1 Advances in Political Economy - Department of Political Science

EDITOR’S PROOF

74 K. Michalak and G. Pech

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preferred outcome in the transition andRcan do nothing about it. Again, incentives

for writing a constitution would be minimal. In the intermediate range, the following

lemma holds:

Lemma 2Fo r 1 >t^0 >0,the setIis non empty and convex.

ProofBy concavity ofv, at least the pointx^0 ,t^0 must be inI. Becausevis strictly

concave,Iis not vanishingly small, i.e. there isε>0 such thatLstrictly prefers to

get(x^0 ,t^0 −ε)with certainty over a lottery with expected outcomex^0 ,t^0 .AsM

andRalso prefer this point, it must be inI. By convexity of preferences and,Iis

also convex. 

Ignoring the trivial caset^0 =0, the result of Lemma2 only hinges on the as-

sertion that expectations over the outcome from freely negotiating the constitution

take the form of a lotterywhich is common knowledge to all players. One possi-

ble way of consistently modelling a bargaining game which provides such a lottery

is to assume that each party is given a chance to implement its preferred outcome

with a probabilityPj.^16 In the case where this opportunity arises, rationality dic-

tates that the party imposes its preferred policy point. Thus, ifLwins, the policy

realization(t, x)is( 1 ,xL),ifMwins, the policy realization is( 1 ,xM)forwM≤w

and( 0 ,xM)forwM>wand ifRwins, the policy realization is( 0 ,xR). Thus, for

partyi, expected utility from freely negotiating the constitution is

Vi^0 =PRvi

(

xR

)

+PMvi

(

xM

)

+PLvi

(

xL

)

+

(

1 −PL

)

wi+PLw

ifwM>w, (1)

Vi^0 =PRvi

(

xR

)

+PMvi

(

xM

)

+PLvi

(

xL

)

+PRwi+

(

1 −PR

)

w

ifwM≤w, fori=L, M, R. (2)

We can modify pay offs by admitting a conflict costKiwhich is incurred if free

negotiations take the form of open conflict. Without changing any of the results of

this paper we may extend the model to cover the case where players form a priori-

coalitions before entering conflict. For example,LandMmay form a coalition

againstRand expect to realize a point on their contract curve if they win. Note that

our model does not attempt to explain conflict but instead uses a conflict scenario to

rationalize a settlement in the shadow of conflict.

2.2 Negotiating a Constitution in the Presence ofc

Suppose a constitutioncspecifying a tax/policy combination(t, x)has been handed

down by the autocrat. Moreover, suppose that a pre-determined set of players nego-

tiates over constitutional reform or de-novo design of the constitution. This set of

(^16) For other specifications, see Michalak and Pech (2012).