Question

Use the following prompt to answer questions 9-10 Candidate A and Candidate B are running in the primary for the "Left" party for the same elected position, and are choosing where to politically position themselves before simultaneously announcing their platforms.. The political preferences of Lefi-party voters eligible to vote in the primary are distributed between "Far Left" and "Moderate," as illustrated in the diagram below with the number of voters subscribing to the given political preference given by the numbers in the diagram: 20 Moderate 10 Far Le 15 Mid-Le 10 5 IS Voters will vote for whichever candidate positions themselves closest to their poltical views, and equidistant voters will be split evenly between the candidates 9. Where will Candidate A position themselves (politically in equilibrium during the primary election? (Assume positioning decisions are made simultaneously Suppose that Candidate A wins the primary. Now, Candidate A will go on to run against "Right" party Candidate Cin the general election. Where voters in the full election are distributed according to the diagram below 10 Far LeftQuite LeftMid-Left 15 5 Left-ishModerate 10 Right-ishMid-RightQuiteFar Right 5 Right 10. Where will Candidate A position themselves (politically) in equilibrium during the general election? (Assume positioning decisions are made simultaneously)

Answer 1

In such problems, both candidates position themselves at the median location. This is because if the other candidate positions himself at some other location, then the guy can win the election by placing himself at the median. Therefore, we just need to find the position at which the voters are split in half. Note that both candidates are equally likely to win the election in equilibrium.

9) In this problem, we have a total of 60 voters. So, we need to find the position held by the 30th voter. This is seen to be the position mid-left. Thus, candidate A positions himself at the mid-left in the primary election in equilibrium.

10) In this problem, there are a 100 voters. So, we need to find the position held by the 50th voter. This turns out to be moderate. Thus, candidate A positions himself as Moderate during the general election in equilibrium.