THE CALCULUS OF DISSENT: CONSTITUTIONAL COMPLETION AND PUBLIC GOODS

JEL Classification: H 10 Key Words: Constitution, Public Goods, Random Choice.

GIUSEPPE EUSEPI

Università di Roma "La Sapienza" Facoltà. di Economia Dipartimento di Economia Pubblica Via del Castro Laurenziano, 9 00161 ROMA - ITALY

I wish to thank Edoardo Eusepi and Stefania De Carli for their assistance in the elaboration of the combinatorial analysis.

 

 

ABSTRACT

Starting from the two-stage model underlying constitutional political economy, this work suggests the introduction of a third stage with the aim of solving the problems, which under certain conditions arise in the public goods market. These problems may be due to: a) a centralized institutional framework, and b) the impossibility to reach an agreement following the majority rule.

In the three-party/three public goods scheme with completely conflicting outcomes (three different choices) in the a) case conflicts could be solved resorting to a federal organization; this, however, would involve a constitutional break off; for the solution of the problem in b) the work addresses a completely neglected issue using a new approach centered around the concept of residuum of consent vis à vis the emergence of dissent. Since choices are never consensual here, and choosing is nevertheless unavoidable the contractarian logic may survive only by resorting consensually to a lottery which assures a random choice. The last part of the paper indicates few fiscal devices to correct inequalities coming from drawing lots; such devices are based on the benefit principle.

 

1. Introduction.

As for many other papers of mine James Buchanan has indirectly inspired also this one. Yet, as this is not a work following in Buchanan's footsteps I shall try to render a critical account of what seems to me the shortcoming of the two-stage scheme in contractarian constitutional political economy. It is precisely this dissatisfaction which has spurred me on to this effort.

Although my belief is that the two-stage model of constitutional contractualism has reached its maturity at the end of the 90s, I nevertheless seek to demonstrate that this maturity does not stand for senility and, in fact, further developments, though dimensionally circumscribed, are at stake. The first point, which will be convenient to discuss in detail, is the somewhat debatable usage of the word contract as though it were a perfect equivalent of consent. That is why in the literature the two terms are employed in a neutral manner.

I think that this neutral usage would trivialize the heuristic importance of the contract. And in fact how could the case of conflictual choices over public goods in a certain political context be solved? Since a consensual choice is impossible here, and since the equivalence assumption impedes that a contractual procedure be used, the only option left will inevitably lead to revolutionary or dictatorial resolutions. This case indicates that the democratic process itself pushes towards a non-neutral usage and, in fact, the contractual route extends the contractual solution to the dissent. It is therefore one of the main tasks of this work that of employing the contractual procedure in the calculus of dissent.

Section 2 proceeds by defining the foundations of the dissent problem and shows that the two-stage model is logically consistent, but lacks in exhaustiveness; thus Section 3 suggests its completion through the introduction of a third stage whose nature is however different from the first two stages, and for this reason is labeled as spurious.

Section 4 deals with the dissent in a centralized organization of the polity, while in the fifth Section the dissent is within the constitutional framework itself. While in the first case it is possible to reach a consensual result through the creation of federal institutions, in the second case the recourse to random choices as a way to overcome the problem of dissent is required. I strongly emphasize here that the dissent problem in the post constitutional market does not imply the abandonment of the two-stage model at all. Section 6 will offer some concluding remarks.

 

2. The non-exhaustiveness of the two-stage models.

The distinctive element in contractarian constitutionalism is the consent that is in fact at the basis of both initial constitutional designs and their revisions. Quite independently of the two-stage model adopted (à la Hobbes, à la Buchanan, à la Frey1), rules are constraints to post-constitutional decisions. The reasoning is, of course, correct, but it does not appear to be exhaustive at all. In my opinion, for the two-stage model to be exhaustive, one should prefigure the attainment of a consent without residua. In clearer words one should prefigure either a unanimous consent or in the worst of cases a simple majority to emerge. If for any reason a less than majoritarian2 result should occur at a post-constitutional level, e.g. in the public goods market, the public goods domain itself will become prima facie a sort of contractual vacuum. If so, for the contractarians there would not be alternatives left, but the abandonment of the contractarian approach itself.

