[EM] "Approval Later-no-Harm", (was "AWP versus DMC and AM")

[Chris Benham]

Ted, James (and anyone interested),

In my last post (Thu.May5)  I  suggested  this
criterion:
"If  x wins, and  afterwards some identical ballots
that approve x are uniformly changed only so that they
approve more candidates than previously; then if there
is a new winner it must be one of  the candidates
approved on these altered ballots."

This is supposed to be a simple test for the property
that approving more candidates should never change the
winner from an approved (on the original ballots)
candidateto a disapproved (on both sets of ballots)
candidate.

This is very similar to this monotonicity-like
criterion:
"If x wins, and afterwards some ballots are changed
only to increase the approval scores of some other
candidates; then if there is new winner it must be one
of the candidates whose approval scores have been
raised."

Or maybe it is better to put it the other way:
"If x wins, and afterwards some ballots are changed
only to decrease the approval scores of one or more
other candidates; then x must still win."

Yes, this seems more succinct. But what to call it,
"Mono-reduce opposition approval"?

Another criterion that applies to rankings/approval
methods interests me, which I might call "Disapproval
Later-no-Harm":

"Ranking a disapproved candidate must never harm an
approved candidate".

(A stronger version would add "or a higher-ranked
disapproved candidate").
This is incompatible with Condorcet, and in a future
post I'll suggest a method that meets it.


Chris Benham






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