[EM] MAM-d vs. The River

[Markus Schulze]

Hallo,

unlike the ranked pairs method, the river method satisfies
Steve Eppley's "independence from Pareto-dominated alternatives"
(IPDA).

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> Clone independence might depend on how he handles
> same-size majorities.

I guess with the random voter hierarchy also the
river method satisfies independence of clones.

******

> I would like some reassurance (in the form of a proof)
> that it satisfies Minimal Defense and Truncation
> Resistance.

The river method has the following property: When candidate A
pairwise beats candidate B then candidate B cannot be elected
unless there is a directed path from candidate B to candidate A
whose weakest link is at least as strong as the pairwise
defeat A:B.

Proof: When you get to the point where you have to decide
whether A:B has to be locked or skipped, A:B has to be skipped
only when (1) locking A:B would create a directed cycle or
(2) already another pairwise defeat X:B has been locked.
In the first case, there must have been a directed path from
candidate B to candidate A whose weakest link is at least as
strong as the pairwise defeat A:B. In the latter case, candidate B
cannot be elected anymore.

With these considerations, it is easy to see that the river method
satisfies the defensive strategy criteria of Steve Eppley's website.

Markus Schulze