A mоvie studiо invited а representаtive аudience tо a preliminary screening of a movie. At the end of the movie the members of the audience were asked to answer a survey comparing the ending of the movie with two alternative endings. For simplicity let us denote the ending the audience saw by A, and the two alternative endings by B and C. Suppose that a member of the audience provided the following answers.Is A at least as good as B? YESIs A at least as good as C? YESIs B at least as good as A? YESIs B at least as good as C? YESIs C at least as good as A? NOIs C at least as good as B? NOWhich utility function encodes this preference information?
A mоvie studiо invited а representаtive аudience tо a preliminary screening of a movie. At the end of the movie the members of the audience were asked to answer a survey comparing the ending of the movie with two alternative endings. For simplicity let us denote the ending the audience saw by A, and the two alternative endings by B and C. Suppose that a member of the audience provided the following answers.Is A at least as good as B? YESIs A at least as good as C? YESIs B at least as good as A? NOIs B at least as good as C? YESIs C at least as good as A? NOIs C at least as good as B? NOWhich utility function encodes this preference information?
A mоvie studiо invited а representаtive аudience tо a preliminary screening of a movie. At the end of the movie the members of the audience were asked to answer a survey comparing the ending of the movie with two alternative endings. For simplicity let us denote the ending the audience saw by A, and the two alternative endings by B and C. Suppose that a member of the audience provided the following answers.Is A at least as good as B? NOIs A at least as good as C? YESIs B at least as good as A? YESIs B at least as good as C? YESIs C at least as good as A? YESIs C at least as good as B? NORepresent the answers as arrows between the alternatives. Draw an arrow for each YES answer from the alternative that is at least as good to the other alternative. Which of the following drawings do you obtain?
A mоvie studiо invited а representаtive аudience tо a preliminary screening of a movie. At the end of the movie the members of the audience were asked to answer a survey comparing the ending of the movie with two alternative endings. For simplicity let us denote the ending the audience saw by A, and the two alternative endings by B and C. Suppose that the audience provided the following feedback.A total of 27 responses were:Is A at least as good as B? YESIs A at least as good as C? YESIs B at least as good as A? YESIs B at least as good as C? YESIs C at least as good as A? YESIs C at least as good as B? YESA total of 14 responses were:Is A at least as good as B? YESIs A at least as good as C? YESIs B at least as good as A? NOIs B at least as good as C? YESIs C at least as good as A? NOIs C at least as good as B? NOA total of 59 responses were:Is A at least as good as B? YESIs A at least as good as C? YESIs B at least as good as A? NOIs B at least as good as C? NOIs C at least as good as A? NOIs C at least as good as B? YESIf the movie studio takes these answers as representing the population, and they want to have the ending that is the best between A, B, and C to most people, what ending should they choose?