Voting, Electoral Rules and Institutions

Elena Manzoni

Introduction

We investigate how the political nature of policy-making affectseconomic outcomes.For example, what explains the divergence between textbook

models of economic polic-ymaking (where the question is: whatare optimal policies?) and real world experience (in which thesepolicies are often not adopted)?

Key ingredients

I heterogeneity in players’ preferences

I rules to aggregate heterogeneity in a collective decision.

- direct democracy;- representative democracy.

Institutions

Institutions refer to “the rules of the game” or more specifically tothe extensive form of the exact game that the agents are playing(Kreps)

How do democratic societies aggregate preferences?How to model elections?Do the details of electoral systems matter?

1. De Sinopoli, Iannantuoni (2007): two-party equilibria ariseunder proportional representation.

2. De Sinopoli, Ferraris, Iannantuoni (2013): comparison ofMultidistrict Majoritarian Systems and ProportionalRepresentation.

3. De Sinopoli, Iannantuoni, Manzoni, Pimienta (2017):Proportional Representation with Government formationstage.

4. Cella, Iannantuoni, Manzoni (2017): comparison ofPresidential and Parliamentary systems in terms of efficiency.

A Spatial Voting Model where Proportional RuleLeads to Two-Party Equilibria

Francesco De Sinopoli and Giovanna Iannantuoni

Introduction

Focus of the paper:

Strategic voting.

Proportional election with more than two parties.

The question of electoral rules and party-system has a longstanding tradition in voting theory:

Duverger’s Law (Riker, 1982).

Duverger’s explanation translated into strategic voting by formalmodels:Palfrey (1989).Cox (1994), Myerson and Weber (1993), Fey (1997).

Duverger’s Hypothesis (Riker, 1982).

Cox (1997).

Main results

Model of proportional election.

Main result: in a large electorate strategic voters vote for only twoparties.

A “unique” Nash equilibrium exists, characterized by a cutpointoutcome.

The model

Policy Space: X = [0, 1].

Parties: M = {1, ..., k, ...,m} ζk ∈ [0, 1].

Proportional Rule: Every voter i can cast his vote for any party.

The pure strategy set for player i :Si = {1, ..., k , ...,m} .A mixed strategy for player i :σi = (σ1

i , ..., σki , ..., σ

mi ).

The model

Policy Outcome: Let v(s) be the vector representing each party’sshare of votes under s

X (s) =m∑

k=1

ζkvk (s) .

Voters: θi ∈ Θ = [0, 1], single peaked preferences.u : <2 → < continuously differentiable in the first argument,ui (X ) = u(X , θi ).

A finite game Γ is characterized by a finite set of playersN = {1, ..., i , ...n} and by their bliss points: Γ =

{N, {θi}i∈N

}.

The cumulative distribution of players’ bliss points is HΓ(θ).

L = arg mink∈M ζkR = arg maxk∈M ζk

Pure strategy equilibria (PSE)

Proposition: Let s be a PSE of a game Γ with n voters:

(α) if θi ≤ X (s)− 1n (ζR − ζL) then si = L,

(β) if θi ≥ X (s) + 1n (ζR − ζL) then si=R.

Definition: Given Γ and HΓ (θ), let θΓ be the unique policyoutcome obtained with voters strictly on its left/right voting forL/R, i.e. let θΓ be implicitly defined by:

θΓ ∈ ζLHΓ(θΓ)

+ ζR(1− HΓ(θΓ)

)

where HΓ(θ) =

[lim

y→θ−HΓ(y),HΓ(θ)

].

Proposition: If θi 6= θΓ ∀i ∈ N, then the strategy combinationgiven by ∀θi < θΓ si = L and ∀θi > θΓ si = R is a PSE.

Mixed strategy equilibria

Let µσ =∑i∈N

σin and X (µσ) =

m∑k=1

ζk µσk .

Proposition: ∀ε > 0, ∃n0 such that ∀n ≥ n0 if σ is a Nashequilibrium of a game Γ with n voters, then:

(α) if θi ≤ X (µσ)− ε then σi = L,

(β) if θj ≥ X (µσ) + ε then σj = R.