The work suggests that this is not the case, and in supporting this thesis it develops an idea recently launched by Buchanan and Yoon3. However, differently from Buchanan and Yoon, who are interested in showing the efficacy of arbitrary rules in a non-natural context4, I explicitly refer here to the contractarian constitutionalism and impute the emergence of conflicts coming from residua of consent on the market of public goods to the non-exhaustiveness of the deductive or the ex ante two-stage scheme. In a sense, in contractual constitutionalism - no matter whether in the Rawlsian version of the veil of ignorance or in that of Buchanan-Tullock5 - there is too much optimism because given consensual bindings a simple majority decision will always emerge on the political market. This ensures not only that the tragedy of being constrained is overcome - since the principle of majority-minority rotation which is at the root of democracy smoothes the problem - but also that within the rotation limits, an equilibrium on the public goods market will always emerge. If instead one would demonstrate, as I shall try to do here, that it is not always possible to reach an equilibrium at a second-stage, or public goods level, we might as well abandon, at least within the limits of these residua of consent conditions, the deductive perspective based on consent over rules and adopt a random choice criterion which involves the resorting to a "lottery" by drawing from a ballot-box - which contains all possible alternatives - the winning one which is legitimated just because individuals' choices have an equal probability to be drawn. The drawing-lots-procedure may appear not to have any linkage with the decision taken behind the Rawlsian veil of ignorance - and in fact here we are dealing with a self-determined individual who is able to know exactly which alternative is the best to him. Yet, he also knows that neither his own choice, nor that of anybody else will have any chance to prevail. In a sense, we could say that each decision-maker has too much information, and not too little6. It is as if he were set beyond the Rawlsian veil. His choice, however, cannot be totalitarian having it the same weight as any other choice taken by anybody else in the polity. Indeed, these choices are mutually exclusive since they are at the same time equally weighing and diverging. There is surely not much room left for dictatorship here! In other words if everybody is a potential dictator, no dictator will prevail. It is easy to concede that the contractarian perspective turns out to be winning, even when a majority does not emerge; the non-trivial point that stands out from this kind of analysis is that the contractarian logic may prove to be a useful tool, although admittedly with some qualifications, also in the calculus of dissent.

It is precisely the reciprocity principle inborn in the contractarian constraint that makes drawing lots consistent, and a fortiori non dilemmatic. Thus resorting to drawing lots, although admittedly in an indirect and surely non-trivial way, resolves the tragedy of being constrained. Along this line of reasoning each individual's consent to abide by the potential rule, which emerges from drawing lots, will restore to certain extent an environment of equal uncertainty not so far from that created through the veil of ignorance or uncertainty in a Rawlsian setting. The point, however, has not to be overstressed; the veil here originates from a failure on the public goods market and it is in a certain way a further barrier against dictators.

However, if the Rawlsian veil became transparent, it would be used by dictators to determine their own best results and to create ex post-justificatory rules. And, in fact, as happens in the Rawlsian case, the drawing from the ballot box involves the constitutionalization of the choice. Such a choice, however, cannot be considered as a genuinely constitutional one in the light of the two-stage scheme. Resorting to a lottery could prima facie appear an incorrect procedure, and into the bargain, it would be incompatible with both majoritarian democracy and consensual contractarian constitutionalism.

Under the dissent condition - although within limits - the random choices we have to resort to may offer a solution to non-consensual choices; this requires that the contract as an instrument of analysis be extended far beyond consensual choices, which are believed the only contractual ones. In order to separate also semantically the constitutional reforms of the standard two-stage paradigm from reforms deriving from the constitutionalization of a public good, I suggest to name the latter case constitutional completion.

 

 

3. The introduction of a third-stage in constitutional political economy.

I shall leave out the presentation of a two-stage model because after two decades of numerous and weighty writings all that which matters7 has already been said. For this reason one of the objects of this work is to deal with what seems to me the foundation stone of contractarianism, and seeks to focus on the renegotiability of a Constitution. If the initial contract does not provide constitutional renegotiation is unimportant even its being approved under the most rigorous version of Wicksell's unanimous consent. In any case, if the two-stage scheme is unable to impede the rising of major conflicts on the political or public goods market, the addition of a third stage to the original scheme is unavoidable. A third stage is, of course, not needed if we assume that in the public goods market there will always emerge Lindahl-Samuelson-like equilibria.

