[EM] DAMC (was: MDDA vs UncAAO, ASM & DMC)
heitzig-j at web.de
Mon Mar 12 08:16:16 PDT 2007
> Offensive order-reversal works in DMC too. If theres less incentive
> for it, its 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
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.
(2) absolute majority defeats: A1>B,A2>B,A3>B,A1>A2>A3, approval:
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
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
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
In other words: We use River with
defeat := absolute majority size defeat
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:
- 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.
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