This literature does not consider the question of what decision-making

procedures society would choose behind the veil of ignorance. We are primarily

concerned with the latter question, albeit in the context of a redistribution

problem. The question of design of ex-post decision-making procedures arises

naturally in an incomplete contracting setting. Indeed, we begin by showing that

dif cult to achieve. Since any form of ex-post deviation is suboptimal from an

ex-ante perspective (w hen the social contract is complete), the social decision

rule that prevents those deviations most effectively is optimal. And the most

effective rule in this respect is unani mity.

One basic reason why a unanimity rule may be undesirable is that the social

contract (or founding constitution) doe s not specify a decision–plan for all

future contingencies. When some unusual event occurs for which a well-adapted

decision is not speci ed in the social contra ct it may no longer be desirable from

an ex-ante perspective to attempt at all cost to prevent deviations from the

status-quo actions spe ci ed in the social contract. In our model it turns out that

some form of majority voting is desirable quite generally when the social

contrast, under m ajority voting Condorcet cycles arise even for strict preference

orderings. This has been seen as an important reason for favoring a unanimity

rule over major ity voting. Indeed, Condorcet cycles have been percei ved to be

suf ciently problematic that a whole strand of literature in Social Choice has

singled out the so-called min-max majority rule (see Caplin and Nalebuff 1988)

as a good rule for ex-post social decisions. This super-majority rule is the closest

rule to a 50 percent majority rule without Condorcet cycles. The basic reasoning

in support of this rule is that it has the bene t of ruling out Condorcet cycles and

it is the most  exible rule with thi s property (see, however, Dasgupta and

Maskin 1997 for an alternative viewpoint).

itly to the possibility of circumventing ex-post vested intere sts that may be

opposed to the implementation of a valuable reform .

The second drawback of majority voting, which is the main focus of this

paper, is that it may give rise to excessive ex-post redistribution, with the

majority expropriating the minorit y. This is the well-known problem of the

“tyranny of the majority.” Once a gain, we show that from an ex-ante perspective

society may be prepared to incur this cost for the sake of greater ex-post

 exibility. H owever, the higher the scope for expropriation is the more stringent

the optimal majority rule will be.

While greater  exibility and minimization of the cost of compensating

vested interests pushes one towards reducing the required size of the majority,

expropriation considerations push the ex-post decision rule towards super ma-

been) seen in similar terms to our theory. In the European Union decisions are

made by the European Council of Ministers. Whereas i mporta nt issues—such as

EU enlargeme nt, treaty changes, and some  scal issues—require a unanimous

vote within the Council, around 80 percent of the Council’s more routine

decisions are taken by a “quali ed majority vote.” A m ain proclaimed achieve-

ment of the recent Treaty of Nice has been the extension of quali ed majority

voting to new areas such as “trade in services and the commercial aspects of

intellectual property” (Baldwin et al. 2001). Every step away from unanimity in

EU decision making is hailed as an im portant victory for ef cient decision

making. On the other hand, when a group of countries successfully holds on to

In this respect, the closest model to ours is Romer and Rosenthal (1983).

Our

model essentially extends Romer and Rosenthal (1983) by introducing,  rst

contractual incompleteness, and second a positive deadweight cost of transfers.

Both assumptions are key to obtain a unique interior solution to the optimal

social contracting problem. Other recent incomplete contract approaches to

constitutional design include: Persson, Roland, and Tabellini (1997) and Pers-

1. Romer and Rosenthal (1983) establish that with private information about payoffs, but no

deadweight costs of transfers, a speci c unanimity rule can implement the full information ef cient

son and Tabellini (2000), who compare presidential and parliamentary regimes,

and G ersbach (2002) and Erlenma ier and Gersbach (1999), who signi cantly

extend our analysis by allowing for more general majority voting r ules than in

our paper. Finally, Aghion, Alesina, and Trebbi (2002) extend the incomplete

social contract approach in this paper to analyze the costs and bene ts of

social contracts, introduces the incomplete contracts assumption, and outlines

our sim ple model of majority-voting. Section 3 derives the optimal ma jority rule

and analyzes its comparative statics properties. Section 4 applies the basic

model to the analysis of several important facets of constitution design, such as

minority protections, vote trading, and federalism. Finally, Section 5 offer s

some concluding comm ents.

2. The Model

As we already noted, the structure of our model is similar to Romer and

political decision making in the legislative period.

