CES Lectures
The political economy of the voting su¤rage.
The extension of the franchise: theory.
Dr T.S. Aidt
Cambridge
March 2012
(Cambridge)
Lecture 2
March 2012
1 / 42
Yesterday
Two visions of the link between institutions and development:
Critical Junctures: At critical historical junctures societies embark on
di¤erent paths of economic and political development.
Inclusive (exclusive) institutions cause economic development (under
development).
The Grand Transition: Political development is the consequence of
long-run economic development.
Economic development causes inclusive institutions.
(Cambridge)
Lecture 2
March 2012
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Where do inclusive institutions come from?
Relatively little about
speci…c institutions: democracy, but what type?; secure property rights,
by how?
the short-run dynamics: what are the mechanisms through which
inclusive institutions replace exclusive ones?
Why should the elites in power (supported by exclusive institutions)
ever want to share power with other social groups by making
institutions inclusive?
How and why did democratic institutions emerge in the Western
world?
(Cambridge)
Lecture 2
March 2012
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France
Denmark
50
Suffrage
100
What are the economic origins of democracy?
Norway
0
Belgium
1850
1900
1950
50
UK
Sweden
Italy
Netherlands
0
Suffrage
100
1800
1800
Source: Flora et al. (1983)
1850
1900
1950
Alternative Theories of Franchise Extension
Franchise = the rules that de…ne who can vote in national elections
from estate based to restricted (by property, income, literacy, gender)
to universal su¤rage.
Preemptive democratization = the “old elite” is worse o¤ than
under status quo.
The threat of revolution hypothesis (Acemoglu and Robinson, QJE
2000).
Proactive democratization = the “old elite” is better o¤ than under
the status quo.
The
The
The
The
The
political ine¢ ciency hypothesis (Lizzeri and Persico, QJE 2004).
party political gain hypothesis (Llavador and Oxoby, QJE 2005)
constitutional exchange hypothesis (Congleton, EJPE 2007).
modernization hypothesis (Lipset, APSR 1959).
enlightenment hypothesis.
(Cambridge)
Lecture 2
March 2012
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This Lecture
The threat of revolution hypothesis (Acemoglu and Robinson,
QJE 2000).
Part of the Critical Junctures vision and argues that franchise extension
was a response by the old elites to revolutionary threats by the
excluded.
The political ine¢ ciency hypothesis (Lizzeri and Persico, QJE
2004).
Part of the Grand Transition vision and argues that franchise extension
was a response by the elites to exogenous changes in their evaluation
of public goods (triggered, e.g., by urbanization).
(Cambridge)
Lecture 2
March 2012
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Acemoglu and Robinson (QJE, 2000): The threat of
revolution hypothesis
The basic idea is that democratization is a consequence of a threat of
revolution.
This threat varies over time and sometime the threat is real;
sometime it is not.
A revolution is costly to all (output lost).
The elite initially in power can employ two strategies to prevent a
revolution from happening:
Redistribute to the poor (welfare, education, labour market reform etc.)
to make living under autocracy preferable to a revolution.
Extend the franchise and introduce democracy (allow the poor to
decide on redistribution themselves).
Democracy is a commitment devise to future redistribution. The
elite cannot promise redistribution for the future while keeping power
itself because in times when the threat of revolution is not real, it is
optimal for it not to carry out the promises.
(Cambridge)
Lecture 2
March 2012
7 / 42
Assumptions I
The demographic structure:
A fraction 1 λ of the population is rich (r)
A fraction λ of the population is poor (p)
λ > 12 , so majority is poor while a small elite is rich.
Individuals live for ever and discount the future with the factor β.
Endowments:
Each rich individual is endowed with hr units of capital
Each poor individual is endowed with hp units of capital
r
hr > hp and hhp is index of inequality.
H = λhp + (1 λ) hr is aggregate capital.
(Cambridge)
Lecture 2
March 2012
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Assumptions II
Technology is linear in capital: Y = AH.
Utility is linear in net income.
Net income
yti = (1 τ t ) Ahi + Tt for i = p, r .
τ t is a tax on income and Tt = τ t AH is a per capita transfer
(redistribution).
Taxes and transfers cannot be person or type speci…c.
b
τ < 1 (deadweight cost)
Notice that poor individuals would like τ t = b
τ and rich individuals
would like τ t = 0.
Limits on taxation: τ t
(Cambridge)
Lecture 2
March 2012
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Political States and Transitions
Three possible political states, indexed by Pt :
"Socialism" (SO): the poor control the capital stock and expropriate
the capital of the rich in a revolution.
"Democracy" (D): the poor (the median voter) control government
and decide the tax structure.
"Autocracy" (E): the rich elite controls government and decides the
tax structure.
Political transitions:
The society is initially an autocracy (E).
