EDITOR’S PROOF
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506ProofDefine the Pareto-setBij(c)for the bargainersiandjgiven the default con-
stitutionc. First suppose thatBij(c)⊂I. In that case, proposals coincide with points
on the contract curve, i.e.Pi→jmaximizesuigivenuj(c)andPj→imaximizesuj
givenui(c). If one proposalPincludes a lower value oftthan the other, the autocrat
is better off by selecting this proposalPinstead ofc. Settingc=Pguarantees that
each proposer has to proposecwhen this is the default outcome. If the proposals
Pi→jandPj→iinclude the same value oft, the autocrat is as well off if he selects
eitherPi→jorPj→iinstead ofc.
Next suppose thatBij(c)∩IBij(c). In that case, the constraint that the pro-
posal has to be inImay be binding. Yet a proposalPmaximizes the proposer’s
utility given that it is inBij(c)∩I. Note thatBij(c)∩Iis convex. WhenLorM
is proposal maker, preferences of the proposal maker are strictly convex and the
optimal proposal is uniquely defined. If this point is selected as default, the consti-
tution is stationary. IfRmakes a proposal the binding segment of the boundary ofI
is strictly convex unless it coincides with thet=0-line.^20 In either case,Rhas a
unique proposal which, if selected as default results in a stationary constitution^21
and we are left with three possibilities: a) In pointP constraintBij(c)is binding
andIis not. This coincides with the case whereBij(c)⊂I. b) ConstraintIis bind-
ing andBij(c)is not. In that case, withPthe proposer realizes the highest utility
inI. If the autocrat selectsc=P, either proposer must propose pointcwhen it
is the default outcome. c) Both constraints are binding. This case coincides with
case b). This proposition allows us to focus on stationary constitutions when looking
for optimal constitutions for the autocrat when discussing the static constitutional
choice problem. In the dynamic constitutional choice problem, the autocrat incurs a
cost when committing to a constitution and, as shown in the proof of Proposition9,
Proposition4 does not apply.3 Static Constitutional Choice
In this section we derive the optimal constitutional choice for the autocrat if he be-
lieves that his demise is imminent. As we know from Lemma3, any default consti-
tutioncwill be accepted by the bargainers. Yet only if the constitution is in the setI,
will it actually impact on the successor’s decision other than by requiring them to
propose amendments only inI. Hence we are going to focus on the autocrat’s con-
stitutional choice as the problem of picking a constitution from within the setI.(^20) To see thatR’s proposal is unique when thet=0 line is binding, recall that by our assumption
thatR’s preferences are lexicographic,R’s preferred point on thet=0-line is uniquely determined.
Hence, the optimal constitutional choice coincides with this point.
(^21) To see that the pointc=( 0 ,xR)is stationary when selected as default in the case wheret=0is
the constraint onR’s proposal, observe thatRas a responder will reject any proposal which does
not coincide withc.