X1

Utility

Spatial Models of Elections.Downs “An economic theory of Democracy”

1 (100)

X2 X3 X4 X5

2 (200) 3 (300) 4 (200) 5 (100)

From the space of Utility…

Max.

% voters

Spatial Models of Elections.Downs “An economic theory of Democracy”

X1 X2 X3 X4 X5

To the space of voters

(100)

(200)

(300)

(200)

(100)

A B50

% voters

Spatial Models of Elections.Downs “An economic theory of Democracy”

Two party System with one mode

A B50

% voters

Two party System with one mode

A B50

% voters

Two party system with two modes and abstensionism

A B

% voters

Two party system with two modes and abstensionism

A B

% voters

Multiparty system

A B C

% voters

Assumptions behind two party convergence• 1. There are only two political parties.• 2. There is a single-round election for any office.• 3. The election chooses a single candidate.• 4. Elections take place within a single constituency.• 5. The election is decided by a plurality vote.• 6. Policies can be located along a single (left-right) dimension.• 7. Candidate policy positions are well defined.• 8. Candidate policy positions are accurately estimated by each voter.• 9. Voters look no further than the next election.• 10. Eligible voters go to the polls if the expected benefits of their vote’s contribution to

the election of the candidate for whom they would vote exceed the“costs” of voting.• 11a. Voters care only about which candidate/party will enact policies closest to their

preferences. They vote for the candidate closest to their own policy location.• 11b. If there are no policy differences among the candidates/parties, then voters will

be equally likely to support each of the candidates/parties.• 12. Parties/candidates care only about winning.• 13. Parties/candidates look no further than the next election.• 14. Candidates/parties accurately estimate the policy preferences of voters, or at

minimum, they can identify the location of the median voter overall and the median voter in each party.

• 15. Candidates are part of a unified party team.

10

Spatial Models of LegislaturesAssumptions

Legislature as a set of n (odd number) individuals Majority Rule One dimension. Legislature must choose a point on a

line. Each Legislator i has an ideal point xi and single peaked

preferences m=median voter with ideal point xm

There is always a status quo in place, labeled x0

There is a division-of-labor arrangement: committee system

c= median voter of the committee with ideal point xc

Three decision making regimes

1. Pure majority rule. • No Committee system; any legislator can offer

a motion to change the status quo x0

• The floor is open for some new motion (against old status quo, if it survived, or the new status quo)

• This procedure of motion-making and voting continues until no member of legislature wishes to make a new motion.

Equilibrium Outcome

Status quo (X0)Xm(parliament’s median voter)

Xm

Xc(committee’s median voter)

Xc

Pure Majority Rule

Three decision making regimes2. Closed-rule committee system • A Committee (c)first gets to decide whether the

legislature will consider changes in the status quo; it has gatekeeping power

• If the “gates are opened” the Committee makes a proposal

• The parent legislature (the floor F) may vote the committee’s proposal either up or down . The proposal is closed to amendments

c

mpropose

Not propose

Xc

X0

X0 Status quo

yes

no

Equilibrium Outcome

Status quo (X0)Xm(parliament’s median voter)

Xm

Xc(committee’s median voter)

Xc

Closed-rule commmittee system

2 Xm-Xc

Gridlock

Three decision making regimes3. Open-rule committee system • A Committee (c)first gets to decide whether the

legislature will consider changes in the status quo; it has gatekeeping power

• If the “gates are opened” the Committee makes a proposal

• The parent legislature (the floor F) may emend the committee’s proposal. Committee concedes its monopoly access to the agenda

c

mpropose

Not propose

Xm

X0

X0 Status quo

emend

no

Equilibrium Outcome

Status quo (X0)Xm(parliament’s median voter)

Xm

Xc(committee’s median voter)

Xc

Open-rule commmittee system

2 Xm-Xc

Gridlock

2 Xc-Xm

Equilibrium Outcome

Status quo (X0)Xm(parliament’s median voter)

Xm

Xc(committee’s median voter)

Xc

Open-rule commmittee system

2 Xm-Xc

Gridlock

2 Xc-Xm

Suboptimalequilibria

Multidimensional space and Decision making

Xb

Xa

Xc

sq

p1

If we take in consideration both dimensions at the same time and no monopoly of the agenda setting power…MacKelvey Caos theorem

p1

p2

= W (p..)

p2

p3

p3

p..

Multidimensional space and decision making dimension by dimension

• As in the pure majority rule anyone is free to make a motion to change the status quo

• However decision making takes place one dimension at a time, in some pre-set order.

• The group (the parliament) continues to focus on amending the status quo on the first dimension until no more amendments are offered , then turns its attention to the next dimension etc.

Multidimensional space and decision making dimension by dimension

Xb

Xa

Xc

Xb1

Xb2

Xc1

Xc2

Xa1

Xa2

Dim2

Dim1

Xm

Multidimensional median

Multidimensional space and closed rule

• Xa is the agenda setter ; X0=Status Quo• W(X0) is the Xa’s opportunity set. As under

closed rule proposals are not subject to amendments, the Xa’s objective is to move the final policy outcome onto the indifference contour of smallest radius (namely closest to Xa’s ideal point ) that still lies in W(X0)

x0

pa

Xa proposes pa and Xc and Xa vote yes.

= W (X0)