The Calculus of Consent: Logical Foundations of Constitutional Democracy

Insofar as participation in the organization of a community, a State, is mutually advantageous to all parties, the formation of a “social contract” on the basis of unanimous agreement becomes possible. Moreover, the only test of the mutuality of advantage is the measure of agreement reached. Modern political theorists have perhaps shrugged off the unanimity requirement too early in their thinking. By noting that the attainment of unanimity is infeasible or impossible, they have tended to pose the false dilemma mentioned above. The early theorists (Hobbes, Althusius, Locke, and Rousseau) did assume consensus in the formation of the original contract. They did so because the essence of any contractual arrangement is voluntary participation, and no rational being will voluntarily agree to something which yields him, in net terms, expected damage or harm. The categorical opposition of interests that many theorists assume to arise to prevent unanimity is much more likely to characterize the operational as opposed to the constitutional level of decision, and it is essential that these two levels of decision be sharply distinguished. It is at the operational level, where solidified economic interests of individuals and groups are directly subjected to modification and change by State action, that violent conflicts of interest can, and do, arise. At the “higher” constitutional level the problem confronted by the individuals of the group is that of choosing among alternative rules for organizing operational choices, and the discussion at this level will be concerned with the predicted operation of these rules. By a careful separation of these two levels of decision, much of the confusion inherent in modern interpretations of the contract theory of the State can be removed. Conceptually, men can reach agreement on rules, even when each party recognizes in advance that he will be “coerced” by the operation of agreed-on rules in certain circumstances. A potential thief, recognizing the need for protecting his own person and property, will support laws against theft, even though he will anticipate the probability that he will himself be subjected to punishment under these laws. Individuals at the level of operational decisions may accept results that run contrary to their own interest, not because they accept the will of the decision-making group as their own in some undefined, metaphysical manner, but simply because they know that the acceptance of adverse decisions (in our terminology, the bearing of external costs) is inherent occasionally in the “bargain” or “exchange” which is, in the long run, beneficial to them. The expected external costs caused by adverse decisions may fall short of the added costs that would be involved in the participation in the more complex political bargaining process that might be required to protect individual interests more fully. In our construction, therefore, there is no necessary inconsistency implied in the adoption of, say, simple majority rule for the making of certain everyday decisions for the group with respect to those activities that have been explicitly collectivized, and the insistence on unanimity of consensus on changes in the fundamental organizational rules. The organizing principle or theme of our whole construction is the concentration on the individual calculus, and it is easy to see that both the unanimity rule at the constitutional level and other less-than-unanimity rules at the operational level of decisions may be based directly on this calculus.*54

While it is clear that something akin to the doctrine of inalienable rights—institutionally embodied in constitutional provisions limiting the authority of legislative majorities—can easily be reconciled with our construction, we should emphasize that this doctrine is not central to our construction. The fact that much of our construction can be reconciled with a strain of orthodox democratic theory, and vice versa, should not obscure the profound differences between our approach and the one which has been implicit in much political theory and philosophy, both ancient and modern. The most basic difference lies in the incorporation into our models of the economic meaning of the unanimity rule, a part of our construction previously discussed in Chapter 7.

Much political discussion seems to have proceeded as follows: “If the interests of two or more individuals conflict, unanimity is impossible. Some interests must prevail over others if action is not to be wholly stifled.” This line of reasoning seems quite plausible until one confronts ordinary economic exchange. Note that in such an exchange the interests of the two contracting parties clearly conflict. Yet unanimity is reached. Contracts are made; bargains are struck without the introduction of explicit or implicit coercion. In this case, no interest prevails over the other; both interests are furthered. Our continued repetition of this simple analogy stems from our conviction that, at base, it is the failure to grasp fully the significance of this point that has retarded progress in political theory.

The “social contract” is, of course, vastly more complex than market exchange, involving as it does many individuals simultaneously. Nevertheless, the central notion of mutuality of gain may be carried over to the political relationship. When it is translated into individual behavior, mutuality of gain becomes equivalent to unanimous agreement among the contracting parties. The only test for the presence of mutual gain is agreement. If agreement cannot be reached, given adequate time for discussion and compromise, this fact in itself suggests the absence of any mutuality of gain. Moreover, where mutuality of gain is not possible, no criteria consistent with the individualistic philosophical conception of society can be introduced which will appropriately weight gains and losses among the separate parties to the institution taking the place of a contract (clearly, a relationship that does not embody unanimous consent is not a contract).

