private organization, then any collective decision-making rule between P/N and Q/N will allow collective organization to reduce interdependence costs. The appropriate constitutional decision would be to collectivize the activity and to specify that all decisions relating to it shall be taken under the rule R/N. This "ideal" organization will still involve interdependence costs of RR', a portion of which must consist of expected external costs resulting from an overextension of activity relative to the bench-mark position.


Assume now that the constitutional decision dictates collective organization of the activity under a decision rule Q/N. External costs are clearly expected to be lower (since the external-costs function slopes downward throughout its range), but decision-making costs are expected to be much higher than under the rule R/N. Under the Q/N rule, relatively fewer resources will be devoted directly to employment in the activity, say road repairs, and, measured in this dimension only, the allocation of resources would more closely approximate some "optimal" allocation. However, under Q/N, far "too many" resources will be devoted to investment in strategic bargaining. A shift from the rule Q/N to the rule R/N will cause relatively more resources to be employed directly in the carrying out of the function involved (more roads repaired to excess) and, if decision-making costs are neglected, this will represent a shift away from the "optimality" surface. However, the incremental external costs involved in this shift will be more than offset by the reduction in decision-making costs that is expected to take place.

Collective Action and Rules for Decision


One of the most important conclusions stemming from our whole analysis is that the decision as to whether or not any specific activity should or should not be organized in the public sector will depend on the decision-making rules that are to be chosen. It is almost completely meaningless to discuss seriously the appropriateness or the inappropriateness of shifting any particular activity from private to public organization without specifying carefully the rules for decision that are to be adopted if the shift is made. If the rules for decision in the collective sector are assumed to be exogenously determined by constitutional provisions and by convention, the choices concerning the organization of activities will be directly dependent on these independent variables, and the whole constitutional-choice process will be severely constrained. As suggested in Chapter 6, it may be quite sensible to shift certain activities to the public sector provided certain rules for decision are adopted, and quite irrational to shift the same activities to the public sector under the expectation of still other rules. Figure 17 is again illustrative. If any decision-making rule less inclusive than P/N should be assumed to be fixed independently of the organizational decision, the individual should rationally reject all attempts to place the activity depicted in Figure 17 in the public sector. Only if the rules for decision fall within the range P/N to Q/N will collectivization of the activity be desirable.

Institutional Variables as Analogues for Decision Rules


As we have previously suggested, it will be possible in many cases to organize the operation of an activity in such a manner that analogues to decision rules may be built into the activity itself. For example, if the activity depicted in Figure 17 is expected to impose some external costs on the individual because of the differential or discriminatory nature of the benefits provided, a differential pricing or taxing scheme may be constitutionally adopted. This institutional change would, of course, modify completely the nature of the activity as conceived by the individual at the stage of constitutional choice, and, other things being equal, this would make the individual much more willing to accept both the collectivization of the activity and the operation of the activity under less-than-unanimity rules for decision-making. For our purposes, it seems best to treat activities organized through different institutional arrangements as different activities. For example, a postal system organized wholly on the basis of user pricing becomes a different activity from a postal system designed to be financed from general taxation. To the individual considering these at the stage of constitutional choice, the shape of the expected-costs functions would be so different in the two cases that it seems best to consider them as wholly distinct activities.*42

Side Payments and the Size of the Public Sector


We have previously said that any form of vote-trading, extending from simple logrolling to full monetary side payments (open buying and selling of votes), tends to allow individual intensities of preference on political issues to be more fully expressed. Any of these institutional modifications in the operation of voting rules will tend, therefore, to lower somewhat the external costs that the activity is expected to impose on the individual. If the individual knows in advance that he can, on an issue about which he feels very strongly, take some action to secure the support of less interested voters, he will expect the external costs of the activity to be less severe. In terms of our diagrammatic construction, the introduction of vote-trading in any form serves to shift downward the combined costs function shown in Figure 17.


