[EM] "Legitimacy" concerns of the Plurality-minded addressed : a Condorcet-Approval hybrid

[Chris Benham]

Here is my second idea for a Condorcet-like method that might be 
saleable to those who are skeptical about pure Condorcet because of the 
possibility of a candidate no first preferences beating a candidate with 
nearly half the first preferences.(The first was my "Improved IRV", an 
IRV-Condorcet hybrid). It is possible that this has been proposed before.

The voters rank the candidates and also indicate an approval cutoff.The 
default cutoff is below first preference.
1. Count the first preference votes. If one candidate has a majority, 
then that candidate wins. If more than one candidate has a majority, 
then eliminate the rest and go to step 3.
2. Count the approvals. If any candidates are approved by a majority, 
eliminate the rest.
If not, eliminate all those candidates whose tally of approvals does not 
exceed half the approval tally of the most approved candidate.
3. Of the remaining candidates, elect the most approved member of the 
Smith set. (If there is tie for this spot, then elect the IRV winner 
among the tied candidates.)

So the plurality-minded supporters of major parties can be assured that 
"nobody's first choice" can win if they withhold their approvals, 
because it will not be possible for any losing candidate to get as much 
as twice the explicit approvals received by the winner.
I think that this is a method that the voters can "grow into" as they 
become more savvy about placing the approval cutoff, so that early 
elections would be IRVish and later ones much more like Condorcet.
I realise that there could be a minor silly strategy problem, with some 
voters trying to block the election of a certain candidate by 
insincerely approving who they think will be the most approved 
candidate(s) just so as to raise the approval threshold. But I am not 
advancing this method as ideal, only as a good method which produces 
winners that people that like and/or are accustomed to Plurality or IRV 
can't plausibly object to. In time the approval threshold feature might 
be seen as no longer necessary and so abandoned.

Chris Benham