Abstract: Imagine an election with m>2 candidates C₁, C₂, ..., C_m, and n > 0 voters. Each voter is required to fill out an individual preference list on which candidates are ranked from most preferred to least preferred. Suppose further the outcome is to be decided by assigning w_j points for j-th place on each individual ballot where w₁ >...>w_m >= 0. Should a candidate amass more points than any other, that candidate is declared the winner. Following Bennett and Briggs, Using and Understanding Mathematics, the standard Borda count assigns the value w_j=m+1-j for j-th place.

This talk investigates which sequences can arise as Borda counts.