MAIN RESULT: ∀η > 0, ∃n1 such that ∀n ≥ n1 if σ is a Nashequilibrium of a game Γ with n voters then:

(α) if θi ≤ θΓ − η then σi = L,

(β) if θj ≥ θΓ + η then σj = R.

On the outcome function

· Two assumptions needed:

(i) Continuous in the share of votes parties obtain.

(ii) X (s−i ,R) > X (s−i , k) > X (s−i , L) ∀k 6= L, R; ∀s−i ∈ S−i .

· With two parties, the outcome function can be any continuousfunction strictly increasing in vR .

(Alesina and Rosenthal 1996, Grossman and Helpman 1999,Iannantuoni 2002)

· Linear outcome function is:

- the utilitarian solution of the bargaining process amongpoliticians with a quadratic loss function;

- the result of a bargaining process of government formation a laBaron and Diermeier (2001).

Application I: Divided government (Alesina and Rosenthal1996)

H (θ) continuously differentiable and strictly increasing.Two-stage game.

I stage: presidential election with plurality rule.

II stage: legislative election with proportional rule.

Position of the legislature:

X leg =m∑

k=1

ζkvk .

Policy outcome:X = (1− α)ζP + αX leg 0 < α < 1.

Given P, the “proportional game” is equivalent to the game withMP parties:

ζPk = (1− α)ζP + αζk .

We have a moderation result:

∂θP

∂ζP> 0.

Example. Three parties (L, C , R). In the legislature L and Robtain votes, while C wins the executive.

More complex institutional systems may have more political partiesthan their components would have separately.

Application II: Representative democracy (Besley Coate,1997)

Three stage game:

I stage: each citizen decides to become a candidate or not facing acandidacy cost of δ,

II stage: the election occurs,

III stage: policy implemented.

Policy outcome:

X =m∑

k=1

ζkvk .

We have:

∂θ

∂ζL> 0,

∂θ

∂ζR> 0.

Only the two extremist citizens are candidates (for δ → 0).

Electing a Parliament

Francesco De Sinopoli, Leo Ferraris and Giovanna Iannantuoni

(2013)

Introduction

In parliamentary democracies policies reflect a legislative debatewhere all political parties contribute to the final outcome.

Role of parties in shaping national policy function of the number ofseats in parliament.

Legislative election differ in many dimensions, the most importantone being: electoral rule.

They analyze:

I Multidistrict Majoritarian System

I Single-District Proportional system

Introduction

The paper studies a society composed by policy-motivated citizenselecting a parliament of k-members belonging to two parties.

Seats in parliament are allocated according to the electoral rule.

Policy outcome defined on the number of seats parties take in theelection.

Multidistrict Majoritarian System

Citizens distributed in k districts vote in each one by majority rule.

The electoral result (i.e. a pure strategy combination) determinesthe number of seats for the two parties (L and R).

Policy outcome decreasing in the number of districts won by theleftist party.

Issue: solution concept to solve the model.

Nash EquilibriaUndominated Equilibria

Multidistrict Majoritarian SystemDistrict-sincerity

DefinitionA strategy combination is district sincere if each player who strictlyprefers (given the strategies of the players in the other districts)that party L/R wins in his district, votes for party L/R.

DefinitionAn outcome is “pure” if it assigns probability one to a given policy.

We prove that the voting game has a unique district-sincereoutcome in pure strategy which is the unique district-sincere“pure” outcome.

Multidistrict Majoritarian SystemTrembling-hand perfection

There exists a unique pure strategies perfect equilibrium outcome,which is the unique district-sincere outcome in pure strategies, andthe unique “pure” outcome induced by perfect equilibria.

Proportional System

Citizens are distributed in one national district electing krepresentatives.

Policy outcome decreasing in the number of districts won by theleftist party.

Issue: solution concept to solve the model.

Nash EquilibriaUndominated Equilibria

Proportional SystemTrembling-hand-perfection.

There exists a unique pure strategy perfect equilibrium outcome,which is also the unique “pure” outcome induced by perfectequilibria.

