[EM] Two-Round MCA ?

[Chris Benham]

Participants,
A recent idea of mine with some relevance to current threads on the 
public accepting a low first-prefernce CW,
and also on whether or not simulations/analysis of  Approval should 
assume zero-information.

There are two trips to the polls, and in the second round there may be 
more than two candidates. In each round
(if there are more than two candidates) the voters approve as many 
candidates as they like, and also mark one of
these as first-preference.
First round: A candidate with a majority of first-prefernces 
wins.(Optional extra rule: If the first-prefernce winner is
also the Approval winner and is approved by a majority, then that 
candidate wins.)
The first-prefernce winner and also any candidates with an 
approval-score  higher than the FPW's go on to the second
round. Candidates can voluntarily drop out. If  only one candidate 
remains, then the FP runner-up qualifies for the second
round  and so do any candidates with a higher approval-score than that 
candidate. (An optional alternative rule is for  that
to be the case regardless.)
Before the second round, all the results and  candidates' approval 
tallies are made public.
In the second round if a candidate receives a majority of 
 first-preferences on the ballots cast in the second round, then that
candidate wins. (Same optional extra rule as in first round).
Otherwise, the winner shall be the candidate with the most approvals 
from BOTH rounds.

This avoids some of the  strategy problems with other versions of 
two-round approval. If  the approvals received in the first
round do not count as part of the candidate's final score, then voters 
might engage in pushover-type strategy and approve
candidates that they think their favourite can easily beat. If the 
number of candidate who make the final round is restricted,
then the major parties will just try to monopolise all the available places

Chris Benham