One popular voting scheme is rank-order voting, where individuals assign a rank (1, 2, 3) to the possible alternatives; the assigned ranks are then added up, and the alternative with the lowest sum win. Consider a choice among four alternative ways of spending public funds a library, a ski slope, a swimming pool, a garbage dump). Can you construct an example in which the outcome (the most preferre4d alternative) is, say, a library, if the vote is among the first three alternatives, while the outcome is a ski slope if the vote is among all four alternatives. This voting scheme thus violates the principle that the chosen outcome should be independent of irrelevant outcomes (the garbage dump was not chosen in either situation.