Comparing outcomes in the two systems

When there is full homogeneity across districts:

I the single district proportional system favors a more moderateoutcome.

When there is extreme heterogeneity across districts:

I the outcomes are the same.

The model

Policy Space: X = [0, 1].

Parties: P = {L,R} θp ∈ X, with θL < θR .

Voters:N = {1, 2, ..., n} θi ∈ X. Voters’ preferences are singlepeaked and symmetric, ui (X ).Si = {L,R}σi = (σLi , σ

Ri )

The model

The electoral rule: Let ϕ : S → {0, 1, ..., k} be the function thatmaps votes into the number of seats for party L.

Policy Outcome: X : {0, 1, ..., k} → X, decreasing in the numberof seats for party L.

The model

Define for j ∈ {1, 2, ..., k} :

αj =X (j) + X (j − 1)

2

We assume no voter i ∈ N has his bliss point equal to αj

Multidistrict Majoritarian Election

I There are k districts: d ∈ D = {1, 2, ..., k}.I Nd is the set of voters in district d , inhabited by an odd

number of voters nd .

I md ∈ M = {m1, ...,mk} is the median voter in district d , suchthat m1 ≤ m2 ≤ ... ≤ mk .

I They define the distributionFm (θ) = {#md ∈ M s.t. md ≤ θ}.

Multidistrict Majoritarian Election

Given a pure strategy combination s = (s1, s2, ..., sn) , DL(s) is thedistricts where L wins.

The electoral rule ϕM is simply:

ϕM(s) = #DL(s).

The Solution

A strategy combination is district sincere if, given the strategies ofthe players in the other districts, every voter who strictly prefersparty L/R winning in his district votes for party L/R.

Let σ =(σ−d , σd

), σ−d = (σi )i∈N�Nd

and σd = (σi )i∈Nd.

Moreover, let Ld(Rd

)denote the nd−tuple of pure strategies of

the players in the district d where everybody votes for L(D).

The solution

A strategy combination σ is district-sincere if for every district dand for every player i in district d :

Ui

(σ−d , Ld

)− Ui

(σ−d ,Rd

)> 0 then σi = L

Ui

(σ−d , Ld

)− Ui

(σ−d ,Rd

)< 0 then σi = R

Let us define:dM =

{0 if m1 > α1

max d s.t md ≤ αd if m1 ≤ α1.

The solution

Proposition

X(dM

)is the unique pure strategy district-sincere equilibrium

outcome.

Corollary: X(dM

)is the unique “pure” outcome induced by

district-sincere equilibria.

The solution

Perfect Equilibria.A completely mixed strategy σε is an ε-perfect equilibrium if

∀i ∈ N, ∀si , s′i ∈ Si

if Ui

(si , σ

ε−i)

> Ui

(s′i , σ

ε−i

)then

σεi

(s′i

)≤ ε.

A strategy combination σ is a perfect equilibrium if there exists asequence {σε} of ε-perfect equilibria converging (for ε→ 0) to σ.

The solution

Proposition

Every perfect equilibrium σ is district sincere.

Proposition

X(dM

)is the unique pure strategy perfect equilibrium outcome.

Corollary: X(dM

)is the unique “pure” outcome induced by

perfect equilibria.

Example

Two districts, N1 = {0.31, 0.4, 0.69}, and N2 = {0.31, 0.6, 0.69}.Parties’ positions are θL = 0.1 and θR = 0.9.

X (0) = 0.9 > X (1) = 0.5 > X (2) = 0.1 hence α2 = 0.3 andα1 = 0.7ui (X ) = − |X − θi |The unique pure strategy district-sincere equilibrium outcome isX (1) = 0.5.

BUT

There are two different pure strategy district sincere and perfectequilibria:

s =(s1, s2

), s1 = (L, L, L), s2 = (R,R,R) and

s =(s1, s2

), s1 = (R,R,R), s2 = (L, L, L)

Example

Moreover, also a mixed equilibrium exists:

σ =(σ1, σ2

)σ1 =

(L, 13L + 2

3R,R)

σ2 =(L, 23L + 1

3R,R).

Hence, X (σ) = 29X (0) + 5

9X (1) + 29X (2).

