[EM] Top-two Approval Pairwise Runoff (TTAPR)

[Kristofer Munsterhjelm]

On 11/11/2016 01:48 AM, Forest Simmons wrote:
> Some of the replies are taking the subject line too literally.  We're
> not talking about top two runoff, but two member PR runoff.  we find out
> who the two member parliament would be then pit those two against each
> other.
> 
> So
> 
> 40 C
> 32 A>B
> 28 B>A
> 
> Suppose that we use PAV with implicit approval
> 
> The A is the first member in the two member parliament.
> 
> The two factions that supported A get their weights cut in half, so C is
> the second member.
> 
> The runoff is between A and C, not between A and B, as some people are
> assuming.
> 
> If the B faction defects, then the two members of the pariliament would
> be B and C, and the pairwise winner would be B, so the method does not
> satisfy CD.

On a more intuitive level, that isn't too surprising. Suppose you have a
Bush-Nader-Gore situation. The runoff doesn't help the voters who want
to know whether to vote {Nader, Gore} or {Nader}, since if they vote
only Nader, Bush and Gore may go to the runoff (i.e. Nader loses). On
the other hand, if they do vote {Nader, Gore}, and Gore is picked for
the first winner, then their ballots will be deweighted and Nader
probably won't come in second anyway.