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.

1. James M. Buchanan and Gordon Tullock, The Calculus of Consent: Logical Foundations of Constitutional Democracy (Ann Arbor: University of Michigan Press, 1962), volume 3 in the series. Hereafter referred to as the Calculus.

2. Volume 16, Choice, Contract, and Constitutions.


3. James M. Buchanan, "Social Choice, Democracy, and Free Markets," Journal of Political Economy, LXII (1954), 114-23; "Individual Choice in Voting and the Market," Journal of Political Economy, LXII (1954), 334-43. Both of these essays are reprinted in Fiscal Theory and Political Economy: Selected Essays (Chapel Hill: University of North Carolina Press, 1960), pp. 75-104.

4. James M. Buchanan, "Positive Economics, Welfare Economics, and Political Economy," Journal of Law and Economics, II (1959), 124-38. Reprinted in Fiscal Theory and Political Economy: Selected Essays, pp. 105-24.

5. Gordon Tullock, A General Theory of Politics (University of Virginia, 1958), privately circulated.

6. Gordon Tullock, "Some Problems of Majority Voting," Journal of Political Economy, LXVII (1959), 571-79.

7. This paper is published in Il Politico, XXV, No. 2 (1960), 265-93. Il Politico is a publication of the University of Pavia, Italy.

Chapter 1

8. T. D. Weldon, States and Morals (London: Whittlesey House, 1947). For a more recent statement of a similar position, see Isaiah Berlin, Two Concepts of Liberty (Oxford: Clarendon Press, 1958).

9. Ibid., pp. 249 and 255.

10. As Otto A. Davis has pointed out in his criticism of an earlier version of this manuscript, the philosophical problem discussed here is by no means confined to constitutional or political theory. Similar problems arise when any "genuine" choice is confronted. A choice among alternatives is made on the basis of some criteria; it is always possible to move one step up the hierarchy and to examine the choice of criteria; discussion stops only when we have carried the examination process back to ultimate "values."

11. The contract theory of the State can be interpreted in this manner; and, if the theory is so interpreted, our whole analysis can be classified as falling within the broad stream of contractarian doctrine. On the specific relationship between the analysis of this book and the contract theory, see Appendix 1.

12. Cf. F. A. Hayek, The Constitution of Liberty (Chicago: University of Chicago Press, 1960), p. 179.

13. Knut Wicksell, Finanztheoretische Untersuchungen (Jena: Gustav Fischer, 1896).

14. Kenneth Arrow, Social Choice and Individual Values (New York: John Wiley and Sons, 1951).

15. Duncan Black, The Theory of Committees and Elections (Cambridge: Cambridge University Press, 1958); also, Duncan Black and R. A. Newing, Committee Decisions with Complementary Valuation (London: William Hodge, 1951).

16. James M. Buchanan, "Social Choice, Democracy, and Free Markets," Journal of Political Economy, LXII (1954), 114-23; "Individual Choice in Voting and the Market," Journal of Political Economy, LXII (1954), 334-43; and "Positive Economics, Welfare Economics, and Political Economy," Journal of Law and Economics, II (1959), 124-38. Reprinted in Fiscal Theory and Political Economy: Selected Essays (Chapel Hill: University of North Carolina Press, 1960), pp. 75-124.

17. Robert A. Dahl and Charles E. Lindblom, Politics, Economics, and Welfare (New York: Harper and Bros., 1953).

18. Bruno Leoni, Freedom and Law (lectures delivered at Fifth Institute on Freedom and Competitive Enterprise at Claremont Men's College, 1957 [mimeographed]); "The Meaning of 'Political' in Political Decisions," Political Studies, V (1957).

19. Henry Oliver, "Attitudes toward Market and Political Self-Interest," Ethics, LXV (1955), 171-80.

20. Anthony Downs, An Economic Theory of Democracy (New York: Harper and Bros., 1957).

21. Gordon Tullock, A General Theory of Politics (University of Virginia, 1958), privately circulated.

22. The basic work in this tradition is Arthur Bentley's The Process of Government (Bloomington: The Principia Press, 1935 [first published 1908]). The most important recent work is that of David B. Truman, The Governmental Process (New York: Alfred A. Knopf, 1951). The works of Pendleton Herring also fall within this general grouping. See his The Politics of Democracy (New York: W. W. Norton and Co., 1940); Group Representation before Congress (Baltimore: The Johns Hopkins Press, 1929).

23. See especially Jacob Marshak, "Efficient and Viable Organizational Forms," in Modern Organization Theory, ed. by Mason Haire (New York: John Wiley and Sons, 1959), pp. 307-20.

Chapter 2

24. In this, we do not go as far as Arthur Bentley, who states that this organic conception is beyond social science. His comment, however, is worth noting: "... we can drag in the 'social whole,' and there we are out of the field of social science. Usually we shall find, on testing the 'social whole,' that it is merely the group tendency or demand represented by the man who talks of it, erected into the pretense of a universal demand of the society; and thereby, indeed, giving the lie to its own claims; for if it were such a comprehensive all-embracing interest of the society as a whole it would be an established condition, and not at all a subject of discussion by the man who calls it an interest of society as a whole...." (Arthur Bentley, The Process of Government [Bloomington: The Principia Press, 1935 (first published 1908)], p. 220.)

25. For a useful critique of the more "orthodox" approach, see David B. Truman, The Governmental Process (New York: Alfred A. Knopf, 1951), p. 50. See also Isaiah Berlin, Two Concepts of Liberty (Oxford: Clarendon Press, 1958).

26. In his careful refutation of the Beard thesis, Robert E. Brown establishes the fact that economic differences, at least in terms of class, were not important in 1787. See Robert E. Brown, Charles Beard and the Constitution (Princeton: Princeton University Press, 1956).

