To the message from T.S. copied below, I would like to give a little more background.
A few months after I came up with the idea of bubble sorting the approval order, I came across an article at http://www10.org/cdrom/papers/577/ in which the authors suggested bubble sorting the Borda order and various other social orders (but did not mention approval). They called the process "local Kemenization." As near as I know Kevin Venzke was the first to suggest the method of eliminating candidates from the bottom of the approval list until a Condorcet winner emerges relative to the remaining candidates. He offered the first proof that this candidate had to be a member of the original Smith set. It is easy to see that this winner W is the same as the MinMax(total approval) winner, who by definition is the candidate whose defeater X with greatest approval is lowest on the approval list, i.e. any candidate other than W is defeated by somebody with greater approval than X. It seems that all Condorcet roads lead to DMC. Forest Date: Tue, 30 Aug 2005 09:20:49 -0700 From: Araucaria Araucana <[EMAIL PROTECTED]> Subject: [EM] Re: reason #17 To: election-methods-electorama.com@electorama.com Message-ID: <[EMAIL PROTECTED]> Content-Type: text/plain On 29 Aug 2005 at 16:06 UTC-0700, Forest Simmons wrote: > More discussion on this is found in the thread which contains the > following seminal message: > > http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015316.html > > explaining how DMC, AWP, and "Approval Margins" (AM) are related to > each other, and how they fit into the family of Condorcet methods, and > also comparing their effectiveness against burying. > > Here's when I first saw the light that DMC was the best Condorcet > proposal: > > http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015418.html > Forest is too modest. DMC/RAV finds the same winner as a method he proposed earlier. At one time, he called it, variously, Approval Sorted Condorcet, Approval Seeded Bubble Sort, or Bubble Sorted Approval. Lately I've taken to calling it Pairwise Sorted Approval. It was first proposed in March 2001: http://lists.electorama.com/pipermail/election-methods-electorama.com/2001-March/005448.html The main difference (advantage?) of the DMC/RAV formulation is that it finds the winner directly. But the social ordering that results from determining the DMC winner, removing that winner, finding the DMC runner up, etc. is exactly the pairwise-sorted approval ordering. Q
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