So confused how the winner turned out to be D. The way I understood the algorithm works, I came with the solution to be B, so I was suprised to see D only for the video to conclude the outcome should have been B in the first place. How did the narrator came up with D as the right solution to the algorithm? Any way I try to compare pairwise I end up with B. How do you even arrive at D?

@guitarinos

4 жыл бұрын

Pairwise elimination with ordering A,B,C,D means, that first, we only look at the pair (A,B) and determine the winner. In our case this is A because 2 agents prefer A over B. The winner is then compared to C, hence we're now looking at the pair (A,C). Here C is the winner, since 2 agents prefer C over A. Finally we compare (C,D) and get the winner D. The question is if it makes sense to impose an ordering like A,B,C,D in advance, since it clearly gives an advantage to the candidates later in the ordering. Indeed, if we take a different ordering, we might get a different winner.

@asifislam3001

3 жыл бұрын

@@guitarinos Hey, but why doesn't the transitivity argument hold? If A is better than B, and C is better than A, and D is better than C, then surely D must be better than B?

@guitarinos

3 жыл бұрын

@@asifislam3001 Not necessarily. In pairwise elimination A is "better" then B whenever more voters prefer A over B. Now if we look at some examples in the video, we can find a counterexample to your claim. Indeed, one can try to spot a cycle A>B>C>A, disproving transitivity of pairwise elimination.