The Calculus of Consent: Logical Foundations of Constitutional Democracy

James M. Buchanan.
Buchanan, James M. and Gordon Tullock
(1919- )
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First Pub. Date
Indianapolis, IN: Liberty Fund, Inc.
Pub. Date
Foreword by Robert D. Tollison.
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Chapter 13Pareto Optimality, External Costs, and Income Redistribution


We have shown that, if full side payments are allowed to take place, any decision-making rule for collective action will lead to positions that may properly be classified as Pareto-optimal, although Pareto optimality may not characterize the process or processes through which the positions are attained. Because of the latter, nothing can be said concerning the "desirability" or the "undesirability" of the changes embodied in the operation of any given decision-making rule short of unanimity. Recall that the definition of a Paretian P-point is as follows: a position from which no change can be made without harming at least one individual in the group. This suggests that, when such a position is attained, no external costs are being imposed on the individual by other individuals. Economists are familiar with the fact that one of the necessary conditions for Pareto optimality is the absence of such externalities. Moreover, as we have previously shown, the presence of external costs is equivalent to the existence of "mutual gains from trade," which can, by definition, be secured to the advantage of all parties.


The introduction of full side payments into the model of collective choice seems to imply, therefore, some restrictions on the applicability of the external-costs function developed in Chapter 6. This function, you will recall, relates the expected external costs on the individual to the decision-making rules. The value of the function decreases as the rule becomes more inclusive, but this value remains positive throughout the range. The relevance of this construction has been demonstrated for the individual constitutional calculus when full side payments are not present. Any rule for collective choice embodying less than full consensus must impose some external costs on the individual since resources will tend to be allocated "inefficiently" because of the choice mechanism. If, however, the introduction of full side payments should negate the relevance of this external-costs function, our analysis of constitutional choice would be rather severely limited.


In this chapter we shall try to show that the individual, at the stage of constitutional choice, will expect collective activity to impose some external costs on him, even if full side payments are allowed to take place in the process of reaching decisions, given any decision-making rule other than unanimity. The apparent contradiction between the existence of external costs and the satisfaction of the orthodox conditions for Pareto optimality, which side payments will tend to produce, must be resolved. In so doing, we shall also be able to relate the introduction of side payments generally to the constitutional-choice models of Chapter 6. A by-product of our discussion will be the integration of income redistribution into our model of collective activity. In one sense, this chapter represents a digression from the main stream of our analysis. It seems necessary, however, to avoid certain logical pitfalls, and the material which follows will provide some foundation for the analysis of later chapters.

Redistributive Elements in Majority Decisions


Under the behavioral assumptions of our models, majority decision-making (or any decision-making with less-than-unanimity rules for choice) will tend to produce some asymmetry in gain-sharing among the individual members of the group for which the choices are made. The members of the effective coalition will receive differentially larger shares of the benefits expected to result from collective action and/or they will bear differentially smaller shares of the costs of collective action providing general benefits for the whole group. This amounts to saying that redistributive elements must be a part of any collective decision reached by a less-than-unanimity rule.


What the introduction of side payments accomplishes is the conversion of all collective decisions to these purely redistributive elements. Unless a public investment project is "worthwhile" in a market-value sense, side payments ("bribes") will arise to prevent action from being taken, regardless of the rule for choice. What side payments cannot prevent are the net transfers of real income among the separate individuals and groups. With full side payments, the decision-making rules determine the structure of the net income transfers only; they do not influence the extent of "productive" collective activity. The latter will always be extended to the limits defined by the satisfaction of the Paretian conditions.*37 It is his inability to say anything about the distributive problem that has inhibited the modern welfare economist. Since he cannot presume to make interpersonal comparisons of utility, he cannot adjudge one Pareto-optimal position to be better than any other or even adjudge one optimal position to be superior to all nonoptimal positions. A move from one point to another on the conceptual optimality surface must remain outside the analytical framework of the welfare economist. Since all decisions, public and private, leading to a point on the optimality surface must be made by a proper comparison of marginal costs with marginal benefits, no external effects of the ordinary sort can be present in the final Pareto "equilibrium." From this the inference seems clear that, under a regime with full side payments, since different decision-making rules act only to effect the location of the position on the optimality surface, the external-costs function of Chapter 6 is not applicable. This function appears from this approach to be meaningless for the analysis of purely redistributive transfers. The geometrical inference is that, for such transfers, the external-costs function would lie along the abscissa. External costs would appear to be zero under any rule.