Chapter 3

27. Philip H. Wicksteed, The Common Sense of Political Economy (London: Macmillan, 1910), chap. V.

28. There are, of course, exceptions. See Arthur Bentley, The Process of Government (Bloomington: The Principia Press, 1935 [first published 1908]). Also note especially Pendleton Herring, The Politics of Democracy (New York: W. W. Norton and Co., 1940), p. 31.

29. For an illuminating discussion of the many ambiguities in the conception of the "public interest," see C. W. Casinelli, "The Concept of the Public Interest," Ethics, LXIX (1959), 48-61.

30. The following criticism of this faith seems especially interesting: "Those concerned in government are still human beings. They still have private interests to serve and interests of special groups, those of the family, clique, or class to which they belong." (John Dewey, The Public and Its Problems [New York: Henry Holt, 1927], p. 76.)

31. To our knowledge, the only specific recent discussion of this paradox is to be found in Henry Oliver's paper, "Attitudes toward Market and Political Self-Interest," Ethics, LXV (1955), 171-80.

32. For an elaboration of this point, see Frank H. Knight, Intelligence and Democratic Action (Cambridge: Harvard University Press, 1960). See also John Laird, The Device of Government (Cambridge: Cambridge University Press, 1944).

33. For a discussion of the contrast between economic and sociopsychological theories and their implied assumptions about human motivation, see Herbert Simon, Models of Man (New York: John Wiley and Sons, 1957), esp. pp. 165-69.

34. It is interesting to note that even when he mentions the possibility of developing a maximizing theory of political behavior in democracy, Robert A. Dahl does not conceive this in terms of maximizing individual utilities. Instead he speaks of maximizing some "state of affairs" (such as political equality) as a value or goal, and asks: "What conditions are necessary to attain the maximum achievement of this goal?" See Robert A. Dahl, A Preface to Democratic Theory (Chicago: University of Chicago Press, 1956), p. 2.

35. The Bentley "school" represents, of course, the major exception. The important recent work of David B. Truman, The Governmental Process (New York: Alfred A. Knopf, 1951), must be especially noted. Truman attempts to construct a theory of representative democracy that specifically incorporates the activities of interest groups. He does not examine the economic implications of the theory.

36. See William H. Riker, "A Test of the Adequacy of the Power Index," Behavioral Science, IV (1959), 120-31; Robert A. Dahl, "The Concept of Power," Behavioral Science, II (1957), 201-15.

37. Riker, "A Test of the Adequacy of the Power Index," 121.

38. Bruno Leoni has questioned this discussion of the power approach. In his view, individuals entering into a political relationship exchange power, each over the other. This "exchange of power" approach seems to have much in common with what we have called the "economic" approach to political process.

39. This discussion is not to suggest that in modern political process, as it operates, elements that are characteristic of the zero-sum game are wholly absent. A single politician or a political party engaged in a struggle to win an election to office can properly be considered as being engaged in a zero-sum game, and in an analysis of this struggle the power-maximizing hypothesis can yield fruitful results, as Riker and others have demonstrated. The point to be emphasized is that our "economic" model concentrates, not on the squabble among politicians, but on the general co-operative "political" process (which includes the game among politicians as a component part) through which voters may increase total utility.

40. Robert A. Dahl, A Preface to Democratic Theory, esp. chap. 1.

41. Robert E. Brown, Charles Beard and the Constitution (Princeton: Princeton University Press, 1956).

42. D. H. Robertson, "What Does the Economist Economize?" Economic Commentaries (London: Staples, 1956), p. 148.

43. Ibid., p. 154.

Chapter 4

44. Arrow seems to suggest, implicitly, that such social rationality is an appropriate criterion against which decision-making rules may be judged. See his Social Choice and Individual Values (New York: John Wiley and Sons, 1951). For a more extensive critique of this aspect of the Arrow work along the lines developed here, see James M. Buchanan, "Social Choice, Democracy, and Free Markets," Journal of Political Economy, LXII (1954), 114-23. Reprinted in Fiscal Theory and Political Economy: Selected Essays (Chapel Hill: University of North Carolina Press, 1960).

45. This is the approach taken by Robert A. Dahl and Charles E. Lindblom. See their Politics, Economics, and Welfare (New York: Harper and Bros., 1953).

46. Several recent attempts have been made to test this transitivity assumption directly through experimental processes. Some results seem to undermine the validity of the transitivity assumption; others to confirm its usage. We note here only that some such assumption is required for any theory of human organization. If intransitivity (instead of transitivity) in individual preference patterns is assumed to characterize behavior, the degree of order that may be observed in either economic or political relations becomes wholly inexplicable.

47. As we shall emphasize later in the book, the process of bargaining, of attaining agreement, itself serves to reduce significantly the range of uncertainty that may exist before bargaining.

Chapter 5

48. An important exception is William J. Baumol's Welfare Economics and the Theory of the State (Cambridge: Harvard University Press, 1952). Starting from behavioral assumptions similar to those employed here, Baumol examines the extension of state or collective activity. He does not explore the economic aspects of the constitutional problems that are introduced in the choices among alternative collective decision-making rules.

49. Our costs approach is related to the negative version of the utilitarian principle, as formulated by Karl Popper. See his The Open Society and Its Enemies (2d rev. ed.; London: Routledge and Kegan Paul, 1952), Vol. II, chap. 5. Cf. also Ludwig Von Mises, Human Action (London: William Hodge, 1949), for a general economic treatise that consistently employs the conception of the minimization of dissatisfaction rather than the maximization of satisfaction.

50. This is not to suggest that this preliminary step is unimportant or that it is not amenable to analysis. At this point, however, such an analysis would carry us too far afield. For our purposes, any delineation of property embodying separable individual or group shares provides a suitable basis.

51. Recall that externalities are defined in terms of reductions in individual utility, not in terms of objectively measurable criteria. Thus, our conclusion holds even though "equilibrium" may be characterized by smoke from a factory being observed to soil household laundry. Such an observation would suggest only that adequate compensations must have been, in some way, organized.