There may, of course, exist situations in which the formation of a “social contract” is not possible. When the negotiating parties are divided into groups that are classified on bases which seem reasonably certain to remain as permanent, independently of the decision-making rules that might be adopted, a “constitution” (in the sense that we have used this term throughout) may not be possible. The individual may never get the opportunity to participate (at the level of the Nation-State) in the choice process that we have been discussing. Under such conditions societies will tend to be controlled by some groups which will tyrannize over other groups. Such a situation must continue to exist, so long as genuinely mutual arrangements cannot be made.

Mutually Exclusive Alternatives

Situations such as these are not, however, what the orthodox theorist seems to have in mind when he makes statements like the one which we have attributed to him above. Implicitly, the orthodox theorist conceives all relevant political choice to take the form of selection between two mutually exclusive alternatives. An appropriate analogue is the choice confronted by the traveler at a fork in the road. He must either take one road or the other; the only other alternative is to stop. If, indeed, political decisions should assume this form, the statement imputed to the orthodox theorist above would be somewhat meaningful; but are the decisions that are confronted in the political process properly conceived as choices among mutually exclusive alternatives? Once more, let us turn to the analogy with market exchange. Such exchange could be converted into choices among mutually exclusive alternatives only if one partner to the bargain or contract should be required to secure gains at the direct expense of the other party. If such a rule were laid down in advance, any “solution” would require that the interests of one or the other of the parties prevail and the interests of the “loser” be subjected to “defeat.” In game-theoretic terms, the assumption of mutually exclusive alternatives is equivalent to assuming that the game is zero-sum. The winnings must match the losings. If, in fact, this is the appropriate conception of the political “game,” it is relatively easy to see that, once several persons (several players) are introduced, and if symmetry in preferences among individuals is postulated, the interests of the larger number (the majority) “should” or “ought” to prevail over the interests of the lesser number.

Clearly this would represent a wholly incorrect and misleading way of analyzing economic or market transactions. The implication of the approach would be that no exchange should take place at all because gainers balance losers in two-person trades and symmetry in preference is to be assumed present. Is this approach, by contrast, the appropriate means of analyzing political transactions? By now it is perhaps obvious that we do not think that political choices should, at base, be conceived in terms of selection among mutually exclusive alternatives. The essence of the contractual conception of the collectivity, quite independently of the empirical validity of this construction, involves the mutuality of gain among all members of the group. However, all participants in a zero-sum game cannot win simultaneously. Games of zero-sum are played, and political choices on many occasions do reduce to mutually exclusive alternatives; but why do we observe zero-sum games being played in the real world? The answer is that such games are played because each and every participant has, implicitly, accepted the “contract” embodied in the rules of the game when he chooses to play. The zero-sum characteristic applies to the “solution” of the game; it does not apply to the “contract” through which all participants agree on the rules. At this second level there must be mutual gains, and the rule of unanimity must apply. At this level there is no way in which a zero-sum solution could apply; the game simply would not be played unless all participants expected some individual benefit at the time of entry.

This reference to game theory may be helpful, but we have not yet clearly shown the statement of the hypothetical orthodox theorist to be demonstrably false. Let us turn to a simple model of a three-man society, engaged in the formation of a “social contract.” Let us call the three men A, B, and C. Suppose that the discussion is proceeding on the fundamental organizational rules that entering into a community or group life might involve. Let us assume that A is very interested in insuring that fishing is collectively organized, because he likes fish and because he also realizes that joint effort is much more productive than individual effort. If we limit our attention to this decision, we may reduce it to a yes-or-no question. Either the catching of fish will be collectively organized or it will not. These appear to be mutually exclusive alternatives, and it seems impossible that agreement could be reached unanimously if, say, C, who does not like fish anyway, does not agree to collective organization of this activity. This is the point at which our hypothetical orthodox theorist of the constitutional process seems to have stopped, but this represents the central error of his interpretation. Let us say now that C, in turn, is interested in insuring that the group allow the gathering of coconuts to be privately organized because he thinks he is a much better climber of trees than A or B. On the other hand, A and B both want to collectivize this activity as well as fishing. Suppose that B, in contrast to A and C, is really more interested in securing some defense against external attack than he is in either fish or coconuts. He wants, first of all, to organize some standing patrol or watch. Under these circumstances it becomes conceivable that the group can reach unanimous agreement of a “constitution” or contract. They can do so by making the appropriate compromises or “trades” among themselves. The process would be equivalent to the logrolling process discussed in Chapter 10, and the only test for determining whether or not the organization of the community is or is not mutually desirable to all parties lies in the possibility that such an agreement can be reached. Our hypothetical orthodox theorist, therefore, errs in not following through beyond the confines of a single issue. Once several issues are introduced, and the variance of interests among individuals and over separate issues is allowed for, trades become possible. Moreover, when trade can take place, the analogy with economic or market exchange is appropriate. No longer must the group reach yes-or-no decisions at the constitutional level; no longer must alternatives be mutually exclusive. The existence of conflicts of interest does not preclude the attainment of unanimity; this merely makes it necessary that discussion proceed until the appropriate compromises are found.

