Survivor, a reality-television show places contestants on a tropical island where they form tribes and alliances. In the game, the contestants, are split into tribes. The first half of the game, the tribes face off in challenges, some for rewards of food, shelter, or luxury items, while others are for immunity, preventing the winning tribe from having to go to Tribal Council.
The second half of the game, tribes are merged and challenges are played at an individual level for individual rewards and immunity. When only two or three castaways remain, those castaways attend a final Tribal Council, where jury members vote to decide which of the remaining castaways should be declared Sole Survivor. Host Jeff Probst holds the audience in suspense as, one at a time, he reads the ballots until one contestant has a majority of the votes and the winner is thus revealed. Maximal suspense seems always to be attained, as ballots are pulled in such an order as to reveal the winner when it is no longer possible to delay the outcome. How lucky the producers are! Or are they?
In the January 2013 publication of The College of Mathematics Journal, senior Mathematics and Computer Science major Nat Kell and Dr. Matt Kretchmar (Assoc. Professor of Computer Science) investigates suspicions that the order the ballots are read is intentionally manipulated to keep the audience in suspense. In their paper, “Suspense at the Ballot Box”, they test this hypothesis using the Poisson binomial distribution, then turn to entropy to confirm that the ballot order is likely altered.