[EM] A better 2-round method that uses approval ballots

[Chris Benham]

I just want to repeat a suggestion I've made here more than once.  Take my previous example where the Centre-Right candidate is elected due to some of the Left candidate's supporters using the Compromise strategy.

49: Right
28: Centre-Right (7 are sincere Left>Centre-Right)
23: Left

Centre-Right beats Right in the runoff 51-49.

But the Right supporters have an easy Push-over strategy to (from their perspective) "rectify" this.

If anywhere between 6 and *all* of them change their vote to approving both of Right and Left, then Left will be dragged back into the runoff with Right and then be beaten.

My suggested 2-round method using Approval ballots is to elect the most approved first-round candidate A if A is approved on more than half the ballots, otherwise elect the winner of a runoff between A and the candidate that is most approved on ballots that don't show approval for A. 

This destroys the incentive for parties to field 2 candidates, and greatly reduces the Push-over incentive
(to about the same as in normal plurality-ballot Top-2 Runoff).

Chris Benham
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