Rubinstein2005-page20

Rubinstein2005-page20 - y Or confusion such as ¤ I both...

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October 21, 2005 12:18 master Sheet number 18 Page number 2 2 Lecture One Q(x,y) (for all distinct x and y in X ) How do you compare x and y ? Tick one and only one of the following three options: I prefer x to y (this answer is denoted as x y ). I prefer y to x (this answer is denoted by y x ). I am indifferent (this answer is denoted by I ). A “legal” answer to the questionnaire is a response in which the respondent ticks exactly one of the boxes in each question. We do not allow the decision maker to refrain from answering a question or to tick more than one answer. Furthermore, we do not allow him to respond with answers that demonstrate a lack of ability to compare, such as: They are incomparable. I don’t know what x is. I have no opinion. Or a dependence on other factors such as: It depends on what my parents think. It depends on the circumstances (sometimes I prefer x but usu- ally I prefer y ). Or the intensity of preferences such as: I somewhat prefer x . I love x and I hate
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Unformatted text preview: y . Or confusion such as: ¤ I both prefer x over y and y over x . ¤ I can’t concentrate right now. The constraints that we place on the legal responses of the agents constitute our implicit assumptions. Particularly important are the assumptions that the elements in the set X are all comparable, that the individual has an opinion about all elements in the set X and that we do not allow him to specify the intensity of preferences. A legal answer to the questionnaire can be formulated as a func-tion f which assigns to any pair ( x , y ) of distinct elements in X exactly one of the three “values”: x  y or y  x or I , with the inter-pretation that f ( x , y ) is the answer to the question Q ( x , y ) . (Alterna-tively, we can use the terminology of the soccer “betting” industry and say that f ( x , y ) must be 1, 2, or × with the interpretation that...
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