Please help, do I have to construct a social preference table? Professor Economi

Question

Please help, do I have to construct a social preference table?

Professor Economicus wants a grader for her class this semester She chooses from students who have taken her class before and looks for three qualities in a grader: speed, accuracy, and sense of humor If student A is better than student B in two of these three qualities, she will strictly prefer A to B, She is trying to rank three students based on their qualities given in the following table. Derive Professor Economicus' preference ranking over these three students, Is ranking transitive? Explain why or why not.

Explanation / Answer

Let us rank the students under each category;

Here I have assumed that average humour sense is inferior to funny.

Here both Gustav and Freiherr are superior to Evgenievich on two skills, Accuracy and humour, so Gustav and Freiherr will be preferred over Evegenievich. Now in Accuracy and speed Freiherr is better than Gustav. So Freiherr will be the most preferred among the two. So eventually Freiherr will be selected.

Let us consider the students in pairs. Now between Gustav and Freiherr, Freiherr is superior to Gustav on two counts. Among Evegenievich and Gustav, Gustav will be preferred because Gustav is better than Evegenievich on two fronts. Between Freiherr and Evegenievich, Freiherr is better because he has better humour sense and accuracy.

Our ranking is clearly transitive, for G > E; F> G and F >E. Here A > B means A is preferred over B when in pairs. The letter E, F and G represents Evegenievich, Freiherr and Gustav respectively.

Rank Speed Accuracy Humour 1 Evgenievich Freiherr Gustav 2 Freiherr Gustav Freiherr 3 Gustav Evgenievich Evgenievich

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