Suppose that a utility function u represents a preference re…
Suppose that a utility function u represents a preference relation on a set X. Consider the function that assigns to each x in X, f(x)=au(x)+b, where a and b are both constants. Suppose that the preference has at least a strict ranking (the agent is not indifference between at least one pair of alternatives). Then, f represents the preference if and only if,
Read DetailsConsider a preference relation on a finite set X={x1,x2,…,xn…
Consider a preference relation on a finite set X={x1,x2,…,xn}. Suppose that it is complete and transitive. Then, the following function represents it: U(xi)= 3log|{j=1,…,n: xi at least as good as xj}|-2020, where |.| represents the cardinality of a set.
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