Proportional Election

One voting district electing k representatives.

Voters’ bliss policies are ordered θ1 ≤ θ2 ≤ ... ≤ θn, and distributedaccording to F (θ) = {#i ∈ N s.t. θi ≤ θ}.

To elect d representatives party L needs a number of votes inbetween [nd , nd+1).

Given a pure strategy combination s = (s1, s2, ..., sn) let NLd (s) be

the set of citizens voting for L under s, and let us define by nLd (s)its cardinality.

There exists a unique d∗ such that nLd (s) ∈ [nd∗ , nd∗+1), and theelectoral rule ϕP is:

ϕP(s) = d∗.

Proportional ElectionLet us define:

dP =

{0 if F (α1) < n1max d s.t F (αd) ≥ nd if F (α1) ≥ n1

Proposition: X(dP

)is the unique pure strategy perfect

equilibrium outcome and the unique “pure” outcome induced byperfect equilibria.

Comparing electoral systems

Let us assume that the minimum number of votes to elect dmembers of parliament with the single district proportional systemis

n

k(d − 1) +

1

2

n

k

In the multidistrict majority system, the leftist party needs at leasthalf of a district votes to carry the district.

Example

Consider a society with six voters, θ1 = θ2 = θ3 = θ4 = 0 andθ5 = θ6 = 1 electing a parliament of two members, two partieswith preferred policies θL = 0 and θR = 1 and the symmetricoutcome X (2) = 0 < X (1) = 1

2 < X (0) = 1.

Hence, α2 = X (2)+X (1)2 = 1

4 and α1 = X (1)+X (0)2 = 3

4 .

ExampleHomogeneity across districts

Multidistrict Majoritarian Election

District 1 is inhabited by {θ1, θ2, θ5}. Hence m1 = 0.

District 2 is inhabited by {θ3, θ4, θ6}. Hence m2 = 0.

The unique district sincere equilibrium outcome of the multidistrict

majority system is X(dM)

= X (2) = 0

ExampleHomogeneity across districts

Single district Proportional Electionm = 0

The unique perfect equilibrium outcome of the proportional system

is X(dP)

= X (1) = 12 .

ExampleHeterogeneity across districts

Multidistrict Majoritarian ElectionDistrict 1 is inhabited by {θ1, θ2, θ3}. Hence m1 = 0.

District 2 is inhabited by {θ4, θ5, θ6}. Hence m2 = 1.

The unique district sincere equilibrium outcome of the multidistrict

majority system is X(dM)

= X (1) = 12 .

ExampleHeterogeneity across districts

Single district Proportional Electionm = 0

The unique perfect equilibrium outcome of the proportional system

is X(dP)

= X (1) = 12 .

Homogeneity across districts: general result

Proposition

Assume that md = m ,∀d, and that X (d) is symmetric around 12 ,

then:

a. if X(dM)≤ 1

2 , X(dM)≤ X

(dP)≤ 1

2 ;

b. if X(dM)> 1

2 ,12 ≤ X

(dP)≤ X

(dM).

Heterogeneity across districts: general result

Proposition

If districts are equally sized and ordered from left to right, then

X(dP)

= X(dM).

Proportional Representation under Uncertainty

Francesco De Sinopoli, Giovanna Iannantuoni, Elena Manzoni,Carlos Pimienta

(2017)

Introduction

I Model of strategic voting in proportional representationelections when voters’ preferences are uncertain.

I Policy-oriented voters vote for politicians belonging to nparties with given policy platforms.

I Elected legislators, characterized by the same bliss policy astheir party, bargain over policy and transfers to form agovernment.

I Finally, the executive implements the chosen policy outcomeand transfers.

The model

I Policy space is X = [0, 1].

I q ∈ X is the status quo policy (no transfer associated to it)

I Finite set of parties P.

The model

I Finite set of voters N = {1, ..., i , ..., n}.I Each voter i ∈ N

I is characterized by a bliss point θi that is his privateinformation. Voters’ bliss points are independently distributedaccording to the commonly known distribution F (·). The onlyassumption we impose on the distribution F (·) is that it hassupport [0, 1] ⊂ R.

