Unfortunately, each system has its downsides. The Condorcet Method will sometimes fail to produce a unique winner. A tie-break method is needed in those cases. The Borda Count sometimes leads to some counterintuitive results. If there are two favorites in a three-candidate race, the voters' ranking of the "irrelevant" third candidate can determine the outcome of the election. This third candidate acts as a spoiler.
Based off of these observations, I wondered what would happen if I used the Condorcet Method as my primary vote-counting technique, and used the Borda Count only as my tie-breaker. Could I use this method to always determine a winner and avoid the "spoiler effect" of the Borda Count?
Imagine the following situation: three candidates A, B, and C are running in an election. Each voter must rank the candidates from most favored to least favored. In the first scenario, 17 votes are cast:
ABC - 6 votes
BCA - 5 votes
CAB - 6 votes
Here, there is a Condorcet tie with A defeating B defeating C defeating A. By the Borda Count, A receives 18, B receives 16, and C receives 17 points. A wins!
In a second vote, two voters changed their vote from BCA to CBA. Note that this does not affect A and C's relative rankings.
ABC - 6 voters
BCA - 3 voters
CAB - 6 voters
CBA - 2 voters
Again, there is a Condorcet tie, but in this case, C steals two extra points from B. A receives 18, B receives 14, and C receives 19 points. C Wins!
Even the Condorcet/Borda hybrid has its shortcomings, and in fact Arrow's Theorem tells us that there is no perfect vote-counting system. If we concede defeat in looking for perfection, we may still seek a best possible vote-counting technique. The above example notwithstanding, the paradoxes of the Borda Count are rare, and rarer still when Borda Count is only used as a tie-breaker.