Note, however, that in an ordinary democratic context, the majority makes the rule, and the minority is ruled. I haven't, of course, much to recriminate against all this. I have something to say, instead, on the generality of the majority rule. In some cases, in fact, the majority rule may turn out to be unattainable, so I shall define this situation - where decisions are conflicting rather than consensual - as the dissent case.

One can readily realize that if none of the proposals win, all outcomes derive from the minorities, thus all decisions are inconsistent. Clearly, one thing is the lack of consent by the minority when there exists a majority; a completely different thing is the dissent case where all outcomes get the support of the minorities. These differences can be, in part, attributed to the type of institutions in existence, e.g. a too centralized state.

The emergence of a dissent problem simply indicates that the two-stage constitutional model needs to be completed, and this can be done through adding a third stage. The latter stage, however, is ostensibly spurious; in fact it springs up only as a consequence of a decisional problem in the political market and not ex ante because under a genuine constitutional logic, rules must constrain individual choices, but for individual choices to be free acts these rules cannot impose mandatory behaviors8. If the rule is viewed as a guarantor of freedom, it cannot allow to forecast which decisions individuals will actually take about certain matters, precisely for being every individual choice a free act and, hence, an unpredictable event9.

On the other hand, the representatives, who are the most important decision-makers in public economy, could fail in reaching the required consent, or even give up the consent stricto sensu as a decisional tool due to the high transaction costs, or simply because public goods might be conflicting.

The conflicts emerging in the decision over public goods, could be prima facie a sign, not only of the failure of the initial constitutional design, but of the contractual constitutional revision as well, since in both cases choices are based on consent. The reason why I am introducing a third stage is that of extending the contractarian logic far beyond the consent, where it is the dissent which dominates. This expression, however, may reveal particularly ambiguous, and it needs to be clarified. Firstly, it could be understood as if simple majority decisions were descriptive of dissent; I shall not, of course, argue of this type of dissent because majority decisions in any case warrant that in the aggregate the consenters prevail over the dissenters. It is perfectly logic that the consent of the majority rather than that of the minority, which in fact suffers it, decide the rule. (This is the core of democracy.)

The contractarian theory has assumed the contract as a synonymous with consent because contracting parties, which are necessarily free, could but consent freely on rules. In the real world constitutions and institutions in general, the contract/consent equivalence - under the residuary conditions here discussed - could impede the attainment of results which, although necessarily of third best, would nevertheless represent the only way to prevent the falling back into chaos. Since, however, the aim of the initial constitutional contract was that of breaking away from chaos, the decisions involving dissent - and therefore a relapse into chaos require, as seen, the reconstruction of something similar to the Rawlsian veil of ignorance. The thought experiment of equal uncertainty about the results that will come out makes reasonably acceptable the different weight that the individual choices have in case of dissent.

It is maintained here that the random choice, or the draw from the ballot box, with individuals in a position of equal uncertainty, may mimic the Rawlsian experiment. Clearly, positions of equal uncertainty assign the vote an equal probability of success ex ante, so guaranteeing an equal weight to the vote; in this way the basic democratic principle "one man one vote" seems safeguarded, and in any case, it solves the decisional problem in the public goods market when there is a dissent. Most of the remainder of the paper deals with this matter.

The dissent argument interjects a sort of interconnection between the constitutional market and the post-constitutional or public goods market, and makes it impossible the complete separation of the two stages in logical-procedural terms. This interconnection could be named as feedback effect, and in fact the dissent at a post-constitutional level must find a solution which is to be constitutionalized. However, even accepting that the contractarian position - which involves a dissent - is correct, there should be nevertheless recognized that the outcome which emerges may appear strongly unequal, not only to an external agent who evaluates it, but also to most of the individuals involved in the decision.