52. The fourth ordering (b < g < a) might, of course, also characterize the activities of a business firm, but this possibility does not modify the argument here.

53. The business firm emerges as the institutional embodiment of this fact, since co-ordination may be achieved more efficiently in this way than through the use of direct contractual relations among all parties to the co-operative endeavor. On this point, see Ronald H. Coase, "The Nature of the Firm," Economica, IV (1937), 386-405. Reprinted in American Economic Association, Readings in Price Theory (Chicago: Richard D. Irwin, 1952), pp. 331-51.

54. At first glance, it may seem awkward to fit the increasing-returns case into our general conceptual scheme. Individual production organized in small units does not normally impose external costs directly on other individuals. Instead, the combination of productive factors into larger producing units results in greater total income for all members of the group. However, stated in opportunity cost terms, any failure of production to be organized in efficient-sized units may be said to impose external costs, even if indirectly. So long as the organizing entrepreneur does not secure for himself the full value of the "surplus" resulting from combining resources, some external "benefits" from this action will be expected by all individuals; and, of course, competition among potential entrepreneurs will act to prevent any such full appropriation of the "social surplus" created by more efficient organization. The entrepreneurial behavior, therefore, may be said to reduce the "external costs" imposed on the individual by inefficient "handicraft" production.

55. For an extended discussion of the problem of externalities in connection with municipal development, see Otto A. Davis, "The Economics of Municipal Zoning" (unpublished Ph.D. dissertation, University of Virginia, 1959). Also see the chapter on "Housing and Town Planning" in F. A. Hayek, The Constitution of Liberty (Chicago: University of Chicago Press, 1960).

Chapter 6

56. This particular assumption is required to avoid ambiguities that might arise concerning the possible "pricing" of collective services. As we shall discuss later, such institutional devices may, in some cases, serve as analogues to more inclusive decision rules.

57. This distinction is often overlooked. See, for example, W. Starosolskyj, "Das Majoritätsprinzip," contained in Wiener Staatswissenschaftliche Studien, Dreizehnter Band (Wien: Franz Denticke, 1916), pp. 26-30.

58. Note that this cost function which ranges over rules that require an increasing share or fraction of a total fixed-sized group to agree will be different from that function which ranges over groups of different size, each of which operates under the rule of unanimity, or indeed of any fixed decision rule. This distinction will be discussed in some detail in Chapter 8.

59. The same results could, of course, be derived through the use of marginal costs rather than total-costs functions. The individual should choose that decision-making rule indicated by equality between the first derivatives of the two total functions, disregarding the signs.

60. Reference here is to the so-called "20 per cent protest rule."

61. As Hayek suggests, the consideration of general rules cannot be undertaken with particular cases in mind. Cf. F. A. Hayek, The Constitution of Liberty (Chicago: University of Chicago Press, 1960), p. 210.

62. We are indebted to Professor Rutledge Vining for this analogy with the formation of the rules of a game, and for his emphasis on the essential differences between the discussion of such rules and the discussion of the appropriate individual strategies in the playing of a defined game.

63. Knut Wicksell, "A New Principle of Just Taxation," in Classics in the Theory of Public Finance, ed. R. A. Musgrave and A.|T. Peacock (London: Macmillan, 1958), pp. 90-92.

Chapter 7

64. For a part of its range, the G curve could, of course, lie below the horizontal axis: that is to say, the "net benefits" may well be negative under certain decision-making rules.

65. Since the conclusions here are not immediately apparent, additional comments may prove helpful. Assume that an industrial plant emits smoke which imposes real costs on local residents. Insofar as these residential property owners must undergo costs which the plant owners do not undergo, the capital value of the plant to the group of residential owners must exceed the capital value of the plant to its current owners. Mutual gains from trade exist, and, if we disregard all decision-making costs, trade will take place. The new owners may not find it profitable to introduce complete smoke abatement. However, since internal marginal costs of production will be increased, some reduction in output will be undertaken, provided that we assume the initial position was one of disequilibrium. For an interesting discussion of many of these points, see Ronald Coase, "The Problem of Social Cost," The Journal of Law and Economics, III (1960), 1-44.

66. For an extended discussion of the relationship between the Pareto criterion and the unanimity rule in collective decisions, see James M. Buchanan, "Positive Economics, Welfare Economics, and Political Economy," Journal of Law and Economics, II (1959), 124-38. Reprinted in Fiscal Theory and Political Economy: Selected Essays (Chapel Hill: University of North Carolina Press, 1960), pp. 105-24.

67. The first aspect of the unanimity rule was stressed in James M. Buchanan's "Positive Economics, Welfare Economics, and Political Economy." At the time this article was written, the author did not fully appreciate the constitutional problem under discussion in this book.

68. "May" is used in the permissive sense here. Sharp differences among individual-utility functions could prevent the attainment of unanimity at the ultimate constitutional level.

69. Note that by saying that less-than-unanimity rules will lead to the making of "nonoptimal" choices, we are not saying that these rules work inefficiently by any other than the simple Pareto criterion.

Chapter 8

70. The results of recent laboratory experiments strongly support the hypothesis that the outcome of two-person bargains will fall on the contract locus. See Sidney Siegel and Lawrence E. Fouraker, Bargaining and Group Decision-Making (New York: McGraw-Hill, 1960).

71. For one of the few discussions relating to this issue, see Richard A. Musgrave, The Theory of Public Finance (New York: McGraw-Hill, 1959), chap. 6.

72. Paul A. Samuelson, "The Pure Theory of Public Expenditure," Review of Economics and Statistics, XXXVI (1954), 387-89; "Diagrammatic Exposition of a Theory of Public Expenditure," Review of Economics and Statistics, XXXVII (1955), 350-56. Richard A. Musgrave, The Theory of Public Finance.

