25 A>B>C 40 B>C>A 35 C>A>B
Borda scores are A 185, B 205, C 210. A pairwise beats B beats C beats A, so there is no Condorcet winner (because everyone has at least one defeat). So the Borda winner, C, wins.
Note that the winner of the Borda count is not necessarily in the Smith set. For example, if there are 8 candidates and 3 voters, with ballots:
A > B > X > D1 > D2 > D3 > D4 > C B > C > X > D1 > D2 > D3 > D4 > A C > A > X > D1 > D2 > D3 > D4 > B
Then A, B, and C form the Smith Set / Condorcet cycle (with 16 points each), while X is the Borda winner (with 18 points).
References[edit | edit source]
- Black, Duncan (1987). The Theory of Committees and Elections. p. 66. ISBN 978-94-009-4225-7. Retrieved 2020-03-31.
- di Fenizio, Pietro Speroni (March 12, 2014). "Is there formal proof that Duncan Black's Electoral System is a Condorcet System?". ResearchGate. Retrieved 2020-03-31.