# Frank Morgan's Math Chat - Ordering Candidates on Ballots

December 7, 2000

News Reporters and A. M. Alier ask for the margin of error in an election, within which perhaps a statistical tie should be declared. In an even contest, one should expect an error roughly on the order of the square root of the number of erroneous ballots, which one might guess to be on the order of the number of spoiled ballots. This would give a margin of error for the Presidential race in Florida on the order of some hundreds of votes. My Washington DC taxi driver Leo Eyombo suggested that in such statistical ties, the outcome should be determined by a poker game or some other game of chance. Perhaps that is just what we are doing in Florida.

Joe Shipman reports that Hopewell Township, New Jersey, just had a tied election for councilperson (3925 votes each, 4 ambiguous absentee ballots currently being scrutinized by a judge). If it is still a tie after the judge's ruling, there'll be a new election.

Old Challenge (Joe Shipman). On the West Palm Beach ballot of the US Presidential election, it apparently turned out to be a big advantage for the Republican candidate to be listed first. Can you come up with a fair procedure for allocating ballot order from year to year between the two major parties, if you assume that being first is an advantage?

Answer (Alex Glasser). Find two equally favorable spots and use the same spots every year. Put the Republican in the upper right and the Democrat lower on the left. "Every year the voter would know where their candidate would be without change (because some say the change in location of the name threw some voters off)." And of course it is preeminently appropriate to have the Republican on the right and the Democrat on the left.

If you need to put one party on top, Joe Shipman notes that you would need a long-term cycle to be fair on local, state, House, Senate, and Presidential elections, perhaps an 8-year cycle such as DRDRRDRD.

International Mathematical Olympiad for high school students will be hosted by the United States next year, July 8-9, 2001. Volunteers are needed: teachers to run the exam (contact Susan Schwartz Wildstrom ssw@umd5.umd.edu>) and college students to live with foreign competing high school students for two weeks before the IMO (contact Eric Walstein ewalstei@mbhs.edu>)

Riddle (Jacob Sturm). What is greater than God, more evil than the devil, the poor have it, the rich want it, and if you eat it you die?

New Challenge (Timur Dogan). Which branches of mathematics or types of problems are the most counterintuitive?

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).