There is even the possibility of sincere/insincere votes with 2 choices with Approval Voting. Namely -- 51 AB 49 B Some or all of the 51 second choice votes for B may be sincere or insincere (assuming that an Approval vote is a YES vote (i.e. the choice is acceptable/ tolerable)). Such 51 voters may or may not have any knowledge of how the other 49 voters might vote. Assuming sincere votes, then B would beat A 100 to 51 (using Approval Voting) The above suggests that there should be head to head votes in ALL cases. Obviously A beats B 51 to 49 using head to head number votes. Math obsessed folks may wish to mystify the above. Good luck. Since so-called strategic voting is insincere voting, then the only obvious way to determine sincere votes would be some sort of voter lie detection device--- not likely as long as the secret ballot exists.