Let us start with a three-individual example facing the choice of three public goods, and let us imagine that the three individuals represent the electorate or the Parliament in a centralized polity (as an alternative we may refer to three political parties each of which is made up of one-third of the Parliamentarians and hence all three make up 100% of the Parliamentarians). In this case the Parliament is the only place entitled to decide and its decision binds all members of the Parliament (electorate). Since decisions are taken by individuals/parties whose choices may be homogeneous or different each other, three outcomes may emerge. It may be useful to represent the three outcomes geometrically. Let A, B, C be the individuals/parties and a, b, c the payoff vectors.

In Figure 1 there is a 100% consent on the payoff, hence the resulting vector lies along anyone of the axes; in this case it is indicated the Y axis.

 

Fig. 1 A geometrical representation of unanimous consent

The outcome is a unique payoff vector (a+b+c) lying in anyone of the axes (it is immaterial whether the axis is X,Y,Z) and its length is three times that of each vector. As the choice is consensual, the angle the resulting vectors make up with the chosen axis is null.

The payoff vector lies along one axis

Fig.2 illustrates a majoritarian choice, in this case the resulting payoff vector is represented by the diagonal of the rectangle contained by a+b and c.

 

 

Fig.2 A geometrical representation of a majoritarian consent (A+B vote for the same alternative)

The payoff vector (a+b+c) belongs to the YZ surface, since the a and b vectors have been drawn along the Y axis and c along the Z axis. It represents the diagonal of the rectangle contained by a+b and c. The angle the resulting vector makes up with the Y axis is smaller than that made up with the Z axis.

The payoff vector lies in the plane surface

Fig.3 represents the dissent case. The resulting payoff vector (a+b+c) does not lie in any of the surfaces ( XY,XZ,YZ ) of the three dimensional space it is, in fact, the diagonal of the cube, and the payoff vector is contained in the space.

 

 

Fig. 3 A geometrical representation of dissent

The resulting payoff vector (a+b+c) does not lie in any of the XY, XZ,YZ surfaces, but it is the diagonal of the cube whose edges represent the choices a, b, c made by A,B,C. The 45 angle this resultant forms with each of the addends represents the "equidistance" from any choice.

The payoff vector is contained in the space

 

In the first alternative a centralized polity may appear not only perfectly compatible with individuals' freedom, but the decision which emerges is also effective and, within limits, efficient. Note, however, that this result is incompatible with the hypotheses that individuals/parties are different, since the decision of 100% would imply that individuals/parties are homogeneous10.

Once the first alternative is discarded due to its internal inconsistency, there may emerge either of the two alternatives. Since the majoritarian alternative is not functional to my discourse, I leave it out of consideration; I focus, instead, on the third alternative that is functional to my model dealing with dissent.

 

4. The problem of dissent, and its solution through consensual constitutional changes.

The example given by Buchanan and Yoon falls in perfectly with the third outcome of my discourse, and, in fact, depicts a context of three individuals who have to take decisions about "thermostat setting", "lights-out time", and "visitors access" in a student dormitory. Ceteris paribus, individual choices depend on individual tastes or needs, but, due to the institution here considered (one room to be shared among three students), individual tastes and needs are met with public goods. The implication is that if it were possible to privatize the three goods, as a consequence of institutional changes, we would not have the third result any more and, in fact, everyone would choose according to his opportunity costs. This is made possible by dividing the room into three single rooms; the three individuals will, of course, pay different prices for heating, electricity, and moreover, they will be able to decide autonomously their visitors' access.

In this case the consensual choice has not involved a mere change in the status quo - that is a constitutional revision - it has instead required a radical overturning of the basic constitutional model. In order to make Buchanan and Yoon's example more palatable at a constitutional and political level, let us imagine that the three actors of the model are not the three students any more, but the three political parties mentioned above. Let us start again with the dissent, or the three-minority case that impedes the decision in the centralized polity.

Conflicts on the public goods market, coming from a centralized system (typical of a unitary state) may find its natural solution by creating a federal system. This solution could be wholly consensual (see Czech Republic and Slovakia, or Belgium), but the contractarian logic must be extended also to decisions which are consensually residuary so that all the emerging rules would be minority rules by definition. To certain extent, when a minority imposes on other minorities, these minorities could be viewed as majorities opposing the decision imposed by the minority. So interpreted, however, this context would be descriptive of a Leninist regime violating democratic procedures.

