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Unformatted text preview: f ( x , z ) = x ² z . However, this ad-ditional consistency condition was not included in the above def-inition since it follows from the other conditions: If f ( x , z ) = I , then by the assumption that f ( y , z ) = I and by the no order effect, f ( z , y ) = I , and thus by transitivity f ( x , y ) = I (a contra-diction). Alternatively, if f ( x , z ) = z ² x , then by no order effect f ( z , x ) = z ² x , and by f ( x , y ) = x ² y and transitivity f ( z , y ) = z ² y (a contradiction). Similarly, note that for any preferences f , we have if f ( x , y ) = I and f ( y , z ) = y ² z , then f ( x , z ) = x ² z . The Questionnaire R A second way to think about preferences is through an imaginary questionnaire R consisting of all questions of the type: R(x,y) (for all x , y ∈ X , not necessarily distinct). “Is x at least as preferred as y ?” Tick one and only one of the following two options: ± Yes ± No...
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This note was uploaded on 12/29/2011 for the course ECO 443 taught by Professor Aswa during the Fall '10 term at SUNY Stony Brook.
- Fall '10