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.

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.

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.

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

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

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

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

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.

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.

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

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

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

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

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.

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

* 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

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