Let us see precisely what the acceptance of such an inference would imply for the constitutional calculus of the individual. Recall that, under our assumptions, the individual, at the time of constitutional choice, is uncertain as to his own role on particular issues in the future. If the inference suggested here is correct, the individual, because of this uncertainty, will not expect positive external costs to be imposed on him by purely redistributive transfers of real income. The reason is evident: he will see that the external benefits which he may secure through imposing external costs on others on certain occasions will tend to equal the external costs which others will impose on him on different occasions. In any single action, the external costs imposed on those from whom income is taken are equal to the external benefits received by those to whom income is transferred. Since, at the constitutional stage, the individual will identify himself with neither of these groups, he will see that the effects tend to balance out as he considers the whole sequence of possible redistributive transfers.


Note carefully, however, just where this line of argument is leading us. If correct, the argument suggests that the individual, at the constitutional level, would never choose to collectivize the redistribution of real income among members of the group. If the external-costs function does not exist for such transfers, then clearly cost minimization of this activity is achieved only by allowing purely private activity. Only in this way will the decision-making costs (the costs of reaching agreement between two or more persons required to form an effective coalition for decisive collective action) be eliminated. If the distribution of real income among members of the society really does not matter, as would be implied by the argument, the most efficient way of organizing "redistribution" is to do nothing about it.

An Alternative Explanation


There seems to be decisive empirical evidence that individuals do not behave as the above argument would indicate. In almost every society some collectivization of income redistribution is to be found; some efforts are made to accomplish real-income transfers among members of the group by collective intervention. How is this observed phenomenon to be explained in terms of our analytical approach? We shall propose an explanation which will incorporate the existence of external costs into a model restricted to purely redistributive transfers. In this explanation the extension of our analysis beyond the limits of orthodox welfare economics can be most easily made apparent.


We may assume that the marginal utility of income declines as the individual receives more income in any particular time period and that the individual recognizes this. We do not require further restrictions on the shape of the individual's utility function. If the individual recognizes that, in any given period, the marginal utility of income will decline as more is received, he will see that, over a succession of periods, his total utility would be increased if some means of "exchange through time" could be arranged. If some institution could be established which would add to his income during periods of bad fortune and subtract from his income during periods of good fortune, the individual's total utility over time could clearly be increased. If, in fact, he could assume that the years of good fortune would be matched by years of bad fortune within his life span, the individual could, conceptually, purchase such "income insurance" from privately organized sellers. However, at the stage of constitutional choice, the single individual cannot make this required assumption. He will recognize that, individually, he may suffer a succession of low-income periods or, alternatively, he may enjoy a succession of high-income periods. Moreover, since income is the primary economic magnitude to be considered in his over-all life planning, the individual will rarely have sufficient wealth at the outset of his life to purchase the "income insurance" that utility-maximizing considerations would dictate to be rational. Nor will potential private sellers of such insurance be in a position to enforce the sort of contracts that might be required to implement such a program in the real world. All of these obstacles to a private "income insurance" would be present even if the most fundamental obstacle were overlooked. This is the fact that the risk in question would be essentially uninsurable by ordinary standards. Since the private individual, by modifying his current behavior, is able to affect his claims for compensations, a privately organized insurance plan might be impossible.


By such considerations as these, the individual may be led to examine the prospects of collectivizing the redistribution of real income to the extent that is indicated to be rational by his utility function. In order to prevent the possibility of his falling into dire poverty in some unpredictable periods in the future, the individual may consider collective organization which will, effectively, force him to contribute real income during periods of relative affluence. Such collective redistribution of real income among individuals, viewed as the working out of this sort of "income insurance" plan, may appear rational to the utility-maximizing individual at the stage of constitutional decision. The essential "uninsurability" of the risk will not, of course, be eliminated by collectivization, but the individual may be more willing to accept the costs of such uninsurability if he knows that all members of the group are to be included in the plan.


Before committing himself, however, the individual must try, as best he can, to analyze the operation of the decision-making rules that may be adopted in carrying out the collective activity of redistribution. Once the constitution is established, the individual actor operates within the predefined rules; no longer must he try to reach full agreement with his fellows. Moreover, in the implementation of income redistribution through collective action, external effects become the essence of private behavior.


