The problem with Condorcet and Borda count

Assume your organization is having an election for President by either Condorcet or Borda count. There are four candidates: A, B, C, and D. The honest preferences of the members are as follows:

  • 36% A > B > C > D
  • 36% B > A > C > D
  • 24% C > A > B > D
  • 4% D > C > B > A

A gets 36% of the first-choice preferences, B gets 36%, C gets 24%, and D gets 4%.

A
B
C
D

In this example, if all voters voted honestly, the winner under either Condorcet or Borda count would be A. But the members do not know that because the election hasn't happened yet. They know that A, B, and C all have a substantial amount of support. Everyone also knows that D is a horrible candidate for President and that almost nobody will vote for him.

Your members are very competitive and are willing to vote strategically to help their first choice candidates. Voters for A, B, and C know that they can increase the chance of their preferred candidate winning by ranking the other viable candidates as low as possible. So many choose to dishonestly rank D as their second choice, knowing that he doesn't have a chance at winning and doing so will hurt the other viable candidates competing with their top choices. The votes are cast as follows:

  • 36% A > D > B > C
  • 36% B > D > A > C
  • 24% C > D > A > B
  • 4% D > C > B > A

Under both Condorcet and Borda count, the winner of the election is D. Despite nearly everyone agreeing that D was the worst possible choice, D won because members tried to help their top choices by manipulating their votes.

You might say, "Well, if everyone knows that such an awful outcome can happen when people manipulate their votes, then people won't manipulate their votes." But if everyone else votes honestly, manipulating your vote in this manner does undeniably help your top choice to win. For voters who feel very competitive and are willing to vote strategically, Condorcet and Borda count pose a dilemma—voting strategically definitely works as long as too many people don't do it, but if too many people do it then everyone is screwed. Condorcet and Borda count should not be used when you think your members are willing to vote dishonestly in this manner.