I Voter i ’s preferences are represented by the utility function

ui (x , θi ) = − (x − θi )2 .

The model

I Si = {1, ..., k, ...,p} is the set of possible ballots for voter i ,where the ballot si = k is a vector of p components with allzeros except for a one in position k , which represents the votefor party k .

I The share of votes of party k given s is vk (s) =1n

n

∑i=1

ski .

I We consider a proportional electoral rule that assigns to eachparty a share of seats in parliament equal to the share of votesthe party has received.

The model

I A ballot profile s induces a composition of the parliament or aset of legislators Ms = {1, . . . , l , . . . , ms}.

I To abstract from issues related to the indivisibility of seats inthe parliament we assume that, for every s, the size of theparliament ms is such that, for every party k, the expressionms · µs

k is an integer value.

I Each legislator l ∈ Ms is characterized by ζl ∈ [0, 1].

I Legislators have the same ideal policy as the party that theyrepresent.

I Legislator l ’s preferences over policies are

ul (x , ζl ) = −(x − ζl )2. (1)

The model

I A legislator may or may not belong to the government.

I If a legislator is not part of the government she only caresabout the implemented policy and, therefore, her final utilityis represented by ul (x , ζl ).

I If a legislator belongs to the government then she also caresabout office-holding benefits B ∈ R and transfers yl ∈ R.

Ul (x , yl , ζl ) = B + ul (x , ζl ) + yl .

where B > 1.

I Transfers have to satisfy budget balance, so that ∑ms

l=1 yl ≤ 0.

I yl = 0 whenever legislator l is not in the government.

Timing

The model is a three-stage game.

I In the first stage voters privately observe their type and casttheir vote.

I A strategy for voter i is a function σi : [0, 1]→ ∆(Si ) fromthe set of possible types of voter i to the set of probabilitydistributions on ballots.

I The vector σi (θi ) = (σ1i (θi ), ..., σk

i (θi ), ..., σpi (θi )) contains

the probability that voter i votes for each party when her idealpolicy is θi .

I Given a ballot profile s, each party k ’s proportion of seats inthe parliament Ms = {1, . . . , ms} is equal to its vote share µs

k .

Timing

I In the second stage both the composition of the governmentand the policy are decided.

I We solve this stage by relying on the bargaining protocolproposed in Baron and Diermeier (2001).

I Every legislator l ∈ Ms has the same probability to beselected as the formateur.

I The formateur, f , selects a coalition G ⊂ Ms such that f ∈ Gand makes a take-it-or-leave-it offer both in policy andtransfers dimensions.

I If the coalition does not have a majority of seats in theparliament or at least one of the members of the coalitiondoes not accept the take-it-or-leave-it offer then thegovernment does not form.

Timing

I In the third stage policy outcome and transfers areimplemented.

I If the formation of government G was successful then policyxG is implemented and transfers are made according to thevector yG .

I If the government formation process was unsuccessful thenthe status quo q is implemented and no transfers are made.

III Stage Policy and TransfersWe first investigate the optimal policy and transfer offer thatmaximizes the formateur’s utility for a given coalition.

I The formateur selects the government G , the policy xG , and avector of transfers yG .

I The optimal policy and transfer vector are that maximize theformateur’s utility for a given coalition G is obtained by

maxx ,y

Uf (x , yf , ζf ) = maxx ,y

B + uf (x , ζf ) + yf (2)

s.t.

B + ul (x , ζl ) + yl ≥ ul (q, ζl ) for all l ∈ G \ {f }, and(3)

0 ≥ ∑l∈G

yl . (4)

III Stage Policy and Transfers

I The optimal policy xG is the utilitarian solution:

xG =1

|G | ∑l∈G

ζl .

I The vector of transfers yG is given by:

yGl = ul (q, ζl )− B − ul (x

G , ζl ) if l ∈ G \ {f },yGl = 0 if l /∈ G , and

yGf = |G |B + ∑

l∈G\{f }

[ul (x

G , ζl )− ul (q, ζl )]

.