A constitution of three federate states would allow to reach all decisions by consent, without any dissent. Since in the federal alternative problems linked to dissent are settled by consent, we need not to resort to the constitutionalization or parameterization of a public good to facilitate choices, as Buchanan and Yoon suggest. I clinch again, however, that the removal of conflicts is not a result reached through amendments or restoration of the original model. As said, the centralized polity model has been simply replaced with a three-federate-state model. An example, drawn from the Italian constitutional history, can corroborate the whole reasoning.

During the preparatory work the Constituent Assembly (1946-47) faced up to the problem of relationships between the Republic, which was about to be born, and the Catholic Church. Leaving aside all the complexities of this matter - the most important of which probably lies in being a relationship between two different states, and as such should fall outside the constitutional field - I shall confine the analysis to the two possible alternatives: (1) to include the Lateran Treaties in the Constitution; (2) to proclaim freedom of religion11.

The approval of the first alternative has involved not only a continuity with the former Fascist regime (which signed the Lateran Treaties in 1929), but also the recognition of Catholicism as a sort of state religion, so discriminating all other religions. Although the majority of the Italian citizens was Catholic at that time, and still is nowadays, the evolution of moral sentiments in the 1990s, in Tideman's words12, might then lead to choose the freedom of religion alternative.

The constitutionalization of freedom of religion would allow to overcome the discriminatory principle embodied in the first alternative, and reach the consent on the religion argument. The second alternative recognizes non-Catholic minorities to follow their own religion. This reasoning is in actual fact an application of the classical theory of clubs, and of the recent theory of FOCJ which are able to eliminate the dissent13.

 

5. When rules come from random choices.

Does it exist a different way from federalism able to solve the conflicts coming from dissent without resorting to the upsetting of the whole basic constitutional model? Following again Buchanan and Yoon (1997) this possibility of completion, which allows to remain within the original constitutional scheme, is feasible through the constitutionalization of a public good as an alternative way to come out of the third and the worst case.

If everyone votes for his own option in the all possible pairwise votings, every choice - apart from the voting sequence - will have one vote in favor by the proponent and two votes against by the non-proponents. The emerging solution, in which all alternatives get an equal number of votes in favor, could be depicted in words which would appear seemingly peculiar "the contractarian calculus of dissent" where the contractarian component is maintained since the procedural choice implies the acceptance by all individuals in conflict to refrain from using the force.

All things considered, no choice based on consent would be possible here, unless a rule-making minority is conceived. But this should be extended also to the other two minorities; consequently, one should prefigure a three-minority context where all minorities are rule-makers and none will be ruled. This is patently absurd. Clearly, on the basis of both unanimity rule and majority rule, none of the minorities is entitled to rule. Because choices on goods are conflicting, and goods are public, individual demands would sum up algebraically, and the sum will always have a negative sign.

So far the exit from chaos through consent - which the democracy's philosophers thought to be the aim of a constitution - would seem hardly attainable in the public goods market; it follows that a metarule making the drawing lots compulsory has to be introduced.

Although the solution to the dissent problem through the device of drawing lots is reasonably the only one justifiable ex ante, it is likewise clear that the positions or the results, which the metarule gives rise to, may reveal strongly unequal ex post. Positions or results will be optimal for the individual whose choice has been drawn while the other two individuals may find themselves, more or less, in an equally bad position if the choice drawn is the median one; if instead, the alternative drawn is one of the extremes, the worst position is that of the individual who is positioned at the opposite extreme, while the position of the individual whose most preferred alternative is the intermediate one is worse, but better than that of the opposite extreme. Let us go back to the three individuals and the three public goods with three discrete values. The possible alternatives will be as many as the ordering set of triplets (See [3] in the Appendix):

 

 

 

The outcome may be:

  1. Unanimous consent where each individual agrees on the same choice.
  2. A majoritarian choice where two persons make the same choice.
  3. Total disagreement where everyone chooses differently.

