[EM] criteria compliance and strategic vulnerability
stepjak at yahoo.fr
Sat May 21 23:21:18 PDT 2005
Hi Chris and James,
--- Chris Benham <chrisbenham at bigpond.com> a écrit :
> >The plurality criterion might be a good one to add. Should I cite
> >Woodall for that? If so, which paper of his?
> Probably this one:
> ["Plurality: if some candidate x has more first-preference votes than
> some other candidate y has votes in total, then x's probability
> of election must be greater than y's."
Do use either wood1994 or wood1996. The above definition (from 2003) is
flawed: the last "greater than" should be "greater than or equal to."
> >Frankly, I'm not sure if I fully understand LNH and LNH. "Adding a
> >preference to a ballot must not decrease the probability of election of
> >any candidate ranked above the new preference." Does that mean adding a
> >candidate who was previously not listed on the ballot?
> If by "listed" you mean "ranked", then yes. Sometimes Woodall's
> language seems to assume that the candidates' names are displayed somewhere,
> and that voters vote on blank sheets of paper by writing down the names
> of candidates the voter wishes to "vote for" in order of preference
> with the
> highest-ranked at the "top" of the "list", and the most-preferred
> also written down "first" (in time). (That explains the "later" in LNHarm.)
> I think at one point Kevin Venzke came up with a "pairwise" version that
> is maybe a bit stronger:
> "Adding a vote to A's pairwise tally versus B must not reduce the chance
> of any candidate winning except B" (my paraphrasing)
Yes, I use that definition when showing CDTT LNHarm failures, so I can
only look at the pairwise matrix and don't need to know who ranked whom
above whom. It is a stronger definition, though, so no harm done.
Probably the only pairwise-only methods which satisfy this criterion
completely are MinMax(opposition) and MinMin(opposition).
> >IMO, two "consistency" criteria that are of greater practical importance
> >>than the ones you list are "Mono-add-plump"
> >>and "Mono-append".
> > Maybe, I don't know. Again, these criteria are not as widely accepted as
> >monotonicity, participation, and consistency. They might have some merit,
> >but I haven't personally discovered it yet.
I don't recall off-hand which "consistency" criteria James has. My opinion
of MAPlump and MAppend is that they should be awfully easy to satisfy in most
cases. Monotonicity implies MAppend. MAPlump just says "adding in bullet votes
for the winner can't make him lose."
Looking at "Properties of single-winner election rules," not a single method
that anyone has here proposed fails either of those criteria. (Specifics:
Symmetrically-completed Coombs, and symmetrically-completed Borda-Elimination
fail Mono-append, and DHSCminDAGS, DSCminAGS, and DSCminDAGS fail MAPlump.
> >Probably WV should have a lower number than Margins in the
> >>"compromising-reversal" row, because sometimes
> >>in WV compromising-compression can be an effective "defensive strategy"
> >>but to achieve the same effect those voters
> >>in Margins have to compromise-reverse.
> > That's interesting. Would you mind showing me an example? It sounds
> >familiar, but I don't have anything like that on the surface (of my mind,
> >or of my voting files).
In WV if you vote A=B you do not create a vote for either side, so no matter
which is the pairwise winner, you're contributing to a weaker win, one that
will be dropped earlier.
In Margins the vote A=B does nothing in particular. If you want to minimize
the strength of the A:B win, you have to guess which of the two is going
to be the pairwise loser, and then rank loser>winner.
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