2. Inferring the rankings from the ratings, elect the CW is there is one. If not, then eliminate the non-members of the Smith set.
3.Those ballots which show as many preference-levels among the remaining candidates as there are remaining candidates (N) are now converted to ballots showing (N-1) preferences by disregarding the smallest gap in the scores of adjacently ranked remaining candidates. If there is a tie for "smallest gap" , then disregard the tied gap between the highest adjacent preferences among the remaining candidates.
4. Inferring rankings from these ballots (amended so that none show more than N-1 preference-levels), elect the CW if there is one. If not , eliminate non-members of the Smith set, repeat step 3 and so on.
An equivalent version which is easier to hand-count but less natural and more awkward to vote is to have the voters rank the candidates and also rank the the gaps in utility between the adjacently-ranked candidates, from largest to smallest.
This is currently my favourite "high-resolution CR-ballot" single-winner method. I think it should comply with Participation, and
probably have fewer and/or less serious strategy problems than plain ranked-ballot Condorcet.
Chris Benham
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