If direct side payments among individuals are allowed for, even this modification is not needed. Return to our illustrative model. Suppose that the only decision confronted is that concerning the organization of fishing. A and B desire collectivization because of the greater efficiency, but C, not liking fish, is opposed. If side payments are allowed, the support of C for the collectivization of fishing for the group may be secured by the transfer of some item possessing real value to C by A and B (e.g., a few cigarettes); and only if C can be so convinced to support the collectivization of fishing will the entering into the agreement with A and B be worthwhile to him.

The Meaning of “Majority Rule”

We have shown that the attainment of unanimity is always possible if there exist mutual gains from entering into the “social contract,” and that the orthodox theorist has tended to dismiss unanimity as a possible alternative to majority or minority rule too hurriedly because of a concentration on mutually exclusive alternatives. Our earlier models have shown, however, that the group may rationally choose less-than-unanimous decision-making rules for the carrying out of operational decisions for the collectivity. We now want to isolate a second major fallacy in the orthodox position. Even in these cases when unanimity is either not possible or not chosen as the rule by the group, we shall try to demonstrate that the dilemma posed by a a majority rule-minority rule dichotomy remains a false one.

Recall that the unique feature of our models for constitutional choice was the demonstration that, unless equal intensity of preferences is postulated, there are no particular characteristics attributable to the 51 per cent rule for choice. This is only one out of many possible decision-making rules. The peculiar position that this proportion has assumed in orthodox thinking seems to be due to the idea that if less than 50 per cent are allowed to make a decision, the more than 50 per cent will be “concluded” or “coerced” into acceptance. Thus, the requirement of a qualified majority really amounts to allowing a minority to rule. If we may again put the words into the mouth of our hypothetical orthodox theorist, he might say: “If more than 51 per cent are required for political decision, this will really allow the minority to rule since the wishes of the 51 per cent, a majority, can be thwarted.” In this construction there is no difference between the qualified majority of, say, 75 per cent and the simple minority rule of 26 per cent. Whereas in our constitutional models there may be a great difference in the external costs expected to be incurred under the 26 per cent minority rule and the 75 per cent majority rule, the orthodox theorist would deny this difference. Moreover, he would claim that the existing provisions for amending the United States Constitution embody the rule of the minority.

Does the requirement of a qualified majority amount to the rule of the minority? Here, as before, the error of the orthodox theorist seems to reflect his emphasis on reducing all decisions to the yes-no, mutually exclusive type, and the implied failure to put quantitative significance on alternatives confronted. If we come to an issue analogous to the fork in the road mentioned above, and if this is the only issue, and if no side payments are allowed, the orthodox theorist would seem to be on reasonably safe ground in saying that the requirement of 75 per cent agreement would allow the 26 per cent to be really controlling for decisions.

However, if the requirement of a qualified majority of, say, 75 per cent is really equivalent to the minority “rule” of 26 per cent, what sort of decisions must be involved? Not only must the alternatives of choice be conceived as being mutually exclusive, but the alternative of inaction must be counted as equivalent to action. The fork-in-the-road analogy mentioned above becomes too general because the alternative represented by stopping the journey is precluded. One way or the other must presumably be chosen. Suppose that there are 100 persons on a hayride and such a fork in the road looms ahead. Suppose that 74 of these persons choose to take the right-hand fork; 26 of them want to go to the left. With the 75 per cent rule in effect, neither road could be taken until and unless some compromises were made. With a 27 per cent rule in effect, the right-hand road would be taken without question in these circumstances. Surely these two rules produce different results. Failure to secure the required 75 per cent is not equivalent to granting “rule” to 27 per cent. If the third alternative of stopping the journey is allowed for, the 75 per cent rule will not allow action to be taken. The orthodox theorist would argue that such inaction, in this case, amounts to “victory” for the “recalcitrant” 26 persons making up the minority. Taken individually, however, these persons are thwarted in their desires in precisely the same way that the individual members of the larger group are thwarted. These individuals must also bear the costs of inaction. The argument may be advanced that, in such hypothetical situations as this, the interests of the greater number should be counted more heavily; but this, presumably, is a question that is appropriately answered only at the time when the decision-making rules are chosen. In our construction it seems wholly inappropriate to introduce this essentially irrelevant ethical issue at the stage of operational decision-making. When it is recognized at the ultimate constitutional stage that the larger the majority required for decision, the lower are the expected external costs that the individual expects to incur as a result of collective decisions being made adversely to his own interest, we may discuss the operation of the various rules quite independently of all attempts to measure utilities and to compare these interpersonally.

