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Lecture 6_Electoral Competition 2010

# Lecture 6_Electoral Competition 2010 - ECON 4109H LECTURE 6...

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ECON 4109H LECTURE 6 Electoral Competition October 6, 2010 ECON 4109H LECTURE 6

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Electoral Competition Candidates select positions on a left-right axis. Each citizen votes (nonstrategically) for the candidate he likes best. Candidate with most votes wins. Candidates care only about winning, not about positions. Each candidate prefers winning to to tying to losing. ECON 4109H LECTURE 6
Electoral Competition There are a continuum of voters located on the interval [ 0, 1 ] There is a probability density function f on [ 0, 1 ] which measures the probability that a voter lies in any sub-interval. Assume that f is continuous, R 1 0 f ( x ) dx = 1, that f ( x ) > 0 for all x [ 0, 1 ] . The probability that a voter lies in the interval [ a , b ] where 0 6 a < b 6 1 is R b a f ( x ) dx . ECON 4109H LECTURE 6

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Median Voter m is the unique position in [ 0, 1 ] such that: Z m 0 f ( x ) dx = Z 1 m f ( x ) dx m is the median position . Observe that: Z m 0 f ( x ) dx = Z 1 m f ( x ) dx = 1 2 ECON 4109H LECTURE 6
Voting Behavior Each voter votes for the candidate who adopts a position which is closest to the one he occupies.

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