**Old Challenge.** Suppose that in a certain US state 12 million potential voters favor Bush, 10 million favor Gore, and 5 million favor Nader with Gore as second choice. The Nader supporters want to be sure than Gore wins, but they would like Nader to get lots of votes, too. If you could send one common short message of friendly advice to the Nader supporters, what would you tell them to do?

**Answer.** Tell the Nader supporters to flip a coin: heads vote Nader, tails vote Gore. This should yield about 50% for Gore and 50% for Nader, for totals of 12.5 million for Gore and 2.5 million for Nader. According to the famous statistics formula for polls, with 95% confidence, the chance error is less than 100% over the square root of 5 million, less than .05%, a mere 2500 votes. The chance of Gore's losing because too many heads come up is infinitesimal.

Probability can work better than planning. For example, telling Nader supporters above a certain age to vote for Gore could fail if most Nader supporters are young.

Todd Feitelson of Millbrook School has reservations: "In truth, each voter should vote his or her conscience, *especially*the Nader voters. That's how change occurs -- not in one election, but over time."

**New Challenge.** Suppose all that any voter in the US cares about is that different parties control the Presidency and the Congress. If there is no communication, how should each voter vote?

Send answers, comments, and new questions by email to Frank.Morgan@williams.edu, to be eligible for* Flatland *and other book awards. Winning answers will appear in the next Math Chat. Math Chat appears on the first and third Thursdays of each month. Prof. Morgan's homepage is at www.williams.edu/Mathematics/fmorgan.

THE MATH CHAT BOOK, including a $1000 Math Chat Book QUEST, questions and answers, and a list of past challenge winners, is now available from the MAA (800-331-1622).

Copyright 2000, Frank Morgan.