The orthodox theorist will not, however, accept this line of reasoning. He will say that the question to be decided in our illustration should be put as follows: Shall the group take the right-hand road or not?—Vote yes or vote no. In this way the qualified majority rule is made to appear equivalent to “minority rule.” A minority of 26 per cent is empowered to block action desired by 74 per cent.

This argument is more sophisticated than the one considered previously, and it is more difficult to refute convincingly. To do so, we must, first of all, clarify the meaning of the terms “majority rule” and “minority rule.” We have used these terms throughout our analysis to describe decision-making processes. Such general usage is no longer sufficient. We must sharply differentiate between two kinds of decisions: (1) the positive decision that authorizes action for the social group, and (2) the negative decision that effectively blocks action proposed by another group. If a group is empowered to make decisions resulting in positive action by/for the whole group, we shall say that this group effectively “rules” for the decisions in question. It does not seem meaningful to say that the power to block action constitutes effective “rule.”

This relevant distinction between the power of determining action and the power of blocking action has not been sufficiently emphasized in the literature of political science.*55 The reason for this neglect seems to be an overconcentration on the operation of simple majority rule. If a simple majority is empowered to determine positive action, there can be no other simple majority empowered to block the action proposed. Two simple majorities cannot simultaneously exist. The distinction becomes clear only when we consider “minority rule.” If we adopt the meaning of this term suggested above, a group smaller than one of simple majority must be empowered to make positive decisions for the collectivity. For example, suppose we choose to consider a 40 per cent decision-making rule. This rule, under our definition, would be operative when 40 per cent of the voters, any 40 per cent, are empowered to take action positively for the whole group. It is clear that the same rule could not also be applied to blocking action. If 40 per cent were also required to block action, then 40 per cent could not be defined as the “rule of the minority” at all. The rule for blocking action must always be [(N + 1) – X] per cent, X being the percentage of the total group empowered to institute or to conclude positive action. Effective minority rule, therefore, must require a majority to block legislation proposed by the minority. Effective “rule” by the 40 per cent minority must involve the requirement that 61 per cent of the voters are required to veto action proposed by a minority.

When the orthodox theorist suggests that qualified majority voting amounts to “rule” by the minority, he is referring to the rule for blocking action. If this line of reasoning is carried to its logical conclusion, we get the paradoxical result that the rule of unanimity is the same as the minority rule of one. Thus the rule of requiring unanimity among members of a jury to acquit or to convict becomes equivalent to the rule that would permit any individual juror to convict or to acquit. Instead of being at the opposing ends of the decision-making spectrum, as our whole construction suggests, the unanimity rule and the rule of one become identical. This paradoxical result suggests clearly that the power of blocking action is not what we normally mean, or should mean, when we speak of “majority rule” or “minority rule.”*56

The distinction between the power of taking action and of blocking action proposed by others is an essential one; it represents the difference between the power to impose external costs on others and the power to prevent external costs from being imposed.

We may illustrate with reference to our familiar road-repair example. Let us assume that the constitution of our model township dictates that all road-repair decisions are to be made by a two-thirds majority. Under these conditions the power to institute action, lodged in any effective coalition of two-thirds of the voters, involves the power to impose external costs on the other one-third, either through the levy of taxes or the failure to repair certain roads to standard. One-third of all voters plus one have the power to veto or block any proposed repair project, but this power is effective only in the sense that a group of this size can prevent the additional taxes being levied. In no way can this minority group impose additional external costs on the other members of the group.*57

The Problem of Biased Rules

We have not yet satisfied the hypothetical orthodox theorist.*58 He may conceivably accept all of our previous arguments but still try to stop us short by saying: What about the situation in which the issue confronted is whether or not a change in the rules should be made? Here the alternatives are mutually exclusive: change or no change. Moreover, should the established order (the status quo) operate in such a way as to benefit special minority interests, then surely the qualified majority rule for changing the “constitution” will allow the blocking power of the minority to be controlling. In effect, the maintenance of things as they are amounts to genuine “minority rule.”

