On Nov 25, 2009, at 3:26 PM, Kristofer Munsterhjelm wrote:
robert bristow-johnson wrote:
my understanding is that the later-no-harm result happens only if
the case of a Condorcet cycle (the prevalence of which i am
dubious about). where there is a Condorcet winner and that person
is elected, is there still possible later harm?
As far as I remember, Condorcet and LNHarm has the property that
LNHarm isn't, by itself, violated as long as there is a CW, but the
transition from CW to no CW (or vice versa) makes it inevitable
that there will be a LNHarm-violating discontinuity *somewhere*.
the degree of inevitability is an issue. if "inevitable" is measured
as a binary value, the i s'pose it's inevitable. if "inevitable" is
measured as a probability of a cycle occurring per election-year,
then i think it's a small number. if cycles are rare, the mean
percentage of elections that have Condercet cycles is small. when we
somehow figure out a merit metric for an election system, a low-
likelihood of a pathology that has low cost (say, if a cycle happens
you elect using IRV rules, how bad can that be?) should contribute
(negatively) negligibly to the merit metric.
In other words, as long as you stay within the CW domain, there is
no LNHarm failure, but there is no way to engineer a completion
rule to maintain this for every CW<->no CW transition.
sure, but i'm still dubious about the product of likelihood times
cost of occurrence of that.
I'm not entirely sure about that, though - can anyone confirm?
and i continue to wonder (really) how a possibly rare occurrence of a
no-CW election (with its LNHarm consequence) becomes a greater
concern than that of the likelihood and cost of electing a candidate
against the expressed wishes of a majority of the electorate. i
think that cost (electing the wrong candidate) is reasonably high and
that the likelihood of it happening is definitely non-zero because it
has happened in the Vermont town i am a resident of.
Not that this bothers me - LNHarm seems to me to be a criterion of
"don't take the full picture into account". Consider a negotiation
situation: if everybody keeps their cards close to their chests
(i.e. vote bullet style), there can be no compromise; but if
they're willing to reach further, one might find an option that,
while not the favorite of any, is good enough for all.
i would call that the essential measure of a popular election. it's
utilitarian: we maximize satisfaction for the franchised about the
governance of whatever organization by pleasing more people with a
decision than we displease. that's the reason we have elections, we
could adopt rules to give it to the minority candidate if that
candidate reaches a certain threshold, but we don't do that for
binary decisions, we consistently give it to the majority.
--
r b-j [email protected]
"Imagination is more important than knowledge."
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