Unit 4: Endogenous Candidates O&S (1996)

Question 1

Set up for Osborne and Slivinski (1996)?

Answer 1

Same as FSW (1990)

Question 2

O+S (1996) What if no citizen enters?

Answer 2

All obtain payoff -infinity (generalised ‘status quo’ policy, x(a), is implemented)

Question 3

O+S (1996) How does voters vote? What do they do if there is a tie of ‘k’ candidates in their preferences?

Answer 3

Sincerely; they vote for whichever candidate is closest to their position

If tie, they allocate 1/k of their vote(s) to each of the k candidates

Question 4

O+S (1996) What does a voters payoff depend on? Example payoff function?

Answer 4

The distance between their bliss point and that of the winner (x(i) and x*)

• |x*-x(i)|

Question 5

O+S (1996) What choice do all citizens have?

Answer 5

To enter or not to enter; if they enter they can implement their preferred policy

Question 6

O+S (1996) What are a and c?

Answer 6

a=benefits of office for the winning candidate

c= cost of entry

Question 7

O+S (1996) What is the payoff function for (possible) candidate i? (3)

Answer 7

• |x*-x(i)| NO ENTRY
• |x*-x(i)|-c ENTER AND LOSE
• |x*-x(i)|-c+a ENTER AND WIN

Question 8

O+S (1996) Payoff for a candidate who doesn’t enter but receives their bliss point?

Answer 8

zero

Question 9

O+S (1996) Why does at least one candidate always run?

Answer 9

If no candidate runs, then one candidate will run as a Unique Candidate - they will have the incentive to run otherwise all receive the payoff -infinity

Question 10

O+S (1996) When else may a one-candidate equilibrium occur?

Answer 10

When the candidate runs unopposed; ie. other candidates (who could enter and win) decide not to enter

This happens when costs>disutility of the policy distance (ie. c-a>|x(j)-x(i)|)

Question 11

O+S (1996) What happens if a-c<0?

Answer 11

benefits less than costs tf can have a one-candidate eq. not necessarily at the position of the median voter tf multiple equilibria are possible!

Question 12

O+S (1996) What happens if a-c>0?

Answer 12

benefits>costs therefore we can have a one-candidate equilibrium, but if we do it’ll be in the position of the median voter! Tf only one equilibria is possible (see submission for detail on this)

Question 13

O+S (1996) What happens when the benefit of office is less than twice the cost but greater than the cost (of entry)? and why?

Answer 13

See notes page 2 side 1 - prove this!

OCE and the candidate ideal position is at the MV choice

Question 14

O+S (1996) What happens when the benefit from office is less than the cost of entry?

Answer 14

There is an OCE that is not necessarily at the MV choice; the winner may be located anywhere along the distance (c-a)/2 (prove this!, see notes!)

Question 15

O+S (1996) Explain what happens in a 2-candidate equilbrium (ie. Contested election)? Define the critical value of ε, when there is an existence of the 2CE?

Answer 15

Two candidates enter and tie, whilst no non-candidate wishes to enter.
If we define the two candidates positions as:
m-ε, m+ε, with ε>0, then each earns 1/2 votes and they tie.
This requires ε to be small enough that there is no other candidate with ideal position in the interval: (m-ε, m+ε)

The critical value of ε for there to be existence of a 2CE is defined by: b>=2(c-ε(F))
where ε(F) is the critical value of ε, depending on the distribution

Question 16

O+S (1996) General conclusions: What does the number of candidates who enter depend on? (2)

Answer 16

1) positively depends on the benefits of winning

2) negatively depends on the cost of entry

Question 17

O+S (1996) General conclusions: Necessary conditions for equilibrium with k candidates?

Answer 17

a>=kc

Question 18

O+S (1996) Explain how the model might be affected if costs can vary between candidates?

Answer 18

eg. if the cost of entry for the median voter is too great, they may not enter therefore the MV position may not be an equilibrium position

Question 19

O+S (1996) Explain the idea behind a 3-candidate equilibrium?

Answer 19

3-way tie, none want to withdraw and no non-candidate wants to enter:
(this means that for all 3 candidates a lottery over all 3 options is preferable to a certain win of their 2nd best choice!)

Question 20

O+S (1996) Explain the two scenarios that may happen in a 3-candidate equilibrium?

Answer 20

1) Each candidate gets 1/3 of the votes, and all their positions are different and equidistant (I think? see notes?)
2) Positions of all 3 candidates are different; 2 get equal vote numbers, and the third gets a smaller share and loses. Intuition: strategic reasoning; it is possible the last candidate may rather a lottery between the two other candidates than to vote for one of them and give them a sure win (empirically observed)

Question 21

O+S (1996) explain what happens if candidates can implement the same policy with different efficiency?

Answer 21

It means that the utility of the same policy being implemented can differ between candidates tf MV candidate (if less efficient than a close candidate) may not win! (ie. if one party is large and established and known for getting things done may be preferred to one unknown and small, but with the MV policy choice!

Question 22

O+S (1996) What is a variation on the model with k winners?

Answer 22

If they all get 1/k of the votes then an extension of this model can look at the following negotiation process that may take place

One other variation may also be a change in the voting rule