73. The approach taken here assumes that the reduction of decision-making costs, taken independently, is desirable. Of course, if individuals secure positive utility in participating in political discussion and bargaining, the importance of decision-making costs is reduced. The analogy with ordinary games comes to mind here. If the purpose of a game is "efficiency," this could best be secured by allowing all players to get on the same "side," as Frank Knight has suggested. Specific rules are adopted which will make for an "interesting" but not an "efficient" game.

It must be acknowledged that this concept is not wholly foreign to the political process. The idea that politics is one of the noblest endeavors is central to the Greek conception. Hannah Arendt's The Human Condition (Chicago: University of Chicago Press, 1958) is a modern statement of this position. For our purposes it is important to note only that, insofar as engaging in political bargaining is pleasurable in itself, the rational individual will choose to weigh the resources costs of this activity less heavily relative to the external costs of collective action. Other things being equal, he will, therefore, choose a set of more inclusive decision-making rules.

74. The aspects of decentralized collective activity discussed here have been developed by Stigler and Tiebout. See George J. Stigler, "The Tenable Range of Functions of Local Government," Federal Expenditure Policy for Economic Growth and Stability (Washington: Joint Economic Committee, 1957), pp. 213-16; and Charles M. Tiebout, "A Pure Theory of Local Expenditures," Journal of Political Economy, LXIV (1956), 416-24.

Chapter 9

1. Our approach is fundamentally different in this respect from that employed by Downs. He also adopts an "economic" approach to democratic process, but, instead of starting at the individual level, he starts with two-party representative democracy and analyzes the political process in terms of the attempts of governments to maximize voter support. See Anthony Downs, An Economic Theory of Democracy (New York: Harper and Bros., 1957).

2. At this point in our analysis we do not imply either praise or condemnation of any behavior of the individual on moral or ethical grounds. Language conventions force us to use the words "moral" and "ethical," and moral principles must be discussed later in the book, but we do not want to prejudice the analysis by moralizing at this early stage.

3. An interesting recent novel about Washington politics, written by an observing journalist, includes logrolling at several levels as an important part of the political picture. See Allen Drury, Advise and Consent (New York: Doubleday, 1959). For the reactions of an "orthodox" liberal student of politics to this approach, see the review of the book that appeared in The Reporter for 11 November 1959.

4. On this point, we agree with the view of Arthur Bentley. His statement on the issue is worth noting: "Log-rolling is a term of opprobrium. This is because it is used mainly with reference to its grosser forms. But grossness as it is used in this connection merely means that certain factors which we regard as of great importance are treated by the legislator as of small importance and traded off by him for things which we regard as a mess of pottage, but which he regards as the main business of his activity. Log-rolling is, however, in fact, the most characteristic legislative process. When we condemn it 'in principle,' it is only by contrasting it with some assumed pure public spirit which is supposed to guide legislators, or which ought to guide them, and which enables them to pass judgment in Jovian calm on that which is best 'for the whole people.' Since there is nothing which is best literally for the whole people, group arrays being what they are, the test is useless, even if one could actually find legislative judgments which are not reducible to interest-group activities. And when we have reduced the legislative process to the play of group interests, then log-rolling, or give and take, appears as the very nature of the process. It is compromise, not in the abstract moral form, which philosophers can sagely discuss, but in the practical form with which every legislator who gets results through government is acquainted. It is trading. It is the adjustment of interests." (Arthur Bentley, The Process of Government [Bloomington: The Principia Press, 1935 (first published 1908)], pp. 370-71.)

5. "Imperfection" is used here only in its purely economic sense. Nothing in the discussion should be taken to suggest that a "perfect" market in political votes would be, in any sense, "perfect" in respect to some set of ideals for the organization of a political system.

6. We are ignoring the costs of decision-making in this example.

Chapter 10

7. A preliminary version of this chapter has been published. See Gordon Tullock, "Some Problems of Majority Voting," Journal of Political Economy, LXVII (December 1959), 571-79. We are grateful to the editors of this journal for allowing us to reprint those parts of the earlier version that are relevant here.

8. See Anthony Downs, An Economic Theory of Democracy (New York: Harper and Bros., 1957) and Duncan Black, The Theory of Committees and Elections (Cambridge: Cambridge University Press, 1958).

9. Owl: "We didn't hear all yo' speech—just heard yo' say git on out and vote."

Pogo: "That's enough—as long as you do that, you cannot go wrong."

(Walt Kelley, The Pogo Papers [New York: Simon and Schuster, 1952], p. 58.) For an excellent general comment, see Christopher Martin, "In Praise of Political Apathy," The Listener (23 June 1960).

10. An interesting example of this is presented in the comparison of voter support for education in local communities where educational expenditures are presented along with other issues for voter approval with those communities where the educational function is organized and financed through separate decision-making units. This comparison was discussed by Julius Margolis in a paper presented before the Conference on Public Finances, Universities—National Bureau of Economic Research Committee, held at Charlottesville, Virginia, on 10 and 11 April 1959. See National Bureau of Economic Research, Public Finances: Needs, Sources, and Utilization (Princeton: Princeton University Press, 1961).

11. No solution which embodies general tax financing of public services valued differently by different individuals can be Pareto-optimal, unless, of course, fully offsetting compensations are allowed.

12. Critics have objected to our usage of the word "Kantian" in this sense. We have no desire to raise complex philosophical issues here, and we point out only that the word is used solely for want of a more suitable single word describing the behavior that is adequately defined in the text.

13. As suggested in footnote 5, the postulated institutions of the model will prevent the emergence of the fully "efficient" solution in any economic sense. The Kantian solution seems, therefore, to be the most nearly "correct" one that can be attained in the model as postulated.

Note that this Kantian solution is not equivalent to our "bench mark" employed in analyzing the individual constitutional calculus in Part II, which does represent a Pareto-efficient point. The Kantian solution of this model becomes equivalent to the bench-mark solution (that is to say, it eliminates all external costs) only if one of the two following conditions is satisfied.

