Coach Steroid likes his players to be big, fast, and obedient. If player A is better than player B in two of these three characteristics, then Coach Steroid prefers A to B, but if B is better than A in two of these three characteristics, then Steroid prefers B to A. Otherwise, Steroid is indifferent between them. Wilbur Westinghouse weighs 340 pounds, runs very slowly, and is fairly obedient. Harold Hotpoint weighs 240 pounds, runs very fast, and is very disobedient. Jerry Jacuzzi weighs 150 pounds, runs at average speed, and is extremely obedient.
(a) Does Steroid prefer Westinghouse to Hotpoint or vice versa?
(b) Does Steroid prefer Hotpoint to Jacuzzi or vice versa?
(c) Does Steroid prefer Westinghouse to Jacuzzi or vice versa?
(d) Does Coach Steroid have transitive preferences?
(e) After several losing seasons, Coach Steroid decides to change his way of judging players. According to his new preferences, Steroid prefers player A to player B if player A is better in all three of the characteristics that Steroid values, and he prefers B to A if player B is better at all three things. He is indifferent between A and B if they weigh the same, are equally fast, and are equally obedient. In all other cases, Coach Steroid simply says “A and B are not comparable.”
(f ) Are Coach Steroid’s new preferences complete?
(g) Are Coach Steroid’s new preferences transitive?
(h) Are Coach Steroid’s new preferences reflexive?