1. A spatial model of an election campaign
The campaign occurs this way:
Candidates announce their platforms: that is, what policy they will enact if elected.
Candidates can change their platforms as many times as they want.
Once both candidates have settled on a platform, voters cast ballots.
The winning candidate must enact the platform she promised in the campaign.

2. The spatial model: defining equilibrium
As in other models discussed in this class, we are interested in identifying an equilibrium
that is, a steady state in which no player wishes to change her action given what all other players intend to do
We’re interested because this seems like a reasonable prediction of how things might turn out.
An equilibrium will be reached in the spatial model if given the platforms of the candidates and the votes of the voters:
no candidate wishes to change her platform, and
no voter wishes to change his vote.

3. The spatial model: assumptions
Three simple assumptions guide how we solve the model.
Candidates care only about getting elected; they do not have preferences over policies.
Voters vote for the candidate whose platform is closest to their preferred policies. If a voter is indifferent, he flips a coin to determine his vote.
Everybody votes.

4. An electorate with five voters
WINNER
DEM
REP
Voter 1
Voter 2
Voter 3
Voter 4
Voter 5
much less
keep same
much more
Federal $ spent on national defense

5. An electorate with five voters
WINNER
DEM
REP
Voter 1
Voter 2
Voter 3
Voter 4
Voter 5
much less
keep same
much more
Federal $ spent on national defense

6. An electorate with five voters
WINNER
DEM
REP
Voter 1
Voter 2
Voter 3
Voter 4
Voter 5
much less
keep same
much more
Federal $ spent on national defense

7. An electorate with five voters
EACH HAS
50-50 CHANCE
OF VICTORY
DEM
REP
Voter 1
Voter 2
Voter 3
Voter 4
Voter 5
much less
keep same
much more
Federal $ spent on national defense
flips coin

8. The spatial model: assumptions
Three simple assumptions guide how we solve the model.
Candidates care only about getting elected; they do not have preferences over policies.
Voters vote for the candidate whose platform is closest to their preferred policies. If a voter is indifferent, he flips a coin to determine his vote.
Everybody votes.

9. Relaxing Assumption 1
Let’s now say that candidates care not one whit about winning the election. They care only about the policy that will be enacted once the election is over.
To establish this assumption, let’s give the candidates ideal points, too.

10. An electorate with five voters and candidates who care about policy
WINNER
DEM
REP
Voter 1
Voter 2
Voter 3
Voter 4
Voter 5 D* R*
much less
keep same
much more
Federal $ spent on national defense
The winner will establish a very conservative policy; does D wish to change her platform?
* candidate ideal point

11. An electorate with five voters
WINNER
DEM
REP
Voter 1
Voter 2
Voter 3
Voter 4
Voter 5 D* R*
much less
keep same
much more
Federal $ spent on national defense
can R do better than this?
* candidate ideal point

12. An electorate with five voters
WINNER
DEM
REP
Voter 1
Voter 2
Voter 3
Voter 4
Voter 5 D* R*
much less
keep same
much more
Federal $ spent on national defense
can D do better than this?
* candidate ideal point

13. An electorate with five voters
EACH HAS
50-50 CHANCE
OF VICTORY
DEM
REP
Voter 1
Voter 2
Voter 3
Voter 4
Voter 5 D* R*
much less
keep same
much more
Federal $ spent on national defense
* candidate ideal point
flips coin

14. The spatial model: assumptions
Three simple assumptions guide how we solve the model.
Candidates care only about getting elected; they do not have preferences over policies.
Voters vote for the candidate whose platform is closest to their preferred policies. If a voter is indifferent, he flips a coin to determine his vote.
Everybody votes.

15. Relaxing Assumption 2
Let’s now say that voters don’t vote just for the candidate whose platform is closest to his preferred policy.
Instead, let’s say that one candidate (in this example, R) has some advantage over the other: maybe she’s more charismatic; maybe she’s the incumbent and has presided over peace and prosperity; maybe she’s emerged victorious in a war; there are lots of reasons why this might be true.
Political scientists call this a valence advantage.
valence: the degree of attractiveness an individual, activity, or thing possesses as a behavioral goal

16. * candidate ideal point
R has a valence advantage of V. Is this still an equilibrium?
DEM
REP
Voter 1
Voter 2
Voter 3
Voter 4
Voter 5 D* R*
much less
keep same
much more
Federal $ spent on national defense
No. If R has a valence advantage, R can do better by moving her platform toward her preferred policy. This is no longer an equilibrium.
* candidate ideal point

17. An election where one candidate has a valence advantage
DEM
REP
Voter 1
Voter 2
Voter 3
Voter 4
Voter 5 D* R*
much less
keep same
much more
Federal $ spent on national defense
If r < V, then Voter 3 votes for R.
If r > V, then Voter 3 votes for D.
If r = V, then Voter 3 votes for R.
r = distance between median voter’s position and R’s platform