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cyclic preferences


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Another name for intransitive preferences, especially when cyclicity exists among more than three alternatives, as in the following example. A die is rolled, and the outcomes I, II, …, VI, denoting the number of dots on the face that comes up, are equiprobable. Before the die is rolled, you are given a choice between two gambles as follows, with payoffs in pounds, dollars, or any other currency:This means that if you choose Gamble A, then if I comes up you win 1 unit, if II comes up you win 2 units, and so on, whereas if you choose Gamble B, then if I comes up you win 2 units, if II comes up you win 3 units, and so on. If you are like most people, you probably prefer Gamble B to Gamble A, because it offers a higher payoff in five cases out of six, despite the fact that the payoff from Gamble A is much greater in the sixth case. Next, you choose between the following pair of gambles:You probably prefer C to B for the same reason as before. Continuing in the same way, you eventually choose between the following gambles:You probably prefer G to F for the usual reason. Taking all your preferences into account, your preference order, from most preferred on the left to least preferred on the right, is GFEDCBA. But G is identical to A, which means that your preferences are cyclic: GFEDCBG. … See also decision theory, money pump. Compare transitive preferences.

Die shows:

I

II

III

IV

V

VI

Gamble A payoffs:

1

2

3

4

5

6

Gamble B payoffs:

2

3

4

5

6

1

Die shows:

I

II

III

IV

V

VI

Gamble B payoffs:

2

3

4

5

6

1

Gamble C payoffs:

3

4

5

6

1

2

Die shows:

I

II

III

IV

V

VI

Gamble F payoffs:

6

1

2

3

4

5

Gamble G payoffs:

1

2

3

4

5

6

Subjects: Psychology.


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