Let us suppose that a constitution is adopted which openly and explicitly states that net-income transfers among individuals and groups will be carried out by simple majority voting. In this situation it seems clear that the maximum possible departure from rational behavior in choosing the amount of redistribution could be present. The individuals in a successful majority coalition could impose net taxes on the minority and receive net subsidies for themselves. In the calculus of the individual participant in a majority coalition, a symmetrical share of the coalition gains will be treated as the marginal benefits of action and balanced off against zero marginal costs. It seems certain that "redistribution," considered as an activity, will be carried relatively "too far" under these conditions.


But "too far" relative to what? This is the difficult step in the analysis. Pareto criteria can be drawn in for ordinary collective action, but they are useless here. Nevertheless, the constitutional-choice model is helpful, and it allows us to answer this question, at least conceptually. Redistribution, under the circumstances postulated, will proceed "too far" relative to the amount that the individual, in the role of constitution-maker, could choose to be rational on the basis of long-run utility-maximizing considerations. In one sense, we may translate this into Pareto-optimality terms at a different level of decision-making. The amount of redistribution that unrestrained majority voting will generate will tend to be greater than that which the whole group of individuals could conceptually agree on as "desirable" at the time of constitutional choice. Since conceptual unanimity is possible on this degree of income redistribution, we may, in a certain sense, call this a Pareto-optimal amount of redistribution. The more orthodox Paretian construction applies only to the operational level of decision, that is, within the confines of established constitutional rules. If we are to discuss the formation of the rules themselves, something quite similar to the Pareto criterion emerges when we consider the "optimal" rules. However, it seems best to avoid using the same terms in both cases.


If, in fact, voting rules are expected to result in real income redistribution being extended "too far" relative to that which the individual would rationally choose, we may clearly say that the organization of this activity will be expected to impose some external costs on the individual. The external-costs function of Chapter 6 is equally as relevant in analyzing this activity as all other collective activities. In our model of collective action which allows full side payments to take place, the external costs that are expected from the operation of any decision-making rule are solely those resulting from the overextension of redistribution. Side payments will insure that the orthodox Pareto-optimality surface will be reached, but the redistribution that will take place through the collective-choice process will not represent the "optimal" shifting among positions on this orthodox optimality surface. Note that we do not require an interpersonal comparison of utility in the usual sense to be able to reach this conclusion. We require only that the individual be able to make decisions based on some presumption about his utility function in different periods of time. In a sense, of course, this does represent an interpersonal comparison of utility, but it is of a sort that individuals must, in fact, make in many everyday decisions.


We reach the conclusion that the attainment of an orthodox Pareto-optimal position is not sufficient to insure that there exist no external effects from an activity. The external costs of redistribution will remain, even if perfectly operating side payments arise to insure that the more familiar externalities are eliminated.

"Income Insurance" and Individual Behavior


The expected external costs from redistributive collective action become more pronounced when it is recognized that the form of the transfers may not be at all similar to that which the rational individual, in the role of constitutional chooser, would select as the "optimal" plan of income insurance. Under the assumptions of our model, there is no reason to expect that simple majority voting, for example, would result in a net transfer of real income from the rich to the poor. There is no assurance that the dominant coalition will, in fact, be such that the transfers will provide the "insurance" considered in the constitutional calculus.


This suggests that the expected external costs of purely redistributive action may, in fact, be so high that the individual, at the constitutional level of choice, may decide that any collectivization of direct redistribution is undesirable. Because of this, he may seek to "institutionalize" the "income insurance" plan via constitutional processes.


An analogy that frequently appears in bargaining theory may prove helpful. At the outset of a hunt each of two hunters may consider that his expected utility will be maximized by agreeing on a predefined rule for sharing the day's catch. Each might realize that, only by agreeing to such a rule, could a "fair" sharing be assured. Otherwise, without rules, the hunter securing the major share of the game would probably think that his good fortune was due to his exceptional skill, and he would be extremely reluctant to part voluntarily with a share of the size that he might otherwise have agreed to under a predefined sharing rule.


