Consider the following choice procedure over a finite set of n alternatives X {,...,n}. The agent...

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Consider the following choice procedure over a finite set of n alternatives X {₁,...,n}. The agent evaluates each alternative using a function v(x). That is, alternative x has a "level" v(x). v can be any function. The agent has a "reference" level v*. Given any set of m alternatives A CX, denote A = {₁,.,im} with 9 1 ≤ i₁ <... < im <n. The agent considers in turn alternatives i i... < until she finds one that has a level v(x) ≥ v*. If she gets to the end of the set A without finding such an alternative, she chooses an alternative in A that has the highest v-level (this last part means C(A) = {x € A: v(x) > v(y) Vy € A}). = 1. This is called the "satisficing" procedure, and it can be justified as optimal search behaviour in simple settings. Can you explain why the name is apposite? 2. Can C(A) be empty? does it satisfy WARP? 3. If the answers are "no" and "yes", then you should be able to ratio- nalize C by complete and transitive preferences. What do they look like? that is, when do we have x ≥ y? and what about a utility representation? Consider the following choice procedure over a finite set of n alternatives X {₁,...,n}. The agent evaluates each alternative using a function v(x). That is, alternative x has a "level" v(x). v can be any function. The agent has a "reference" level v*. Given any set of m alternatives A CX, denote A = {₁,.,im} with 9 1 ≤ i₁ <... < im <n. The agent considers in turn alternatives i i... < until she finds one that has a level v(x) ≥ v*. If she gets to the end of the set A without finding such an alternative, she chooses an alternative in A that has the highest v-level (this last part means C(A) = {x € A: v(x) > v(y) Vy € A}). = 1. This is called the "satisficing" procedure, and it can be justified as optimal search behaviour in simple settings. Can you explain why the name is apposite? 2. Can C(A) be empty? does it satisfy WARP? 3. If the answers are "no" and "yes", then you should be able to ratio- nalize C by complete and transitive preferences. What do they look like? that is, when do we have x ≥ y? and what about a utility representation?

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Finite sets are the sets having a finitecountable number of members Finite sets are also known as co... View the full answer