Let , be the three payoffs for the public good X, all possible results are illustrated in the following table.

A

B

C

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

 

Alternatives are partioned as follows:

1 - Cases of unanimous agreement = 3. (See [3]).

A

B

C

 

2 - Cases of majoritarian agreement all over the decisions = 18. (See [4], [5])

A

B

C

 

 

3 - Cases of dissent = 6 (See [2]).

 

A

B

C

 

Note that in the calculation of the alternatives the order of the arrangement is fundamental!

 

, and

 

represent three different alternatives even though they give rise to the same kind of majority/minority.

Let us extend our reasoning to a context in which the three persons A,B,C, have to decide about

X, Y, Z each of which allows for three choices:

for public good X

for public good Y

for public good Z

Up to this point we have examined only the X dimension. As said for X may be extended to the Y and Z dimensions since they are independent. Hence for each dimension 27 alternatives will emerge; for the three dimensions the total number of alternatives will be [1] in the Appendix.

 

 

 

 

X

 

 

Y

 

 

Z

 

 

 

 

 

 

 

 

 

 

 

 

A

B

C

A

B

C

A

B

C

 

 

 

 

 

 

 

 

 

 

1

2

3

4

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The table illustrates some of the possible alternatives (samplings of 9 elements). Let us examine the n

alternative:

 

 

A has chosen

For decision X

B has chosen

 

C has chosen

 

A has chosen

For decision Y

B has chosen

 

C has chosen

 

A has chosen

For decision Z

B has chosen

 

C has chosen

 

We shall have of course:

3 cases of unanimous consent over the decision X

3 cases of unanimous consent over the decision Y

3 cases of unanimous consent over the decision Z

hence (See [3]).

 

 

 

cases of total agreement or unanimous consent over all three decisions.

18 cases of majoritarian consent over the decision X

18 cases of majoritarian consent over the decision Y

18 cases of majoritarian consent over the decision Z

hence (See [4], [5])

 

 

cases of partial or majoritarian agreement over all three decisions.

6 cases of dissent over the decision X

6 cases of dissent over the decision Y

6 cases of dissent over the decision Z

hence (See [2]).

cases of total disagreement over all three decisions.

Suppose now that an agreement over a decision has been reached through a lottery.

The total number of alternatives is reduced to (See [6]).

(Number of the alternatives for each decision, multiplied as many times as the decisions.)

If Bs choice is drawn, A and C will then suffer, more or less, an equal damage. If, instead, C's choice is drawn the position of the other two will be different, and surely A will be more damaged than B.

From this, one could infer that the contractualism, might basically produce unfairness, albeit its procedural fairness. But this is not so. For instance, the Constitution could provide for a clause saying that in the case of a random choice, the individual whose option has been drawn, should pay more than the others. Let us go back to our example. If the choice is consensual, ceteris paribus each individual will pay a third of the total cost. If, instead, the rule comes out from a lottery the Constitution could impute, say, between 40 and 50% of the total cost to the winning individual. Despite the corrections advanced here and clearly based on the benefit principle, the equity problem is not fully solved; through the constitutionalization of this tax device a great political instability coming from an otherwise regressive tax system is nevertheless prevented.

 

6 - Concluding remarks.

Although it can be maintained that there exist global markets (including some public services) and local markets (many local public services) quite independently of the political units or state organization, it does not follow that there is no link between the constitutional and the public goods market. This work has sought to demonstrate that if the traditional two-stage scheme is supplemented with a third stage providing few appropriate constitutional devices it is possible to eliminate the case of dissent from the contract. This may be done by raising to the constitutional rank the choice that comes out from drawing lots.

 

 

 

Notes

1 I have shown elsewhere that Hobbes's model is not contractarian as suggested by Buchanan, and that, although strange this may appear, the model à la Buchanan and à la Frey largely overlap, and even where these models appear to be conflicting, they complete each other. See G.Eusepi (1999).

2 In this case, of course, the dissent among the parties rather than the consent becomes the characteristic feature. Consequently, on the grounds of the dominant theory on the calculus of consent, the tragedy of being constrained would re-emerge.

