Every so often (especially in mathematics), unforeseen connections between different ideas arise and beg explanation. This happened to us when, in an effort to generalize the voting procedure known as the Borda count, we began to see vectors of the form (-1, 1), (1, -2, 1), (-1, 3, -3, 1), (1, -4, 6, -4, 1), and so on. As you might imagine, we were instantly intrigued by this unanticipated relationship with Pascal's triangle, and we quickly set out to find an explanation. This article describes some of our initial findings.
© 2008 Mathematical Association of America
Jameson, Marie K., Gregory Minton, and Michael E. Orrison. "Borda Meets Pascal." Math Horizons 16.1 (2008): 8-10, 23. Print.