Since the introduction of vote-trading under consideration applies only to political votes or political support, the expected external costs from private organization should not be modified by such an institutional difference. From this it follows that the constitutional decision as to the organization of the activity will depend also on the extent to which vote-trading is permitted and the extent to which such trading is expected to approximate perfect side payments in final results. The direction of this effect is clear. The more perfect the vote-trading "market," the wider the range of collective activities that will tend to be selected at the stage of constitutional choice. The less perfect the "market," the more restrictive must be the range and scope of collective action. The society that is characterized by strong and effective ethical and moral restraints, which prevent vote-trading, will find it more essential to place constitutional curbs on the political decisions of the majority than will the society in which these restraints are less effective.*43

The Choice of Rules


The discussion continued in this and the preceding chapters emphasizes clearly the ambiguity that is necessarily introduced when reference is made to the "ideal" allocation of resources or, in our particular case, to the size of the public sector as being "too large" or "too small." We have demonstrated that the criteria against which the size of the public sector is usually measured are not fully appropriate. In many instances "optimal" positions represent hypothetical ideals impossible of attainment. Normative judgments can be made only after a comparison of realizable alternatives.


An important, and closely related, point is also illustrated here. The individual, in his role as constitution-maker, does not choose directly the size and the scope of the public sector, "the allocation of resources." Individuals choose, first of all, the fundamental organization of activity. Secondly, they choose the decision-making rules. In a somewhat broader context both of these choices can be conceived in terms of rules, and rational decisions must always be based on some comparison of the working out of alternative rules of organization over a sequence of issues. This emphasis on the fact that policy-makers always choose among organizational rules and not among "allocations" is often forcefully made by Professor Rutledge Vining. Our discussion of the constitutional calculus makes Vining's criticism of the orthodox or standard discussion of policy norms quite meaningful. To make normative statements concerning whether or not governments undertake "too much" or "too little" activity seems to be rather wasted effort unless one is prepared to suggest some possible modifications in the organizational rules through which decisions are made, aside, of course, from the purely propagandist and nonscientific effects of such pronouncements.

Notes for this chapter

The direction of effect is, of course, just the opposite of that which results from the private organization of genuinely collective activities. It has been commonly recognized that, in such cases, the individual decision-maker will not be able to take into account the full benefits to the whole group when he makes his own private decisions. Therefore, the standard Pigovian analysis proceeds: there will tend to be relatively too little investment in such activities. The fact that collective decision-making, as it is organized by less-than-unanimity voting rules, has not been recognized to produce precisely the opposite results seems to be due to the implicit assumption that collective decisions are made, if not explicitly by some voting rule of unanimity, as if unanimity prevails.

The difficulty in treating redistributive transfers (even at the purely conceptual level) within the framework of our model lies in the fact that the "income insurance" calculus, outlined in Chapter 13, involves essentially an "exchange through time" among individuals rather than any "exchange among individuals at a point in time," which is central to the orthodox Paretian construction. The elimination of all external costs under the requirement of unanimity discussed in Chapter 7 follows directly from the consideration of collective allocational decisions only.

Paul A. Samuelson, "The Pure Theory of Public Expenditure," Review of Economics and Statistics, XXXVI (1954), 387-89, and "Diagrammatic Exposition of a Theory of Public Expenditure," Review of Economics and Statistics, XXXVII (1955), 350-56; R. A. Musgrave, The Theory of Public Finance (New York: McGraw-Hill, 1959), chap. 4.

For an example of a brief but interesting discussion of some of the activities (currently undertaken by the federal government) that might be reorganized through the introduction of user pricing, see "Picking Up the Check," The New Republic (9 January 1961).

This analytical conclusion is supported by historical experience. The comparison between the government of Robespierre and the one that followed in 9 Thermidor is instructive. Of the latter it has been noted: "These men had howled with the wolves while the Reign of Terror lasted, but since their sole aim was to acquire money and to keep their skins, they were the kind of men with whom respectable people can do business." (J. Christopher Herold, Mistress to an Age: The Life of Madame de Staël [London: Hamish Hamilton, 1959], p. 151.)

End of Notes

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