Dear Mike, you wrote: > Offensive order-reversal works in DMC too. If there�s less incentive > for it, it�s because truncation works just as well in DMC. DMC is > vulnerable to truncation in a sense that MDDA, MAMPO and wv Condorcet > are not, as examples below will demonstrate.
I like MDDA much, but I think it can still be improved. Some disadvantages are in my opinion the lacking clone-proofness and immunity from absolute majority complaints. By the latter I mean that some absolute may complain that they all prefer some option Y to the MDDA-winner X without us being able to point out a sequence of "stronger" majority defeats leading back from Y to X. Both these problems with MDDA arise from the distinction whether all options are defeated by an absolute majority or not. Consider these examples: (1) absolute majority defeats: A>B, approval: B>A. MDDA-winner: A (2) absolute majority defeats: A1>B,A2>B,A3>B,A1>A2>A3, approval: B>A1>A2>A3. MDDA-winner: B It seems to me that in (2), B is at least as defeated as in (1) and that in (2), A1 should win. Also, MDDA is not immune from 2nd place complaints, that is, when the winner is removed, the new winner may have had an absolute majority size defeat against the original winner. And the MDDA-winner may also have by majority size defeated by her most approved contender. I want to suggest a modification of DMC which is motivated by MDDA and does neither have these problems MDDA has, nor the one you pointed out DMC has: Recall that DMC can be described in at least three different ways: Either: Define defeat strength as the approval score of the defeating option and then apply an immune cycle-resolution method (e.g., River, Ranked Pairs, or Beatpath, all give the same in this case). Or: Sort options by descending approval; then, as long as some option defeats its upper neighbour, exchange the topmost such pair of options. Or: Remove every option which is defeated by a more approved (="definitively defeated") one and then elect the CW of the remaining options. In order to make DMC immune to your kind of example, we take the first of the above descriptions but use only defeats which are supported by an absolute majority: Def. DAMC (Definite Absolute Majority Choice): ---------------------------------------------- Make a list of absolute majority size pairwise defeats. Process this list in order of descending approval score of the defeating option. Keep the defeat at hand iff (i) the defeated option is not already defeated by the kept defeats and (ii) the new defeat does not build a cycle with those defeats already kept. From those options not defeated in the end, elect the most approved one. In other words: We use River with defeat := absolute majority size defeat and defeat strength := approval score of defeating option and resolve the remaining ambiguity by Approval. I'm pretty sure that this method has the following properties: - monotonicity - clone-proofness - IPDA and ISDA - immunity from absulute majority complaints (in the above sense) - immunity from 2nd place complaints - the winner is never defeated with absolute majority by a more approved option or by the most approved contender. What I'm not sure about so far is whether using Beatpath or Ranked Pairs instead of River gives the same winner, and what would happen when we used the "resorting" or the "definitively defaeted" version of DMC with absolute majority size defeats only. Yours, Jobst
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