The Borda Count is a common way of making a choice among more than two alternatives. As defined in the text, each member of society assigns a rank to the social alternatives \((1,2, \ldots)\), with 1 corresponding to first choice, and so on. The ranks each alternative gets are summed over all the individuals. The alternative with the lowest sum wins; the second choice has the second-lowest sum, and so forth. Set up an example to show that the Borda Count violates the independence of irrelevant alternatives. Use a three-person society with three alternatives and rank them using a Borda Count. Then introduce a fourth alternative.