5. Suppose that you and your friend go to movies and afterwards assign a rating ranging...

 

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5. Suppose that you and your friend go to movies and afterwards assign a rating ranging from 0 to 10 to the movie you saw. You go to see two movies, first "Terminator 2" with the great actor Arnold Schwarzenegger and then the adaptation of Jane Austin's boring novel "Emma". Afterwards, you say that I rated "Terminator 2" as an 8 and "Emma" as a 2, and your friend comment that she rated "Terminator 2" a 5 and "Emma" a 4. (a) Do you and your friend agree on which movie is better? (b) How would your answer change if your friend's ratings had been reversed? (c) Can you tell for sure whether you liked "Terminator 2" more than your friend did? (d) Suppose that the only thing you really care about in evaluating movies is the fraction of "action" time (as opposed to thoughtful conversation) and let the fraction of screen time devoted to action be denoted a1. Suppose that the only thing your friend cares about when evaluating movies is the fraction of time strong women appear on screen, and let that fraction be denoted ra. "Terminator 2" has a = 0.8 and r2 = 0.5 while Emma has ri = 0.2 and r2 = 0.4. Consider the functions U(r1) = 10r1 and V(r2) = 10x2 and suppose that you use the function U to determine your movie rating and your friend uses the function V. What ratings do you give to the two movies? (e) One day you decide that you will assign ratings differently,using the function U(21) = 5.25r. Will you rank any pair of movies dif- ferently using this function rather than your previous function U ? What approximate values do you now assign to "Terminator 2" and "Emma"? (f) Suppose your friend had instead chosen the function V(r2) = 10(1 – r2). Will she now rank movies differently? 5. Suppose that you and your friend go to movies and afterwards assign a rating ranging from 0 to 10 to the movie you saw. You go to see two movies, first "Terminator 2" with the great actor Arnold Schwarzenegger and then the adaptation of Jane Austin's boring novel "Emma". Afterwards, you say that I rated "Terminator 2" as an 8 and "Emma" as a 2, and your friend comment that she rated "Terminator 2" a 5 and "Emma" a 4. (a) Do you and your friend agree on which movie is better? (b) How would your answer change if your friend's ratings had been reversed? (c) Can you tell for sure whether you liked "Terminator 2" more than your friend did? (d) Suppose that the only thing you really care about in evaluating movies is the fraction of "action" time (as opposed to thoughtful conversation) and let the fraction of screen time devoted to action be denoted a1. Suppose that the only thing your friend cares about when evaluating movies is the fraction of time strong women appear on screen, and let that fraction be denoted ra. "Terminator 2" has a = 0.8 and r2 = 0.5 while Emma has ri = 0.2 and r2 = 0.4. Consider the functions U(r1) = 10r1 and V(r2) = 10x2 and suppose that you use the function U to determine your movie rating and your friend uses the function V. What ratings do you give to the two movies? (e) One day you decide that you will assign ratings differently,using the function U(21) = 5.25r. Will you rank any pair of movies dif- ferently using this function rather than your previous function U ? What approximate values do you now assign to "Terminator 2" and "Emma"? (f) Suppose your friend had instead chosen the function V(r2) = 10(1 – r2). Will she now rank movies differently?

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