Rubinstein2005-page106 - 12:18 88 master Sheet number 104...

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October 21, 2005 12:18 master Sheet number 104 Page number 88 88 Lecture Eight We will talk about preferences over L ( Z ) . An implicit assumption is that the decision maker does not care about the nature of the random factors but only about the distribution of consequences. To appreciate this point, consider a case in which the probability of rain is 1 / 2 and Z ={ z 1 , z 2 } , where z 1 = “having an umbrella” and z 2 = “not having an umbrella.” A “lottery” in which you have z 1 if it is raining and z 2 if it is not is not equivalent to the “lottery” in which you have z 1 if it is not raining and z 2 if it is. Thus, we have to be careful not to apply the model in contexts where the attitude toward the consequence depends on the event realized in each possible contingence. Preferences Let us start by thinking about examples of “sound” preferences over a space L ( Z ) . Following are some examples: Preference for uniformity : The decision maker prefers the lottery
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