3 J.M.Buchanan, Y.J.Yoon (1997).

4 The natural context is, of course, the constitutional one and consequently the non-natural context is the one in which there is not a clear-cut distinction between choice among rules and choice within the rules. It is evident that from Buchanan and Yoon's viewpoint this paper falls under the natural context .

5 J.M.Buchanan, G.Tullock (1962).

6 See G.Brennan, L.E.Lomasky (1989), especially Introduction and ch.2.

7 See for instance J.M. Buchanan (1975), G,Brennan, J.M.Buchanan (1985), D.C.Mueller (1995).

8 See B.S.Frey (1996).

9 J.M.Buchanan (1969).

10 Homogeneous parties would equal, of course, to a unique party.

11 The reading of art.7 of the Constitution is quite ambiguous, but in the end it assumes the first alternative.

12 N.Tideman (1997).

13 J.M.Buchanan (1965), B.S.Frey, R.Eichenberger (1996).

REFERENCES

BRENNAN G., BUCHANAN, J.M. (1985), The Reason of Rules: Constitutional Political Economy, (Cambridge: Cambridge University Press).

BRENNAN G., LOMASKY, L.I.(eds.) (1989), Politics and Process. New Essays in Democratic Thought, (Cambridge: Cambridge University Press).

BUCHANAN, J.M. (1965), "An Economic Theory of Clubs", Economica, XXXII, February 1-14.

BUCHANAN, J.M. (1969), Cost and Choice.An Inquiry in Economic Theory, (Chicago: Markham Publishing Company).

BUCHANAN, J.M. (1975), The Limits of Liberty - Between Anarchy and Leviathan (Chicago: University of Chicago Press).

BUCHANAN, J.M., TULLOCK, G. (1962), The Calculus of Consent, (Ann Arbor:University of Michigan Press)

BUCHANAN, J.M., Y.J.YOON (1997), "The Efficacy of Arbitrary Rules", Draft presented at the conference on Constitutional Issues in Modern Democracies, Taormina, Italy, September 25-27, 1997.

EUSEPI, G. (1999), "Changing Rules by Changing Rulers. A Contractarian View on Constitutional Revision", Paper presented at the Public Choice Meeting, Lisbon, Portugal April 7-10, 1999.

FREY, B.S. (1979), "Economic Policy by Constitutional Contract", Kyklos, 32, pp.307-319.

FREY, B.S. (1996), "A Constitution for Knaves Crowds out Civic Virtues", Economic Journal, July.

FREY, B.S., EICHENBERGER, R. (1996), "FOCJ: Competitive Governments for Europe", International Review of Law and Economics, 16, pp.315-327.

MUELLER, D.C. (1995), Constitutional Economics, (Cambridge: Cambridge University Press).

TIDEMAN, N. (1997), "The Constitutional Conflict Between Protecting Expectations and Moral Evolution", Draft presented at the conference on Constitutional Issues in Modern Democracies, Taormina, Italy, September 25-27, 1997.

 

 

APPENDIX

GENERAL CASE

 

Suppose a set P = of persons who have to choose among a set of choices C = of a set of options
O =

All possible alternatives are given by:


[1]

 

that is by the product made as many times as the number of options of the samples with replacement of elements of size p, where

o = the number of options,

the number of choices for the kth alternative,

p = the number of persons.

Let us imagine p = 3, o = 1, c(1) = 2 the possible combinations which may come out are represented by samples with replacement of two elements of class 3 selected three by three. The total alternatives are:

.

We examine only the case where the choices are equal or lower than the choosing persons . Only if for each decision we may have total disagreement or dissent. Hence,

[2]

where = represents the number of permutations of p elements (samples without replacement of p elements p by p). The cases of total agreement or unanimous consent will be

[3]

If we will not have residuum of consent.

Let o = 1 and (only one option among the r possible choices ). One of the possible ways to have persons who agree on choice persons agreeing on choice persons agreeing
on is


[4]

considering all the possible ways to obtain p as a sum of addends , ,..., the number of all combinations is


[5]

Going back to the o alternatives, assuming that p persons agree on one of them, the remaining alternatives which we may have are:

[6]