III Stage Policy and Transfers

I Under this policy choice and transfers, the utility of eachmember of the coalition l ∈ G \ {f } other than the formateuris the utility from the status quo:

Ul (xG , yG

l , ζl ) = B + ul (xG , ζl ) + yG

l = ul (q, ζl ).

I The utility to the formateur is

Uf (xG , yG

f , ζf ) = |G |B + ∑l∈G

ul (xG , ζl )− ∑

l∈G\{f }ul (q, ζl ).

I The bargaining power is in the formateur’s hands so that heextracts all the rent associated to xG .

I As a consequence, the formateur’s utility is weakly higher thanthe utility from the status quo, Uf (x

G , yGf , ζf ) ≥ Uf (q, 0, ζf ).

II Stage: Government Formation

We now focus on the structure of the optimal coalition. Theoptimal size of the coalition leads always to consensusgovernments. This result builds on the existence of sufficientlyhigh office-holding benefits B.

Proposition

Given that for each possible coalition G the formateur offers theefficient policy xG , and given the associated transfers yG , theoutcome of the government formation process is always G = M.

I Stage: Strategic Voting

I In the electoral stage voters, whose bliss policy is privateinformation, vote under proportional representation.

I We prove that strategic voters vote only for the extremecandidates (i.e. candidates belonging to the extreme parties).

I Such a behavior is rational because it allows voters toinfluence the final outcome in the strongest possible way.

I Stage: Strategic Voting

Policy-oriented voters essentially vote only for the extreme parties,L and R. This result holds for all but a set of voters whose lengthis inversely related to the size of the electorate, n, hence itbecomes negligible for large electorate elections.

Proposition

Let σ be a voting strategy profile used in an equilibrium of themodel. For every voter i ,(α) if θi ≤ X (µσ)− 1

n then σi (θi ) = L, and(β) if θi ≥ X (µσ) + 1

n then σi (θi ) = R.

Do the right thing.Incentives for policy selection in presidential and parliamentary

systems.

Michela Cella, Giovanna Iannantuoni and Elena Manzoni

Research questions

What are the links between institutional designs, types ofuncertainty and incentives offered to politicians?

Which constitutional system helps implement efficient policy?

What we do

I Democracies are characterized by the interplay of theexecutive and the legislative bodies when choosing the policyto be implemented.

I We analyze two-period Presidential and Parliamentarysystems.

I The differences between the two systems are

- confidence vote;- observability of policy proposals.

Empirical facts

I Presidential and parliamentary systems seem to inducedifferent policy outcomes (Persson and Tabellini, 2000);

I The binary distinction between parliamentary and presidentialsystems may be too coarse to explain variety of policyoutcomes (Voigt, 2001);

I The difference in policy outcomes between presidential andparliamentary systems is mostly originated by stableparliamentary systems (Bettarelli et al., 2015).

Findings

I The Presidential system performs better than theParliamentary system when legislators are fully informed onthe state of the world.

I The result is driven by an efficient behavior of the parliamentin the Presidential system.

I The Parliamentary system induces better characteristics andbehavior of the executive in the second period.

I The Parliamentary system may outperform the Presidentialone if we relax the full information assumption.

Related Literature

I Persson and Tabellini (2000, 2003): importance of institutionsfor policy outcomes

I Besley and Coate (1998): judge system by how it selects theefficient policy

I Diermeier and Vlaicu (2011): importance of the confidencevote and uncertainty over legislator preferences

I Vlaicu (2008) and Vlaicu and Whalley (2013): hierarchicalstructure

I Becher (2013): compares presidential and parliamentarysystems in terms of fiscal policy, focusing on the dissolutionpower of the executive.

The Model

I Two periods: 1, 2.

I Three types of agents: executive, legislators, voters.

I st ∈ {sa, sb} state of the world; each state is equally likely.

I gt ∈ {A,B} is the policy choice at time t.

I A costs cA > 0, B is costless.

I The status quo policy is g0 = A.

