3 Choices

[DEMOREP1 at aol.com]

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.