## Frank Morgan's Math Chat |

June 22, 2000

_____Plurality (whoever gets the most votes wins)

_____Runoff (between two highest vote getters)

_____Approval voting (voter votes for all acceptable candidates and the candidate so approved by the most voters wins)

_____Ranking (voter ranks the candidates from 1 to n and the candidate with the smallest sum of rankings wins)

All four methods have paradoxical consequences, in which a majority of the
voters would prefer another candidate over the winner. (See "Ask the
Experts" and Math Chat of November 8, 1996.) Results of this poll will
appear in the next Math Chat July 6 and in the November issue of *Discover*
magazine.

**New Challenge.** Design your own voting system and submit it to MathChat
<Frank.Morgan@williams.edu>. The winning answer will appear in the next Math Chat July 6.

**Old Challenge.** (Salvador Segura Gomis). What is the shortest line segment fencing off prescribed area 0
**Answer** (Joseph DeVincentis). We may as well assume that A is at most 1/2, since a larger area on one side corresponds to a smaller area on the other
side. For A up to 1/4, fence off a corner diagonally. For A from 1/4 to
1/2, just use a horizontal fence.

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.