Between the two periods a state of nature is re alize d that determines both

the cost of providing diff erent types of public good and their private bene ts to

each agent. We shall assume that there are n different types of public goods that

can be provided in the legislative period and that there are n possible cost

realizati ons s

, s

}. To keep things as simple as possible we take

the cost structure in each realization to be such that it is worth supplying at most

one type of public good. That is, in each realization only one type of public good

k @ c. We adopt the convention that under cost realization s

the low cost type

The N citizens differ in the utility they derive from the production of public

good i. Let b

i. We assume that b

can take two values, b

that the N citizens can be divided into two categories: those who gain from the

provision of public good i and those who lose. We shall refer to a citizen with

b

probability that any one citizen is fortunate is given by m

. We shall assume that

we shall henceforth de ne a state of nature as any particular realization of the

pro le s

, (b

)

) f or 1 # i # n and 1 # j # N. Each citizen is also endowed

with some private wealth w

public good i, and by t

, then we ca n

write citizen j’s payoff in state s

g

.

arrangem ents available the net expected bene t is strictly positive, so that all N

Suppose that in the constitutional period citizens are able to foresee all possible

future states of nature and to agree on a common description of the complete

state space. In this case the citizens are able to specify in advance what public

good should be supplied and how it should be  nanced in every state of the

incomplete constitution. In addition, some outcomes may be attainable only if

they are speci ed before the state of nature is realized and all citizens have

learned their preferences and positions in society.

An implicit assumption here is that citizens in our model onl y have

preferenc es over  nal outcomes and do not derive any intrinsic bene t from

future freedom of choice. It could be argued that this is a misrepresentation of

people’s preferences and that in reality people value the fact that the future is not

entirely predetermined. It is beyond the scope of this paper to address this

important issue. As will become clear in the next section, however, our analysis

does not cruc ially depend on a speci c modelling of preferences. Since we

assume later that it is not technologically feasible to write a complete social

3. Note that the distortionary cost l is only incurred when raising taxes from each individual in

One solution to this program is straightforward and is given by:

g

indeed maximize the ex-ante utility of a citizen. Note also that the complete

making rules for the choice of public good supply in the legislative period.

4. One might want to argue that citizens should be able to avoid all deadweight cost of insurance

by setting up an insurance fund in the constitutional period to which all citizens would be willing

to contribute. In that case, the solution would be the same whether citizens are risk-averse or not.

5. In particular, we rule out mechanisms where the decision to produce the public good or not and the

allocation of taxes and subsidies across agents would depend on messages sent by agents ex post.

Most, if not all, existing c onstitutions say very little about the size of govern-

ment or the natur e of government activities. They are instead devoted to a

detailed speci cation of rules for future social decision making. The constitu-

tions we consider in this model, if anything, specify too much rather than too

little in terms of future publ ic good supply relative to what is actually speci ed

As mentioned in the introduction, there are two drawbacks with majority voting

that are often emphasized. First, the majority may be tempted to exploit the

minority. Second, with no restrictions on feasible tax schemes, majority voting

gives rise to cyclic voting. Because of these drawbacks it is not clear a priori that

majority rule would necessarily dominate unanimity. Also, beca use of cyclic

voting it is not clear what the outcome i s under m ajority voting. The  nal

outcome will be driven by the objectives of whom ever happens to have control

over the agenda, a nd in the constitutional period it is di f cult to predict who will

be the agenda set ters in the legislative period. Alternatively, even if the agenda

number of fortunate citizens is not suf cient to form a majority a residual

number of ‘ha rmed’ citizens is also part of the majority coalition.

The harme d

citizens in the majority coalition are picked at random fr om the population of

harmed citizens. In situations where the number of fortunate citizens is larger

than the majority requirement, m ember s of the major ity are picked at r andom

among the fortunate citizens. The agenda setters in the m ajori ty coalition are

6. See our discussion paper, Aghion and Bolton (2002) for an analysis of other status-quo points.

7. It is actually always optimal for an agenda setter(s) to include as many fortunate citizens as

possible in the majority, as this minimizes the cost of compensating those who are made worse off

by the public good.

always taken to be fortunate agents. To get a majority to vote for their plan,

when fortunate citizens are not a majority in the population, the agenda setters

may need to compensate the harmed citizens in their majority.

Once a majority coalition has been determined in this way a public good supply

and tax scheme is put to a vote. The outcome is either the status-quo, if the proposal

tractable and transparent.

We assume throughout the paper that when a voter is indifferent between

the status-quo outcome and the pr oposed change he votes in favor of the change.

To summarize, the timeline of moves and events in our model is as follows:

1. at date 0 a constitution is written specifying: a) agenda setting rules in the

3. fortunate citizens form a coalition, which has control over the agenda; if

the fraction m

of fortunate citize ns exceeds the majority re quirem ent m

,

then the Nm

fortunate citizens who form the coalition is drawn at random

from the population of fortunate citizens Nm

of

fortunate citizens is less than the majority require ment m

) harmed citizens

contingent on whether the taxed individual is in the maj ority or the

minority,

5. all agents vote in favor or against the proposed budget,

6. if the budget is approved by the required majority Nm

7. if it is not, the status-quo is implemented.

8. Finally all agents consume their after-tax weal th.

We shall also consider vote trading between Stages 4 and 5.

3. The Opti mal Majority Rule