Summarizing the Ballots

  1. Replace the word Sausage with the letter S, Pepperoni with the letter P, etc.

  2.  
  3. If several people have exactly the same list of preferences, we will list them together. Suppose 5 people all vote S, P, M, A. We will use a table of votes and write:

  4.  
    S
    P
    M
    A

    The first choice always goes at the top, then the second choice, and so on. The number 5 indicates that 5 people had this exact ballot.
     
  5. In our examples we don't want 24 or 120 columns, so we will suppose that all of the club members happened to choose one of 3 or 4 different rankings. Our voting methods will work the same way no matter how many possible orderings exist.
Let's look at an example.