October 21, 2005 12:18masterSheet number 23 Page number 7Preferences7Table 1.1A response toQ(x,y)andQ(y,x)A response toR(x,y)andR(y,x)xyYes, NoIYes, YesyxNo, Yesfunction fromXontoYthat is required to preserve the open sets. Ineconomics, the one-to-one correspondence is required to preservethe more informal concept of interpretation.We will now construct a one-to-one and onto correspondence,Translation, between answers toQthat qualify as preferences bythe first definition and answers toRthat qualify as preferences bythe second definition, such that the correspondence preserves themeaning of the responses to the two questionnaires. In other words,Translationis a “bridge” between the responses toQthat qualify aspreferences and the responses toRthat qualify as preferences.To illustrate the correspondence imagine that you have two books.Each page in the first book is a response to the questionnaireQwhichqualifies as preferences by the first definition. Each page in the sec-
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