[EM] Does Top Two Approval fail the Favorite Betrayal Criterion [?]

[Chris Benham]

Yes. 
Say there are three candidates: Right, Centre-Right and Left, and the approval votes cast are

49: Right
21: Centre-Right (all prefer Right to Left)
23: Left
07: Left, Centre-Right (sincere favourite is Left)
 
Approval votes: Right 49, Left 30, Centre-Right 28.

The top-2 runoff is between Right and Left and Right wins
70-30.
 
All the voters who approved Left prefer Centre-Right to Right. The 7 voters who approved both Left and Centre-Right can change the winner to Centre-Right by dumping Left (their sincere favourite) in the first round.

49: Right
28: Centre-Right 
23: Left
 
Now the top-2 runoff is between Right and Centre-Right and Centre-Right wins 51-49.

Seven voters have succeeded with a Compromise strategy.
 
Chris Benham
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