This argument gets us to the heart of the whole discussion of majority rule as a doctrine of popular sovereignty, to which we referred earlier in this chapter to some extent. We have discussed the applicability of the unanimity rule at the stage of making original constitutional decisions. At any point in time subsequent to the formation of the original “contract,” the social organization must be presumed to be operating within the framework of certain established rules. These organizational rules define the way in which certain collective decisions will be made, including decisions to change the “contract.” If these basic rules suggest that, for some decisions, more than a 51 per cent majority is required for positive action, it is surely the established order of affairs that may be said to be “ruling,” and not the particular minority that may or may not be securing “benefits” through the continuance of this established order.

This is not to suggest that the established order must prevail for all time, once it is accepted, nor that, either at its beginning or at any particular moment in time, this order is necessarily “optimal.” The “social contract” is best conceived as subject to continual revision and change, and the consent that is given must be thought of as being continuous. However, the relevant point is that change in this “contract,” if it is desirable at all, can always find unanimous support, given the appropriate time for compromise.

Again we revert to the game analogy. We may, if we like, think of players as being continually engaged in two kinds of mental activity. First, they are trying to figure out moves or strategies with which their own interests can be advanced within the context of a well-defined game. Secondly, and simultaneously with this activity, they can be conceived as trying to figure out a possible change in the rules that would make for a better game. In this second activity they will realize that they must choose rule changes on which all players can agree if the game is to continue. A proposed change in the rules (or in the definition of the game) designed especially to further individual or group interests, majority or minority, would be recognized to be impossible. The other players could simply withdraw from the game.

Our conception of the constitutional-choice process is a dynamic one quite analogous to the game mentioned above. We do not conceive the “constitution” as having been established once and for all. We conceive the contractual aspects to be continuous, and the existence of a set of organizational rules is assumed to embody consensus. We think of the individual as engaging continuously both in everyday operational decisions within the confines of established organizational rules and in choices concerned with changes in the rules themselves, that is, constitutional choices. The implicit rule for securing the adoption of changes in these organizational rules (changes in the structure of the social contract) must be that of unanimity. This is because only through the securing of unanimity can any change be judged desirable on the acceptance of the individualistic ethic.

This does not imply, as is so often suggested, that the requirement of unanimity on changes in the rules (on the constitution) embodies an undue or unwarranted elevation of the status quo to a sacrosanct position. In the first place, the idea of status quo in terms of established organizational rules is hazy at best. The stability of the established rules for organizing public and private decisions does not, even remotely, tend to stabilize the results of these decisions measured in terms of the more standard variables such as income, wealth, employment, etc. The municipal-zoning ordinance may be accepted by all parties until someone has the opportunity to sell his own property to a developer at a huge capital gain. At this point in the sequence, the individual standing to gain would certainly desire a change in the rules to allow him to exploit this unforeseen opportunity, but it is precisely because this sort of thing is unforeseen that the zoning ordinance can be adopted in the first place. Ex post, the individual faced with the opportunity to gain is likely to object strenuously to the status quo (that is, to the zoning ordinance), but securing a variance for one individual alone is equivalent to changing the rules of the ordinary game to the strategic advantage of one player. In the continued playing of the “social game,” individuals will each confront situations in which they desire, strategically, to change the rules; but it is because these situations are distributed stochastically that agreement becomes possible. If a change in the rules (a change in the status quo) is mutually beneficial, it will, of course, be adopted. Empirical evidence from the operation of voluntary organizations suggests that rules are often changed.

An individual need not, of course, accept the “contract” that exists. He may rationally consider the rules to be undesirable. Faced with this conclusion, two choices remain open to him. He may seek to convert others to his point of view, and, if arrangements can be worked out through which all others come to agree, the “constitution” can be changed. Secondly, the individual may choose to reject the “contract” entirely; he may revert to a “state of nature”—in this case a revolt against established social order. On ethical grounds the individual must always be granted the “right” to make such a choice, but, once he has done so, the remaining members of the group have no contractual obligation to consider the revolutionary to be subject to the protections of the “contract.” This “right of revolution” is not modified as it extends beyond the single individual to a minority or even to a majority of the population. In this, as in other aspects of our construction of the constitutional implications of a consistent individualistic philosophy, the shifts in the fraction of the population approving or disapproving certain changes are not of central importance.