Empirical evidence points strongly toward some such explanation as that developed here. Not only do most societies with democratically organized governments undertake some collective action with a view toward redistribution of real income, but the manner in which this action is taken suggests clearly that the external effects are sensed acutely by the framers of political constitutions. In the first place, arbitrary and discriminatory redistributive transfers of income and wealth among individuals and groups are normally prohibited. For direct transfers to be effected, some general bases for classifying individuals are usually required. Secondly, the whole constitutional emphasis on securing and guaranteeing the basic human rights and civil liberties can be broadly interpreted as aiming toward an equalization of opportunities rather than an equalization of rewards. If the legal and institutional framework is such that the distribution of emerging rewards is tolerably acceptable, the direct collective intervention to effect the redistribution that may be dictated is reduced. Insofar as the "income insurance" can be provided by improving the rules within which the "economic game" is played, the individual, at the stage of constitutional choice, may be spared the expected external costs of too much and possibly wrongly directed redistribution through collective action. This point was recognized by Knut Wicksell, himself a genuine humanitarian, when he suggested that efforts toward improving distributive results should be centered on reforms of the institutions of property instead of on the redistributive potential of the fiscal system.


Finally, and most importantly, redistribution of real income, per se, is rarely collectivized, in spite of the almost universal acceptance of some collective effort to intervene in the distribution process. Surely there must exist some explanation for the continuing reluctance of societies in the Western world to throw open the redistributive potential of the fiscal system to the ordinary mechanism of collective choice-making. The most plausible explanation seems to be found in the very real fear of the external effects that such an unrestricted collectivization of redistribution might generate. Instead of following this path, Western governments have opened the way for more and more effective redistribution which is accomplished indirectly through the tax financing of public goods and services. By incorporating highly progressive, but nominally general, taxes with special-benefit public services in the fiscal process, the redistribution that is carried out far exceeds that which could be accomplished directly.


This points up the difficulty of putting to practical use the conceptual separation of the allocational and the distributional aspects of the budget, a separation urged recently by R. A. Musgrave.*38 If such a separation were, in fact, required, much less effective redistribution would be carried out since the individual, fearful of the external costs of unrestricted redistribution, would not allow governments as much power as they now possess indirectly.

Allocational and Redistributional Externalities


From the operation of any collective decision-making rule short of unanimity, therefore, the individual normally expects two distinct sorts of external costs to be imposed on him as he considers his possible role over an extended series of issues in a sequence of time periods. If side payments ("bribes") are not allowed, or if only partially effective substitutes are sanctioned, there can be expected to arise some allocational externalities. That is to say, the collective-choice process will cause resources to be employed "inefficiently."


The effects of introducing logrolling or side payments into the collective-choice mechanism are those of "squeezing" out these allocational inefficiencies. If side payments are conceived to be perfectly organized, all such allocational inefficiencies will tend to be eliminated. There will remain only the redistributional "inefficiencies," which can also be called "externalities," with which we have been primarily concerned in this chapter.


The impact of these expected redistributional externalities (these redistributional external costs) on the individual constitutional calculus could scarcely be overemphasized, for it seems to be this expectation which causes the individual to refrain from assigning to the collective sector many activities which he would tend to collectivize if such externalities were absent. Examples are easy to come by. Full efficiency in resource usage in the United States might require the co-ordinated development of the water resources of each regional watershed. The full range of externalities in the allocational sense cannot be exploited except through the co-ordination of development extending over a geographic area encompassing several states. If we accept these presumptions as being true, does it follow that "nationalization" of this function should be supported by the rational, utility-maximizing "average" citizen of the United States, as he might be assumed to adopt a rule of making such a choice? The answer is not nearly as clear as some modern welfare economists, and applied cost-benefit analysts, would like to make it. If such projects are to be financed, or if the individual expects them to be financed, out of general tax revenues collected from the whole population of the country, the redistributional externalities expected may well be sufficiently large to offset the allocational externalities that may be continued by failure to undertake co-ordinated development.



As suggested at the beginning, this chapter has represented somewhat of a digression from our main line of argument. It has been designed to show that our analysis of the constitutional-choice problem (contained centrally in Chapter 6) is applicable to the collective redistribution of real income among persons, despite the apparent contradiction between the attainment of the orthodox Pareto-optimality surface and the continuing existence of net external costs. The contradiction was resolved by showing that our analytical model, extending as it does to the choice of rules for choice, is more extensive than the standard Paretian construction. External costs, in our model of constitutional choice, are made up of two elements: those resulting from what we have called allocational externalities, and those resulting from what we have called redistributional externalities.

Notes for this chapter

This does not imply that the same amount of productive collective activity will be undertaken under all rules if side payments are fully effective. The distribution of real income itself influences the final allocation between public and private goods that will satisfy the full Paretian conditions. On this point, see 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).

End of Notes

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