(1) All voters have the same conception of the idealized standard of road repair: that is, all of the dots along the horizontal line in Figure 12 fall at the median point. In this case, no one is ever disappointed by a decision. "Consensus" is automatically achieved, and, given Kantian behavior for all individuals, the actual voting rule is unimportant.

(2) The distribution of the total costs of road repair among individuals is allowed to vary to correspond with differences in "tastes" concerning the idealized standard of repair. This second condition is, of course, prevented by the assumption that general taxation is employed as the revenue-producing device.

14. In practice, the problem of securing the unanimous consent of the required 51 persons might be insoluble. However, since we are discussing a rather unique special model, we may ignore this possibility.

15. In his paper, "The Theory of the Reluctant Duelist" (American Economic Review, XLVI [December 1956], 909-23), Daniel Ellsberg contends that accepted game-theory notions really apply only to "reluctant" players. Our case of voters is a particularly pure example. The voter must "play the game" by entering into bargains with 50 of his fellows, even though this leads to rather unsatisfactory results, simply because, given the rules, any other course of action would be worse.

This is not to suggest, however, that, given the fiscal institutions postulated in our model, simple majority rule is necessarily less desirable than some other decision-making rule. As the analysis of Part II demonstrates, this may or may not be the most "efficient" rule. What is clear from the analysis of our model is that the fiscal institutions postulated cannot produce "efficient" results under any collective decision-making rule short of unanimity.

16. The fact that he is taxed for other roads not counted in his bargain reduces his real income and, hence, to some extent, reduces his desire for the consumption of road-repair services.

17. See P. W. Bridgeman, The Way Things Are (Cambridge: Harvard University Press, 1959), pp. 268-69.

18. Not necessarily for all. There might be one or more farmers whose personal preferences for road-repairing called for such a large investment as to make the "maximizing equilibrium" preferable to the "Kantian median."

19. The late C. O. Hardy once referred to this argument as the one which assumes the operation of "Dr. Nourse's invisible left hand": that is, men will further their own interest by acting in the public interest.

20. As a practical example, assume that all Easterners should be intensely interested in general programs of water-resource development. Southerners are assumed to be wholly indifferent, and Westerners, by contrast, are, we assume, interested only in their own particular area projects. In this case Easterners should welcome the introduction of logrolling among the Western maximizers, since only in this way can over-all programs of water-resource development be approved.

Chapter 11

21. The treatment will be based directly on the constructions contained in the helpful survey of Luce and Raiffa. See R. Duncan Luce and Howard Raiffa, Games and Decisions (New York: John Wiley and Sons, 1957).

For our particular purpose, we have not found the specific attempts to relate game theory and political theory to be useful, although these contributions may be helpful in a somewhat more general sense. See Karl Deutsch, "Game Theory and Politics: Some Problems of Application," Canadian Journal of Economics and Political Science, XX (1954), 76-83; Martin Shubik, ed., Readings in Game Theory and Political Behavior (New York: Doubleday, 1954); and Richard C. Snyder, "Game Theory and the Analysis of Political Behavior," contained in Research Frontiers in Politics and Government (Brookings Institution, 1955).

22. As William Riker has pointed out in his comment on an earlier version of this book, all political situations that take on genuine "game" characteristics can, for some purposes, be analyzed under the zero-sum restriction. Through the interpretation of individual payoffs in a relative rather than an absolute sense, any positive-sum game can be converted into a zero-sum game. Since our purpose, however, is that of examining the economic meaning of the solutions to the various games analyzed, this conversion to a zero-sum model is not suitable.

23. See J. Von Neumann and O. Morgenstern, Theory of Games and Economic Behavior (3d ed.; Princeton: Princeton University Press, 1953), p. 264.

24. Note that this does not contradict our argument of the last chapter in which it was suggested that individual farmers would not remain Kantians. The difference between the two cases is that there we were considering a whole series of separate but related actions, while here we are considering the possible shifting of coalitions prior to the taking of a single action.

25. In this particular model, the "equitable" solution is equivalent to the "Kantian" solution discussed in the preceding chapter. We shall employ the different term here, however, because these two imputations will not be the same under different circumstances.

26. T. C. Schelling, "For the Abandonment of Symmetry in Game Theory," Review of Economics and Statistics, XLI (August 1959), 213-24. Reprinted as Appendix B in The Strategy of Conflict (Cambridge: Harvard University Press, 1960), pp. 267-91.

27. This property attributed to simple majority rule has been called that of anonymity. May also calls it the equality condition. This terminology seems to be especially misleading since the psychological equality assumed is something quite different from the political equality insured by the fact that each individual has one vote. Cf. K. O. May, "A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decisions," Econometrica, XX (October 1952), 680-84.

Note also that Dahl's conception of political equality requires that each individual's preference be given equal weight. See Robert A. Dahl, A Preface to Democratic Theory (Chicago: University of Chicago Press, 1956), p. 37.

28. Assuming, of course, that the objective values imputed reflect accurate subjective estimates of the relative values of road repair.

29. See the discussion in Chapter 12 for some questions about this particular "solution."

30. Luce and Raiffa, Games and Decisions, p. 193. Note that this is a much more limited usage of the term "individual rationality" than that which we have employed in Part I.

31. In the terminology of some of the commonly used criteria for determining the allocation of public funds among separate projects, a minimum benefit-cost ratio of ½ would be required for a project to secure approval in a collective-decision process embodying simple majority rule.

32. This adjustment was not necessary in the earlier models because we assumed, in each case, that the total initial assets were collected in general taxation: that is, we assumed that $1 was disposed of in each case.

