Forest,
"What nicer distribution can you think of.."
"Nice" (and "nicer") is a fuzzy emotional/aesthetic term that I might apply to
food, music, people etc.
but seems unscientific and out-of-place here (and I'm not sure exactly what
it's supposed to mean).
I can see that such a distribution is more comfortable for methods that try to
elect the centrist candidate.
I see IRV as FPP that trades most of its monotonicity criteria (including
mono-raise and Participation but
not mono-add-top, mono-add-plump or mono-append) to gain Clone-Winner and
Majority for Solid
Coalitions (and Mutual Dominat Third and Condorcet Loser).
It keeps FPP's compliances with Woodall's Plurality criterion, Later-no-Harm,
Later-no-Help and Clone-Loser.
The "representativeness criteria" it meets generally allow for a bigger set of
allowable winners than say
the Smith set, and its monotonity failures mean that it chooses a winner from
this set a bit erratically.
But I think your use of the term "pathology" (comparing it to a disease and so
something that is self-evidently
unacceptable) is biased and out of place.
I also think that the argument that IRV makes a good stepping-stone to PR is
strong. Truly proportional
multi-winner methods meet Droop Proportionality for Solid Coalitions
(equivalent in the single-winner
case to Majority for Solid Coalitions, aka Mutual Majority.)
Single-winner STV's virtues of Later-no-Harm and Clone Independence survive
into the multi-winner
version (which of course meets Droop Proportionality SC), while for
multi-winner methods the Condorcet
criterion and Favourite Betrayal are both incompatible with Droop PSC. Also I
think Later-no-Harm
compliance is more valuable for multi-winner methods than for single-winner
methods.
Chris Benham
Forest Simmons wrote (Sat. Nov.29):
>From: Chris Benham
> > Forest,
> Given IRV's compliance with the "representativeness criteria" Mutual
> Dominant Third, Majority for
> Solid Coalitions, Condorcet Loser and? Plurality; why should the bad look of
> its "erratic behaviour"
> be sufficient to condemn IRV in spite of these and other positive criterion
> compliances such as
> Later-no-Harm and Burial Invulnerability?
A picture is worth a thousand words. It shows the actual behavior, including
the extent of the pathology.
> > "....in the best of all possible worlds, namely normally distributed voting
> > populations in no more
> than two dimensional issue space."
> >CB: Why does that situation you refer to qualify as "the best of all
> >possible worlds" ?
> Three points determine a plane, so we cannot expect a lower dimension than
> two. What nicer
>distribution can you think of. than normal? But any distribution whose
>density only depends on distance
>from the center of the distribution would give exactly the same results for
>any Condorcet method, without
>making the IRV results any nicer.
Forest
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