I The efficient policy is

g ∗ (st) =

{A if st = saB if st = sb

The ModelVoters/citizens

I N voters;

I Voters have utility

u(gt , st) =

{1 if gt = g ∗ (st)0 if gt 6= g ∗ (st)

The ModelExecutive

I θe ∈ {0, 1} private information, γ is the probability of thehigh type;

I The executive observes the state of the world in each period;

V e = 1− c (g1) + θeu(g1, s) + π (1− c (g2) + θeu(g2, s)) + εθe

I π is the probability of being in power in period t = 2;

- π = 1 for the presidential system,- π ≤ 1 for the parliamentary system;

I θe is the ex-post voters’ belief on the probability that theexecutive is policy-oriented.

The ModelParliament

I L members l = 1, ..., L, with type θl ∈ {0, 1}, independentand private information;

I γ is the probability of the good type;

I each legislator observes the state of the world in each period;

V l = (1− θl )R + θlu(g1, s) + π((1− θl )R + θlu(g2, s)

)+ εθp

I θp is the ex-post voters’ belief on the probability that themajority of the parliament is policy-oriented.

Presidential system

I The same executive and parliament are in power for bothperiods (π = 1).

I Citizens observe only the implemented policy (and not theproposed one).

Presidential systemTiming

θl , θe t = 0

E and P observe s1

V observes s1

t = 1

Eg e1 P

g e1

A

Y

N

E and P observe s2 t = 2

Eg e2 P

g e2

A

Y

N

Parliamentary system

I There is the confidence vote: if the parliament rejects theexecutive’s policy proposal new elections are called for bothbodies (π < 1).

I Citizens observe both the proposed and the implementedpolicy.

I Probability that the majority of the parliament ispolicy-oriented

Γ =L

∑k= L−1

2 +1

(L

k

)γk(1− γ)L−k .

Parliamentary system: Timing

θl , θe t = 0

E and P observe s1

V observes s1

t = 1E

g e1 P A

g e1

N

Y

V

P

E and P(or E and P) observe s2 t = 2E

g e2

P

g e2 A

NY

E

g e2

P

g e2 A

NY

Presidential systemEquilibrium

E : θe = 0 E : θe = 1 P : θl = 0 P : θl = 1t = 1 g ∗/B g ∗/B N ⇐⇒ (B, sA) N ⇐⇒ (B, sA)t = 2 g ∗/B g ∗/B N ⇐⇒ (B, sA) N ⇐⇒ (B, sA)

I policy-oriented and office-oriented legislators behave alike;

I all types of executive are indifferent between proposing g ∗ orB;

I average probability of doing the right thing W = 1.

Parliamentary systemEquilibrium 1 (high cA)

E : θe = 0 E : θe = 1 P : θl = 0 P : θl = 1t = 1 B g ∗ Y N ⇐⇒ (B, sA)t = 2 g ∗ g ∗ N ⇐⇒ (B, sA) N ⇐⇒ (B, sA)

I in the first period office-oriented legislators approve everypolicy proposal;

I policy-oriented executive always proposes the efficient policy;

I office-oriented executive proposes B in period 1 and theefficient policy in period 2;

I average probability of doing the right thing W < 1.

Parliamentary systemEquilibrium 2 (low cA)

E : θe = 0 E : θe = 1 P : θl = 0 P : θl = 1t = 1 g ∗ g ∗ Y N ⇐⇒ (B, sA)t = 2 g ∗ g ∗ N ⇐⇒ (B, sA) N ⇐⇒ (B, sA)

I in the first period office-oriented legislators approve everypolicy proposal;

I all types of executive always propose the efficient policy;

I average probability of doing the right thing W = 1.

Comparison of the two systems

I The parliament performs better in the presidential system, asboth policy-oriented and office-oriented legislators voteagainst the wrong policy proposals in both periods.

I It is more likely to have a policy-oriented executive in power inthe second period in the parliamentary system, asoffice-oriented legislators are replaced more often thanpolicy-oriented ones by a negative confidence vote.

I The executive is more likely to behave efficiently in theparliamentary system due to the observability of the policyproposal (second period) and the presence of the confidencevote (first period).

