Basic Utility Theory Used in Shepsle and Bonchek

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A Utility Function is centered at the individual's
ideal point -- "C" in the figure below.
Given two alternatives, O_y and O_n, the individual
picks the alternative for which she has the greatest
utility:

if U(O_y) > U(O_n), she chooses (votes for) O_y
if U(O_n) > U(O_y), she chooses (votes for) O_n