A political transition to socialism (SO) happens after a revolution.
A political transition to democracy (D) happens after an extension of
the franchise.
(Cambridge)
Lecture 2
March 2012
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Social States and the Revolution Technology
After a revolution the poor controls the entire capital stock, but it is
costly to revolt and a fraction of capital 1 µt is lost, i.e., the
per-period utility of a poor after a revolution is
utp (SO ) =
µt AH
λ
while the rich get nothing (utr (SO ) = 0).
The two possible social states, index by St , control the cost of
revolution:
In state B, µt = 0 and revolution is not desirable.
In state G , µt = µ 2 (0, 1) and a revolution may be desirable.
q = Pr(St = G ).
q controls the opportunities for social unrest, while µ controls the cost.
Together they control the "threat of revolution".
(Cambridge)
Lecture 2
March 2012
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The Timing of Events Within a Period
1
The social state is revealed.
2
If Pt = E , the elite decides whether or not to extend the franchise. If
it decides not to do so, it sets the tax rate for the period. If Pt = D,
the median voter sets the tax rate for the period and stage 3 does not
apply.
3
The poor decide whether or not to initiate a revolution.
1
2
4
If they do, then the economy transits to socialism and the poor share
the remaining output each period thereafter.
If they don’t but the elite extended the franchise, then the median
voter (one of the poor) resets the tax rate. Otherwise, the tax set by
the elite in stage 2 applies.
Production takes place, incomes are earned and consumed.
(Cambridge)
Lecture 2
March 2012
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Markov Perfect Equilibrium
The poor is one player and the rich is another player in a dynamic
game.
A strategy of the rich is a function of the state (Pt , St ) while a
strategy of the poor is a function of the state and actions taken by
the rich within that period (the tax rate set and the decision to
extend the franchise).
A pure strategy Markov Perfect equilibrium is a strategy combination
such that the strategies of the rich and the poor are best responses to
each other in all states of nature.
(Cambridge)
Lecture 2
March 2012
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Overview of the Model
time t
P=E
τr
ot
N
(St , E )
ex
te
nd
fr
an
ch
ise
time t+1
Ex
te
nd
fr
an
ch
ise
Elite
(Cambridge)
n
tio
olu
v
e
r
Asset
redistrbution
no
rev
olu
tio
n
τr stands
τ p = τˆ
P=D
Pt+i=SO all i
Pt+1=E
Pt+i=D all i
The poor
Lecture 2
March 2012
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Optimal Behavior in Democracy (P=D)
Suppose the elite have extended the franchise either this period or at
some point in the past.
The median voter is a poor citizen and the optimal policy choice is to
set τ t = b
τ no matter what the social state is (given that democracy
is better than socialism).
The political state continues to be democracy in the next period and
in every period after that.
The payo¤s to a representative poor and rich individual are:
(Cambridge)
V p (D ) =
(1
V r (D ) =
(1
Lecture 2
b
τ ) Ahp + b
τ AH
1 β
b
τ ) Ahr + b
τ AH
1 β
March 2012
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Revolution or Not?
Suppose that the elite has not extended the franchise.
The poor can initiate a revolution:
If the social state is G , the cost of a revolution is relatively low and
payo¤s are
V p (SO, G )
=
V r (SO, G )
=
AHµ
λ (1 β )
0
If the social state is B, the cost of a revolution is high and
V p (SO, B ) = V r (SO, B ) = 0.
It is not optimal for the poor to revolt in social state B: accepting
autocracy without any redistribution is better (Ahp > 0).
The revolution threat is only real in social state G .
The rich prefer democracy to socialism: V r (D ) > 0.
(Cambridge)
Lecture 2
March 2012
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State (B,E)
It is never optimal for the poor to revolt in social state B.
Since the threat of a revolution is absence in social state B, it is not
optimal for the elite to democratize or to redistribute income to the
poor: it can hold on to power anyway.
The payo¤ of a poor citizen is
V p (B, E ) = Ahp + β (qV p (G , E ) + (1
(Cambridge)
Lecture 2
q )V p (B, E ))
March 2012
17 / 42
State (G,E) and the Revolution Constraint
A revolution could happen, but whether it does or not depends on the
what the elite "o¤er" the poor.
If o¤ered nothing, the poor revolt if V p (SO ) >
hr
(1
>
hp
(1
Ah p
1 β
or
µ) λ
λ) µ
This is the revolution constraint:
For µ = 1 it always binds and it never binds for µ = 0.
Inequality needs to be su¢ ciently large to make revolution a real
threat, i.e., without inequality the elite will neither democratize nor
establish a welfare state.
(Cambridge)
Lecture 2
March 2012
18 / 42
Creating a Welfare State
Instead of democratizing the elite could keep power, but change the
tax structure to redistribution to the poor (create a "welfare state").