Comparison of the two systemsHigh cA (γ = 1

2 , ε = 110 , cA = 9

10 )

Presidential Parliamentary

P(g e1 = g ∗(s1))

[12 , 1]

34

P(g1 = g ∗(s1)) 1 78

P(θe = 1|t = 2) 12

58

P(g e2 = g ∗(s2))

[12 , 1]

1

P(g2 = g ∗(s2)) 1 1

W 1 1516

Comparison of the two systemsLow cA (γ = 1

2 , ε = 110 , cA = 3

10 )

Presidential Parliamentary

P(g e1 = g ∗(s1))

[12 , 1]

1

P(g1 = g ∗(s1)) 1 1

P(θe = 1|t = 2) 12

12

P(g e2 = g ∗(s2)

[12 , 1]

1

P(g2 = g ∗(s2) 1 1

W 1 1

Comparison of the two systems

I The presidential system provides a better incentive scheme tothe parliament and achieves first best when legislators observethe state of the world.

I The parliamentary system generates better behavior andquality of the executive through a disciplining and a selectioneffect.

I When legislators are asymmetrically informed on st first bestcannot be achieved in the presidential system, and theparliamentary system may outperform it.

Asymmetric information on the state of the worldAn example

We assume γ = 12 , ε = 1

10 , cA ∈[

310 , 1

).

We change the following assumptions:

I legislators do not know the state of the world but observe acommon signal about it;

I probability that the majority of Parliament is policy-oriented isΓ, so legislators’ do not come from the same pool as theexecutive;

I after a negative confidence vote the executive is alwaysreplaced, while the parliament stays in power with probabilityπl = 2

3 .

Asymmetric information on st

Legislators observe a common signal σt on the state of the world:

σt =

{sA with probability 2

3sB with probability 1

3

if st = sA;

σt =

{sB with probability 2

3sA with probability 1

3

if st = sB ;

Legislators perfectly observe s1 before the beginning of period 2.

We assume ρ ∈[

712 , 2

3

).

Presidential systemEquilibrium

θe = 0 θe = 1 θl = 0 θl = 1t = 1 B g ∗ Y Yt = 2 B g ∗ N ⇐⇒ (B, sA) N ⇐⇒ (B, sA)

and(g e1 , s1) = (B, sA) and(g e

1 , s1) = (B, sA)

I policy-oriented and office-oriented legislators behave alike andfollow their signal only in period 2 if (g e

1 , s1) = (B, sA);

I policy-oriented executives propose g ∗ and office-orientedexecutives propose B;

I average probability of doing the right thing W pres = 1116 +

ρ8 .

Parliamentary systemEquilibrium

θe = 0 θe = 1 θl = 0 θl = 1t = 1 B g ∗ Y N ⇐⇒ (B, sA)t = 2 B g ∗ N ⇐⇒ (B, sA) N ⇐⇒ (B, sA)

and(g e1 , s1) = (B, sA) and(g e

1 , s1) = (B, sA)

I office-oriented legislators approve every proposal in the firstperiod;

I policy-oriented legislators follow their signal in the first period;

I every legislator in the second period follows his signal only if(g e

1 , s1) = (B, sA).

I policy-oriented executives propose g ∗ and office-orientedexecutives propose B;

I average probability of doing the right thingW parl = 11

16 +ρ8 − Γ

(14 −

1532ρ + 1

8ρ2).

Comparison of the two systemsWelfare and legislators’ quality

Legislators’ quality in our framework is characterised by twodimensions: expertise (ρ) and intrinsic motivation (Γ).

I Expertise affects welfare of both systems, while intrinsicmotivation only affects the performance of the parliamentarysystem.

I In this region, the parliamentary system is more responsive toexpertise than the presidential one.

I W parl > W pres when 14 −

1532ρ + 1

8ρ2 < 0 which happens for

ρ > 15−√97

8 .

I |W parl −W pres | is increasing in Γ.

Conclusions

I Systems are differentiated by two characteristics: confidencevote and observability of policy proposal.

I The presidential system provides undistorted incentives tolegislators.

I The parliamentary system improves the executive’sperformance through disciplining and selection effects.

I When legislators know the state of the world, the presidentialsystem achieves first best.

I When they don’t, the parliamentary system may outperformthe presidential one.