Chapter 12

33. We should emphasize that the graphical construction of Figure 13 is wholly conceptual. A point inside, on, or outside the frontier has no descriptively physical meaning. The graphical apparatus is employed solely to assist the reader in making a conceptual separation among three sets of situations or points: (1) those that are nonoptimal by the Pareto criterion, (2) those that are optimal by the same criterion, and (3) those that are unattainable. The situations or points are classified only on an observed agreement or a failure to agree among the individuals in the group. It is essential that these qualifications be kept clearly in mind, especially by those economist readers who may have been accustomed to discussions of the Pareto criterion in units of measure embodying specifically observable physical dimensions (income, goods, etc.) independent of observed agreement.

34. R. Duncan Luce and Howard Raiffa, Games and Decisions (New York: John Wiley and Sons, 1957), p. 193.

35. Ibid., p. 195.

36. The symmetry in benefit schedules referred to here is not equivalent to the equal or symmetrical intensities of preference referred to in Chapter 9. The discussion at that point was similar to this, but note that there we postulated that the preference, negative or positive, of each individual was valued equally.

Chapter 13

37. 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.

38. R. A. Musgrave, The Theory of Public Finance (New York: McGraw-Hill, 1959).

Chapter 14

39. 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.

40. 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.

41. 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.

42. 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).

43. 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.)

Chapter 15

44. Note that this relationship between voting rules and the stability of solutions is not identical to the relationship between the size of the total group and the stability of solutions. As suggested earlier, game theorists argue that the stability properties of solutions to n-person games become less pronounced as the total group is enlarged in size. Within any group of given size, however, the change from less inclusive to more inclusive voting rules would not seem, a priori, to exert any clearly predictable effect on the stability of solutions obtained.

45. The following reference to Washington's position on this issue is revealing: "On the final day, after the constitution had been engrossed, and the printers had begun printing 500 copies, a motion was made to reduce the congressional constituencies from 40,000 to 30,000. 'When the President rose,' as Madison's notes record, 'for the purpose of putting the question,' he said that 'although his situation'—as president—'had hitherto restrained him from offering his sentiments on questions pending in the House, and it might be thought, ought now to impose silence on him, yet he could not forbear expressing his wish that the alteration proposed might take place. It was much to be desired that the objections to the plan recommended might be as few as possible.—The smallness of the proportion of representatives had been considered by many members of the Convention, an insufficient security for the rights and interests of the people. He acknowledged that it had always appeared to himself among the exceptionable parts of the plan; and late as the present moment was for admitting amendments, he thought this of so much consequence that it would give him much satisfaction to see it adopted.' " (Carl Van Doren, The Great Rehearsal [New York: Viking Press, 1948], p. 170.)

46. Actually, with such a small group, the costs of bargaining would be quite modest and direct democracy would be more efficient. Larger and more realistic models, however, are harder both on the draftsman and the reader.

47. The voters do not, of course, necessarily form the square submatrix shown. Any combination of nine voters distributed three each in three constituencies is sufficient to constitute a dominant coalition.

48. See Anthony Downs, An Economic Theory of Democracy (New York: Harper and Bros., 1957), pp. 142-64.

49. The more inclusive rule for selecting representatives will guarantee to the individual that his own interest will be more likely to be "represented" in the assembly. This being true, his own interest stands a greater chance of being represented in any decisive coalition in the assembly. The danger of adverse collective actions is clearly reduced.

50. It should be emphasized that the derivation of the sign matrix depends strictly upon the relationships among the variables that we have assumed to be present. These relationships are based on what seem to be reasonable assumptions about individual constitutional calculus. Essentially, we have assumed that the constitutional variables, as defined, are compensating rather than complementing. It seems rather difficult to imagine the complementary relationship as applying generally, although it would not, of course, be difficult to imagine a complementary relationship between two narrowly defined constitutional variables. However, it should be noted that there is no mathematical reason why the general relationship among the variables considered need be compensatory.

51. Research now in progress suggests that the general analytical model is also useful in application to other problems of social organization. For example, the problems of the usage of common-property resources and of the degree of decentralization within a unified organizational structure can both be analyzed with essentially the same model as that introduced in this book.

Chapter 16

52. See Figure 19 and the discussion relevant to it.

53. This is not to deny that such a system might have some advantages over a single house. In particular, it might provide for more careful consideration of issues.

Chapter 17

54. Note that essentially the same position has recently been taken by Morton A. Kaplan: "Thus social rules may often be considered as game payoffs, and we are willing to take lower contract payoffs at any particular time or to take risks of lower payoffs that we would be unwilling to accept if we had not internalized these social rules. And most men also have an interest in supporting the socialization process, for, although it constrains them, they are better off than if none was constrained." (Morton A. Kaplan, Some Problems in the Strategic Analysis of International Politics, Research Monograph No. 2, Center of International Studies, Princeton [12 January 1959], p. 9.)

55. This is not to suggest that the distinction has not been clearly understood by political theorists and that its recognition has not affected political institutions. The executive power to veto legislation adopted by a representative assembly finds its basic rationale in the recognition of this distinction. Cf. Benjamin Constant, Réflexions sur les Constitutions (Paris: Nicolle, 1814), pp. 50f.

56. The tendency to slip inadvertently from one meaning into the other is well illustrated by a recent statement made by Anthony Downs: "... it is better for more voters to tell fewer what to do than vice versa. The only practical arrangement to accomplish this is simple majority rule. Any rule requiring more than a simple majority for passage of an act allows a minority to prevent action by the majority. ..." (Italics supplied.—Anthony Downs, "In Defense of Majority Voting," unpublished mimeographed paper written as a general critique of Gordon Tullock's paper, "Some Problems of Majority Voting," which was an early version of Chapter 10. In Downs' favor, however, it might be noted that he supports present procedures for the amending of the Constitution.)

On this general issue, see also Willmoore Kendall, John Locke and the Doctrine of Majority Rule (Urbana: University of Illinois Press, 1941), p. 116.

