Three people are voting on which of four movies that they should go and see. The

Question

Three people are voting on which of four movies that they should go and see. They vote strategically. person 1: D R C L (most preferred on the left, least preferred on the right) person 2: L R D C person 3: C L D R Suppose the voting method is to choose between the pairs D, C versus L, R, and then, whichever pair wins, choose one or the other. Voters are being strategic, not necessarily voting for their favorites. Who would win? Suppose instead that they started with a choice between D, L versus C, R, but used the same procedure. Who would win? Suppose they started with the third possibility, a choice between D, R and C, L. Who would win? When we make these predictions about who would win, are we assuming that the players know each others' preferences?

Explanation / Answer

Using Borda Count Method

a) Between Pair D,C and L,R as both pairs have same score it would be prefered to choose D,C pair as both are in priority for majority;

b) Between Pair D,L and C,R its clear win for D,L pair as they have highest score;

c) between D,R and C,L its tie as both pairs have same score so C,L will be prefered as both are in priority for majority.

d) No players does not know about each others preferences

Movie First Rank Second Rank Third Rank Fourth Rank Total Score C 1/3 0/3 1/3 1/3 (1*4+0*3+1*2+1*1)/4=1.75 D 1/3 0/3 2/3 0/3 (1*4+0*3+2*2+0*1)/4=2 L 1/3 1/3 0/3 1/3 (1*4+1*3+0*2+1*1)/4=2 R 0/3 2/3 0/3 1/3 (0*4+2*3+0*2+1*1)/4=1.75

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