Suppose voters are uniformly distributed along a continuum between 0 and 1. There are two candidates....
Suppose voters are uniformly distributed along a continuum between 0 and 1. There are two candidates. Voters will vote for the candidate who locates closes to them. Candidates only care about receiving more votes than the other candidate (and prefer a tie to losing).What is the rationalizable set of locations for each candidate?
Homework Answers
The rationalizable location will be 1st quarlitle and 3rd quartile --
For, uniform distribution
Consider, X -Location of voter
Then X ~ U(0,1)
i.e, f(x) = 1 , 0<x <1
So, rth quartile is ---
thus, m=r/4
now, put r =1 for 1st quartile and r=3 for 3rd quartile
So, 1st quartile = 0.25
3rd quartile = 0.75
So, candidates locations are at 0.25 and 0.75 along a continuum
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