57. This conclusion assumes that individuals of the blocking coalition are rationally motivated. If, instead, these individuals should all be irrational, they might refuse to enter into "bargains" advantageous to them, and, by this refusal, they might be said to impose "external costs" on others. For example, suppose that a two-thirds majority rule is in operation. Suppose now that 66 out of 100 voters propose a project that will be genuinely beneficial to all 100 voters. To prevent this project from being adopted all 34 other voters must be irrational. If only a few are irrational, the project will be carried. This example suggests that the rationality assumption is not important for the conclusions reached. Individuals will, by and large, tend to approve all proposals that provide them with expected net benefits. This relatively weak version of the rationality assumption seems to be all that is required.

58. Note that we refer to the orthodox theorist, not orthodox institutions. In the real world the overwhelming majority of democratic constitutions cannot, in fact, be amended by simple majorities. Many theorists simply refuse to apply their theoretical structure to constitutions.

Chapter 18

59. The persons in our analytical models may seem to be ethically unattractive, but it should be noted that intellectually they are considerably more "attractive" than the human beings included in more orthodox models of political behavior.

60. The prevailing attitude seems to be quite closely related to the "grossness" of the form that vote-trading activity takes. Truman notes that legislatures and constitutional assemblies have, on occasion, defined vote-trading as a crime, and the Mississippi constitution of 1890 required all legislators to take an oath that they would not engage in vote-trading activity. (David B. Truman, The Governmental Process [New York: Alfred A. Knopf, 1951], p. 368.)

61. Note that the central point made here is precisely equivalent to that raised in connection with the symmetry in gains among the members of a dominant majority coalition in Chapter 12. Symmetry may only be predicted with reasonable certainty if side payments operate perfectly. With partial, but incomplete, side payments, symmetry no longer seems essential for "solution."

62. Alexander Hamilton is said to have remarked that the British Constitution would fall when corruption came to an end. See Sir Henry Maine, Popular Government (New York: Henry Holt, 1886), p. 102.

Chapter 19

63. David B. Truman, The Governmental Process (New York: Alfred A. Knopf, 1951). See also Arthur Bentley, The Process of Government (Bloomington: The Principia Press, 1935 [first published 1908]), and Pendleton Herring, The Politics of Democracy (New York: W. W. Norton and Co., 1940).

For a discussion of recent European works on the problem of pressure groups, see Wilhelm Röpke, " 'I gruppi di pressione' e l'ultima istanza," Studi economici, XIV (1959), 480-85. See especially Joseph H. Kaiser, Die Repräsentation organisierter Interessen (Berlin: Duncker and Humblot, 1956).

64. Major Economic Groups and National Policy, The American Round Table, Digest Report (Chicago, 1958).

65. Cf. Röpke, " 'I gruppi di pressione' e l'ultima istanza," 484.

66. For an instructive analysis of the modern pressure-group problem in terms of its historical development out of economic liberalism, see Professor Goetz Briefs' paper, "Some Economic Aspects of Pluralistic Society," delivered at the meeting of the Mt. Pelerin Society in Oxford in September 1959.

Chapter 20

Appendix 1

67. The study of individual and business-firm behavior with a view toward establishing norms for improving strategic economic positions within a given organization of affairs is appropriately the task of "business administration." The point here is that this whole field of scholarship must be kept rigorously separate from that of political economy.

A similar analogy may be drawn from game theory, where the distinction has been more fully appreciated. The norms for individual-player strategy in a well-defined game must be kept quite distinct from the norms that may be advanced for "improving" the game itself through some change in the rules that describe it.

68. Cf. Isaiah Berlin, Two Concepts of Liberty (Oxford: Clarendon Press, 1958), p. 6.

69. Cf. Ludwig Von Mises, Human Action (London: William Hodge, 1949), p. 2.

70. Benedict Spinoza, A Treatise on Politics, trans. by William Maccall (London: Holyoake, 1854).

71. Essays, Moral and Political: Selections, included in Hume's Moral and Political Philosophy (New York: Hafner Publishing Co., 1948), pp. 295-306.

72. Henry D. Aiken seems to overlook this basic point in his otherwise excellent introduction to selections from Hume's writings. See Henry D. Aiken's introduction to Hume's Moral and Political Philosophy, p. xliv.

The relevant part of Hume's works is Treatise of Human Nature, Part II.

73. For a discussion of "methodological individualism," see Ludwig Von Mises, Human Action, pp. 41-44.

74. Althusius' basic work is Politica methodice digesta (1603-1610), ed. by C. J. Friedrich (Cambridge: Harvard University Press, 1932). I have also had the opportunity to consult in typescript a translation-in-substance of this work undertaken by Stanley Parry, C.S.C.

75. Wolff's ideas are discussed by J. W. Gough in his book, The Social Contract (2d ed.; Oxford: Clarendon Press, 1957), pp. 158-60. The original source is Christian Wolff, Institutiones Juris Naturae et Gentium (Halle, 1750).

76. Fouillée's work is discussed by Gough in The Social Contract, pp. 221-24. The particular work that seems directly relevant is A. Fouillée, La Science Sociale Contemporaine (1880).

77. See Leon Duguit, Law in the Modern State, trans. by Frida and Harold Laski (London: Allen and Unwin, 1921). Note especially the interpretation that Laski placed on Duguit's work in the Introduction.

78. William J. Baumol, Welfare Economics and the Theory of the State (Cambridge: Harvard University Press, 1951).

79. Wilhelm von Humboldt (Breslau: Eduard Trewendt, 1851). English translation: The Sphere and Duties of Government, trans. by Joseph Coulthard (London: John Chapman, 1854).

80. The Sphere and Duties of Government, p. 125.

81. Ibid., p. 126.

82. Ibid., p. 128.

Appendix 2

83. Sometimes, of course, games are not well designed. Checkers, for example, involves a very much more limited number of possible combinations than chess. In recent years expert players have learned these combinations so thoroughly that the principal determinant of victory is who has the first move. Thus, checkers tournaments among experts now consist of a large number of games, most of which are won by the first player, and the decision over the entire series depends on the possible occurrence of mistakes in the play of one or the other player. For ordinary players, the regress, if not infinite, is still so long that the existence of genuine "correct" strategies has no effect on the game.