The elite prefer temporary redistribution to democracy if that is
enough to prevent the revolution.
Is it?
Let τ r be the tax proposed by the elite.
The payo¤ of a poor citizen is
V p (G , E , τ r )
= (1 τ r ) Ahp + τ r AH
+ β [qV p (G , E , τ r ) + (1
q ) V p (B, E )]
Credibility problem: the elite can only promise to redistribute when the
threat of revolution is real (state G ).
Democratization, on the other hand, is irrevocable, so it e¤ectively
commits the elite to future redistribution.
(Cambridge)
Lecture 2
March 2012
19 / 42
Some Calculations...
V p (G , E , τ r ) = (1
τ r ) Ahp + τ r AH
+ β [qV p (G , E , τ r ) + (1
q ) V p (B, E )]
V p (B, E ) = Ahp + β (qV p (G , E , τ r ) + (1
q )V p (B, E ))
Solve these two equations for V p (G , E , τ r ):
V p (G , E , τ r ) =
(1
τ r ) Ahp + τ r AH β (1
1 β
q ) (H
hp ) Aτ r
The most that the elite can promise is τ rt = b
τ each time St = G so
the maximum value of a welfare state is:
(Cambridge)
V p (G , E , b
τ ) = max V p (G , E , τ r )
Lecture 2
March 2012
20 / 42
Equilibrium
Theorem
For all q 6= q , there exist a unique pure strategy Markov Perfect
Equilibrium such that
1
If q < q , then the revolution threat will be meet by democratization
the …rst time the social state is G .
2
If q > q , the revolution threat will be meet by temporary
redistribution and the economy never democratizes.
(Cambridge)
Lecture 2
March 2012
21 / 42
Illustration of the Equilibrium
Vp
V p (D)
V p (G, E ,τ ,̂ q )
Democracy
V p (SO)
Temporary redistribution
V ( E ) + τˆ( H − h )
p
p
V p (E )
0
(Cambridge)
q
q*
1
Lecture 2
March 2012
22 / 42
Sketch of Proof
Proof.
(Sketch) Notice that
V p(G, E, b
τ j 1) = V p (D ) > V p (SO )
p
V p(G, E, b
τ j 0) = 1Ah β + b
τ (H hp ) < V p (SO )
∂V p ( G ,E ,b
τ jq )
∂q
>0
so there exist a V p ( G , E , b
τ j q ) = V p (SO ).
Check equilibrium for q < q ,
(B, E ) "not extend, τ r = 0" is SBR to "no revolution"
τ"
(G , E ) "extend" is SBR to "no revolution, τ = b
τ.
(B, D ) and (G , D ) only the poor take an action τ = b
(B, SO ) and (G , SO ) no one take actions.
(Cambridge)
Lecture 2
March 2012
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Insights
1
Democracy emerges when this is the only way to meet the threat of
revolution.
2
The better organized the poor are and the more frequently they pose
a revolution threat (high q), the more UNLIKELY is it that the
franchise is extended. Democracy emerges when the revolution is
unlikely!
3
Unequal societies are more likely to democratize
1
2
3
The poor has more to gain from a revolution
Easier for the elite to redistribute
The …rst e¤ect dominates...
(Cambridge)
Lecture 2
March 2012
24 / 42
Summing up the threat of revolution hypothesis
Democratization is preemptive and driven by the threat of social
unrest.
Democracy is a commitment devise used as a last resort by the
elites.
The democratic window of opportunity is often open during
recessions.
The threat of violent social change is the trigger, but economic
factors such as inequality and unbalanced growth decides if a society
is near the trigger point or not.
(Cambridge)
Lecture 2
March 2012
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The political ine¢ ciency
hypothesis.
(Cambridge)
Lecture 2
March 2012
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Lizzeri and Persico (QJE, 2004): The political ine¢ ciency
hypothesis.
The basic idea is that political parties seeking to win elections do not
(always) behave in the interest of their supporters.
Key distinction between public goods which bene…ts all and targeted
transfers (redistribution) which only bene…t some.
Under restricted su¤rage, the parties may use redistributive policies to
win elections which
not only exclude the un-enfranchised but also up to half the elite;
only give the supporters of the winning party slightly more than they
would get through provision of public goods.
Expanding the franchise reduces the incentive of the parties to use
redistribution to win election and encourages provision of public
goods.
Universal su¤rage with public goods can be Pareto superior to
restricted franchise with redistribution because all members of elite
get utility from public goods.
(Cambridge)
Lecture 2
March 2012
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Assumptions I
Two political parties compete in each election i 2 f1, 2g.
vote share maximization.
the policy o¤ered by the majority party gets implemented.
Continuum of citizens with measure 1, each endowed with $1 and
indexed by c. Preferences are:
V (c ) = G + φ (c )
where G is the utility of a public good and φ(c )
the net transfer received.
