Ordinal Ballots Preference Schedule Preference List
Ordinal Ballots • List your choices in order with the favorite on top and ‘least favorite’ on bottom Ballots must be • Complete (you must rank all candidates) • Linear (no ties) • Transitive (If you prefer A to B and B to C, then you must prefer A to C.)
How many different ordinal ballots are possible? • Try this first for two candidates A and B. • Next try it for three candidates A, B and C. • What about for four candidates A,B,C and D? • Can you see a pattern to the numbers? What is it?
Factorials • 1! = 1 • 2! = 1·2 = 2 • 3! = 1·2·3 = 6 • 4! = 1·2·3·4 = 24 • Etc. • Note: 0! is defined to be 1.
TV Program Vote Again • Vote again for The Office, Family Guy and The Mentalist, this time making a preference list with your top choice on top. • How many possible lists will there be?