stion Page 1 of 3 Problem Set 1: Due in class on Tuesday July 7. Solutions to this homework will be posted

05 Jun stion Page 1 of 3 Problem Set 1: Due in class on Tuesday July 7. Solutions to this homework will be posted

Question
Page 1 of 3

Problem Set 1: Due in class on Tuesday July 7. Solutions to this homework will be posted

right after class, hence no late submissions will be accepted. Test 1 on the content of this

homework will be given on Tuesday July 14 at 1:40pm sharp. Group solutions are welcomed

and encouraged. (There is no limit on the group size.)

Problem 1 (20p)

Figure 1 Figure 2

Figure 3 Figure 4

Figure 5 Figure 6

Figure 7 Figure 8

Figure 9 Figure 10

Figures 1-10 above depict preference and indifference relations of ten different people on a

set of three or four alternatives. (For each decision maker her set of alternatives constitutes

the entire domain of choice.) Alternatives are marked as dots and preferences are marked

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with arrows: the direction of an arrow is the direction of the preference relation, no arrow

between two dots means that an individual is indifferent between these two alternatives.

In each of the ten figures preference relation either is or is not transitive and also,

independently of the transitivity of the preference relation, the indifference relation is or is

not transitive.

In the following table put “true” or “false” in each of the 20 empty cells.

Preference relation is

transitive

Indifference relation is

transitive

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Problem 2 (10p)

Assume a voter has a strict preference over any two candidates in the set of Clinton, Obama

and Edwards; in other words, it is not the case that he is indifferent between some two

candidates in this set. In addition, assume that the voter is not rational.

(1) Prove that a voter who prefers Obama over Clinton has to prefer Edwards over Obama

and Clinton over Edwards. Present your reasoning.

(2) Prove that if all voters are not rational then either (i) all of them have identical

preferences or (ii) the set of all voters is split into two subsets such that in each subset all

voters have identical preferences.

Problem 3 (8p)

Let’s see now how likely would we observe a rational outcome if a decision maker acted

randomly. Consider the case of three alternatives X, Y and Z. Assume that deciding

between any two of these alternatives, e.g., X and Y, the decision maker rolls a die and

depending on the outcome decides Y

?

X or X