84. One of the differences between the problem bothering the mathematician and the problem solved by the economist involves the number of independent actors in each "game." While I think that this is less important than the difference between contrived "fair" games and natural situations, it does have some importance. The fewer the independent actors, the more likely that their mutual attempts to adjust their strategies to those of the other players will lead to an infinite regress. The attempt of the probability theorists to solve a two-person game was, therefore, an effort to solve the most difficult case. This should increase the respect we have for Von Neumann's eventual solution.

85. As many economists will already have guessed, I am indebted to Professor Rutledge Vining for this point.

86. Duncan Black, The Theory of Committees and Elections (Cambridge: Cambridge University Press, 1958). The bulk of the theoretical material in this book was originally published in a series of articles in 1948 and 1949.

87. Ibid., pp. 189-238. The pamphlets are also reprinted there.

88. Black also reinvented the subject.

89. Lewis Carroll raised questions even about this case using an analysis which, in effect, contrasted an intense minority and an indifferent majority. (Ibid., pp. 216-17.)

90. This would certainly be so if the preference curves were single-peaked (see explanation below) on an array from A to E. As an example, simple plurality voting might have brought the Communists to power in France.

91. In an effort to be brief, I do not give examples of all of the types of problems which I discuss. The reader who doubts my statements about the possible outcome of some system of voting should consult Black, where one can find proofs and examples.

92. See Black's work (pp. 50-51, 125-40, 173-74, and chap. XVI) for a proof which demonstrates that there could almost never be a majority for complex issues.

93. I ignore chapters XII-XV and XVII in what follows, not because they are unimportant, but because they are not strictly relevant to our subject here.

94. Kenneth Arrow, Social Choice and Individual Values (New York: John Wiley and Sons, 1951).

95. Particularly by my coauthor, James Buchanan, in "Social Choice, Democracy, and Free Markets," Journal of Political Economy, LXII (1954), 114-23. Reprinted in Fiscal Theory and Political Economy: Selected Essays (Chapel Hill: University of North Carolina Press, 1960). Duncan Black also has taken the position that rationality is a characteristic of rational beings, not of institutional arrangements. Arrow himself regards this criterion as weaker than his others. (Social Choice and Individual Values, p. 60, footnote.)

96. If votes are traded, then the order of preference of the individual voter becomes less important than the strength of his preferences. The cyclical majority, vital to Arrow's proof, results from the likelihood of certain orderings of preferences, together with the apparently obvious assumption that voters vote according to their preferences on each issue. Logrolling, which results in many voters voting against their own preferences on many issues, simply is not covered by Arrow's book.

97. "Social Choice, Democracy, and Free Markets."

98. The word "irrelevant" does not seem to me too good a descriptive term, but I cannot think of a better one. Arrow apparently got the term from E. V. Huntington, "A Paradox in the Scoring of Competing Teams," Science (23 September 1938), 287-88.

99. For some reason Arrow does not prove this proposition which is indispensable to his general proof. In fact, he does not even mention it. The criterion of independence of irrelevant criteria is introduced and explained on pp. 26-28, but its vital importance in eliminating all forms of voting except those prescribed by Robert's Rules is never mentioned. Possibly he felt that it was obvious.

100. This motion would be dominated by proposals to reduce repairs on 49 of the farmers' roads by 2 per cent. Further, if it were known in advance that this sort of thing would happen, then it would be taken into account by the people in constructing their logrolling bargains. They would offer 1 per cent more than they expected to pay and demand 1 per cent more than they expected to receive.

101. See Black, The Theory of Committees and Elections, p. 187. See also Condorcet's system discussed by Black on pp. 174-75.

102. Harold Hotelling, "Stability and Competition," The Economic Journal, XXXIX (1929), 41-57.

103. Joseph A. Schumpeter, Capitalism, Socialism, and Democracy (New York: Harper and Bros., 1942).

104. Anthony Downs, An Economic Theory of Democracy (New York: Harper and Bros., 1957). Downs studied under Arrow, and Arrow's influence on his work was significant.

105. Gordon Tullock, A General Theory of Politics (University of Virginia, 1958), privately circulated.

106. In order to avoid misunderstanding, I should point out that, although Downs has obviously obtained his basic model by the process I describe, it has wide implications and is not merely a theory of the operation of the British government.

107. When we first considered undertaking this book, the possibility of thoroughly discussing parties was briefly considered. Generally speaking, the addition of formal parties does not change the conclusions we have drawn but adds a complicating factor to the reasoning. Further, in the United States, party discipline is very weak, and use of a monolithic-party model would have been completely inappropriate. Use of a weak-party model would have complicated the reasoning beyond endurance without changing the final conclusions much. Since the book showed signs of being too long anyway, we decided to put this matter off for future consideration.

108. James Buchanan, "The Pure Theory of Government Finance: A Suggested Approach," Journal of Political Economy, LVII (1949), 496-505.

109. In nondemocratic states the preference schedule of an individual may be what the State device is intended to maximize; but the king is not the State, regardless of what Louis XIV said, and the State itself has no "welfare function."

110. Paul A. Samuelson, "The Pure Theory of Public Expenditure," Review of Economics and Statistics, XXXVI (1954), 387-89.

111. Karl A. Wittfogel, Oriental Despotism (New Haven: Yale University Press, 1957).

112. Knut Wicksell, Finanztheoretische Untersuchungen (Jena: Gustav Fischer, 1896).

113. J. Roland Pennock, "Federal and Unitary Government—Disharmony and Frustration," Behavioral Science, IV (April 1959), 147-57.

114. This article reappears in a somewhat modified form as Chapter 10 of this book.

End of Notes

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