In elections, how do we select a winner based on voter preferences? Different voters have different preference profiles: one voter may prefer the candidate A as the first choice, then B as the second choice, then C as the least preferable candidate (A > B > C), another voter may prefer A > C > B. If there are only two candidates A and B, we can select the one preferred by the majority of voters. For simplicity, let us assume that there are no ties.
If we have three or more candidates, we can first select two of them and out of the selected two, dismiss the candidate who is preferred by the minority of voters (i.e., for which most people prefer the other candidate to this one). Then, we can select two of the remaining candidates, dismiss one, etc., until only one candidate is left. This candidate is declared a winner. (Again, we assume that there are no ties.)
Give an example of preference profiles when this seemingly natural scheme has a flaw: The selected winner depends on the order in which we present the pairs of candidates.