Unit 3: exogenous candidates Flashcards
Note:
Here, we do not distinguish between a party and a candidate
Assumptions for this analysis?
Complete info. SPPs Continuous policy space Large number of voters, n (n is odd) Increasing disutility with distance from the peak (i.e preferred policy)
Condition for ‘i’ being the preferred candidate?
if |x-α(i)| < |x-α(j)| for all i isnt equal to j, i is the preferred candidate
x is the voter’s position
α(i) and α(j) are positions of the two candidates i and j
How do voters vote in this model? What if they are indifferent between two options?
They know the positions of α(i) and α(j) and chooses the one closest to their own preference!
If indifferent, 50:50 coin toss
How is the winner decided in this model?
By getting a majority of votes (coin toss if two candidates draw)
What is a Downsian environment?
Where candidates only care about winning (not necessarily what policy is implemented)
How are candidates payoffs determined in a Downsian environment?
Payoffs = benefits from winning (a) x prob. of winning (pi)
V=(pi)a
Prove that, in a Downsian 2 exogenous candidate scenario, with median voter x(m), the Unique Nash Equilibrium (UNE) is at x(m)=α(1)=α(2), and that the expected benefit from both candidates entering is a/2, where a is the benefit from winning the election. (use diagrams)
See notes, side 1 of page 1
For candidates only motivated by ideology, what does their utility depend on? Give an example of how their utility function may look?
Only the distance between their preferred position and the implemented policy!
U(x) = -|x-x(i)| where x is implemented policy and x(i) is their preferred policy
Show that, with 2 ideology motivated candidates, if they have policy preferences on the same side of the median voter’s preferred point, that x(m) will be a NE, but not a UNE?
see notes, top of side 2 page 1 (see diagrams in slides?)
Show that, with 2 ideology motivated candidates, if they have policy preferences on the opposite side of the median voter’s preferred point, that x(m) will be a NE and a UNE?
see notes side 2 page 1 midway down
Give an example of a utility function of a candidate who is motivated by both ideology and benefits?
U(x) = a-|x-x(i)|
Show that, with 2 ideology and benefits motivated candidates, who have party policies on different sides of the MVPP, the UNE is at x(m)?
See notes bottom of page 1 side 2
Show that, with 2 ideology and benefits motivated candidates, who have party policies on the same sides of the MVPP, the UNE is at x(m)?
see notes
Possible extensions to the exogenous candidate models?
a) uncertainty over median voter position
b) n is even
c) increase number of candidates
d) entry cost for candidates
e) 2 (or more) policy space dimensions introduced