Policy platforms and technology
0 is the utility of
Provision of G requires all resources.
Redistribution can be person speci…c,
φi (c ) = 0 means 100% tax, φi (c ) 2 (0, 1) means taxation and
φi (c ) > 1 meansRnet transfers.
Budget balance: c φi (c )dc = 1.
So, it is either public goods or redistribution.
(Cambridge)
Lecture 2
March 2012
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Assumptions II
Two franchise regimes:
Universal su¤rage: all citizens can vote.
Restricted su¤rage: only a fraction η can vote (the elite).
Electoral competition takes place sequentially,
Stage 1: Party 1 proposes a platform.
Stage 2: Party 2 having observed party 1’s platform proposes its
platform.
Stage 3: The enfranchised citizens cast their vote and the majority
party implements its platform.
The franchise is initially restricted but can be extended if no member
of the elite objects.
(Cambridge)
Lecture 2
March 2012
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Universal suffrage
$
G
Case 3
Transfers to
majority cannot
win election
2
Case 2
Transfers to
majority can
win election
Case 1
PG inefficient
1
0
1/2
1
Voters
Restricted suffrage
$
G
Case 3
Transfers to
majority cannot
win election
2/η
Case 2
Transfers to
majority can
win election
Case 1
PG inefficient
1/η
0
1/2
1
Voters
Universal su¤rage
Case 1: G
1. (Public goods are ine¢ cient).
Party 1 o¤ers transfers of $1 to each.
Party 2 o¤ers 1 + ε to almost all (and expropriate a few to …nance this).
Case 2: 1 < G
2. (Public goods are e¢ cient)
Party 1 o¤ers public goods to maximize its vote share (at 1 G1 ).
Party 2 o¤ers transfers G + ε to G1 > 12 voters and nothing to the rest
(1 G1 ). This increases its vote share above 50%.
Case 3: G > 2. (Public goods are really e¢ cient)
Party 1 o¤ers public goods.
Party 2 also o¤ers public goods giving it a vote share of 50%.
(Cambridge)
Lecture 2
March 2012
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Restricted su¤rage (=scaled version of universal su¤rage)
Case 1: G
1
η.
(Public goods are ine¢ cient for elite)
Party 1 o¤ers transfers of $ 1η to each voter in the elite.
Party 2 o¤ers 1η + ε to almost all (and expropriate a few to …nance
this) and wins.
Case 2:
1
η
<G
2
η.
(Public goods are e¢ cient for elite)
Party 1 o¤ers public goods to maximize its vote share.
η
η
Party 2 o¤ers transfer G + ε to G > 2 of the elite voters and nothing to
the rest of the elite. This increases its vote share to above 50% of the
enfranchised elite voters.
Case 3: G > η2 . (Public goods are really e¢ cient for elite)
Party 1 o¤ers public goods.
Party 2 also o¤ers public goods, giving it a vote share of 50%.
(Cambridge)
Lecture 2
March 2012
32 / 42
All get G
G
Elite gets $1/ η
1/η
Some elite get G
Some elite get 0
2/η
G
All get $1
1
No way
Some get G
Some get 0
2
All get G
Maybe Yes, please So what?
The logic of franchise extension
The members of the elite are not treated equally by the winning
party: some are expropriated to buy the rest.
The winning party does NOT maximize the utility of those who vote
for it: they are given just enough transfers to make them indi¤erent.
Universal su¤rage makes it harder for parties to use distribution to
maximize their vote share because there are more voters and this
focuses electoral competition on public goods.
If universal su¤rage means public goods provision and restricted
su¤rage means redistribution within the elite, then extension is a
Pareto improvement:
the excluded elite is strictly better o¤
the included elite is no worse o¤.
(Cambridge)
Lecture 2
March 2012
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What are the drivers of reform?
Su¤rage reform is a response to exogenous shifts in the valuation of
public goods by the elite.
This could be caused by urbanization (and the need for sanitation,
infrastructure, etc.).
This could be caused by technological progress that allows public goods
to be provided more cheaply.
Democratization, then, is part of the Grand Transition.
(Cambridge)
Lecture 2
March 2012
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Summing up
Two answers to the franchise extension puzzle.
Extensions were preemptive and caused by revolutionary threat from
the excluded.
Extensions were proactive and caused by the interaction between
political ine¢ ciencies and preference or technological shifts favoring
public goods over transfers.
(Cambridge)
Lecture 2
March 2012
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What is Next?
Empirical evidence
Historical narrative – easy to give examples and often the same
examples are used to support di¤erent theories!
Statistical testing – hard because it is di¢ cult to quantify the "threat
of revolution" and "preference shifts within the elite".
(Cambridge)
Lecture 2
March 2012
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