Jameson, I don't like this version at all. These methods all have the problem that the voters have a strong incentive to just submit approval ballots, i.e. only use the top and bottom grades. Your suggested way of determining a winner among candidates who first get a majority in the same round only makes that incentive a bit stronger still. I agree with a Mike Ossipoff suggestion, that we elect the member of that set of candidates with the most above-bottom votes. Also, given the strong truncation incentive, I think 5 grades is one too many. In my opinion 4 grades would be adequately expressive.
My favourite Bucklin-like method is "Irrelevant-Ballot Independent Fallback-Approval" (aka IBFA) that I introduced in May 2010. http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026479.html "A, B, C, D" are probably better names for the ratings slots than the "Top, Middle1, Middle2, Bottom" in that post. Comparing it to Bucklin, it meets Independence from Irrelevant Ballots which means that adding or removing a few ballots that bullet-vote for nobody (ignored on all the other ballots) can't change the winner. The small "price" paid for this (apart from greater complexity) is that it fails Later-no-Help. That is mostly a benefit because it weakens the truncation incentive. The other advantage of IBIFA over Bucklin is that it is far more likely to elect the Condorcet winner. If the winners are different then the IBIFA winner will always pairwise beat the Bucklin (or Majority Judgement) winner. Chris Benham Jameson Quinn wrote (19 June 2013): Here's the current version of the article. Note the new paragraph on strategy at the bottom. --------- Majority Approval Voting (MAV) is a modern, evaluative<http://wiki.electorama.com/wiki/Evaluative> version of Bucklin voting <http://wiki.electorama.com/wiki/Bucklin_voting>. Voters rate each candidate into one of a predefined set of ratings or grades, such as the letter grades "A", "B", "C", "D", and "F". As with any Bucklin system, first the top-grade ("A") votes for each candidate are counted as approvals. If one or more candidate has a majority, then the highest majority wins. If not, votes at next grade down ("B") are added to each candidate's approval scores. If there are one or more candidates with a majority, the winner is whichever of those had more votes at higher grades (the previous stage). If there were no majorities, then the next grade down("C") is added and the process repeats; and so on.
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