The 1996 elections, a book, and voting

A voting paradox is where the election outcome is not what we think it should be. For instance, if a majority of the voters find that both Anni and Katri are distinctly preferred to Sue, then we would not expect Sue to win the election! If she did, then something is wrong. But, this can happen! (For examples, see the links in the last paragraph.) Election paradoxes may be amusing, but they are serious; they indicate that, inadvertently, we may be selecting someone whom we really believe is the inferior choice!

During this election year, we can expect to find all sorts of voting paradoxes which are direct consequences of the lousy election procedure we currently use. For instance, independent of what you might think about Pat Buchanan, it is clear from press reports, comments made by the candidates, etc. that an important reason Buchanan did reasonably well during the early primaries is because Dole, Forbes, Alexander, and the other candidates "split the vote." This suggests the disturbing possibility that there could be elections where the voters do not elect who they really want. (There are many examples of actual elections where this has happened.) This, of course, is what makes Perot's possible entry into the November elections both interesting and worrisome.

What should be done? Mathematics shows that more reasonable election conclusions occur by using the Borda Count. (This is where, for three candidates, a voter's top- and middle-ranked candidates are assigned, respectively, two and one points. The candidates are ranked according to the total number of assigned points.) For some history, JC Borda was a French mathematician who, in June of 1770, worried whether the French Royal Academy of Science was making bad decisions because of their voting procedure. He created a clever example to show why our commonly used plurality method (each voter votes for one candidate) can cause serious problems. He then showed that his method was an improvement. The Academy was convinced; it used Borda's method until the 1800s when Napoleon Bonaparte had it changed. Readers interested in the problems of voting, some history, and the properties of the Borda Count might be interested in my recently published book Basic Geometry of Voting.

If you are interested, you can obtain at least a flavor of what can go wrong with elections from my short description of an experience I had (during the 1991 Mathematics Awareness Week) in a fourth grade classroom. One lesson I learned from this event is that we should not take small kids for granted. A more extensive review of recent results in this field that were discovered with the use of mathematics (but, if you can count, you can read the article) is The symmetry and complexity of elections.

Home page for Donald G Saari