[EM] DH3 "horribly common"?

[Warren Smith]

>lomax: Reading the scenario, I'm struck by how utterly unlikely it seems 
that voters would actually behave in the way described. Essentially, 
if practically the entire electorate decides to go on an exaggeration 
binge, a bad outcome could occur. Well, duh!

On what basis is the claim made that this problem is not only common, 
when on the face of it it seems that it would be extremely rare, but 
it is "horribly-common"?

What does "horribly-common" mean? From the meaning of "common," I'd 
have to assume that "horribly-common" means "practically all the time."

--I actually am aware of one case in which DH3 in fact did happen in
a real vote (which I was involved in) with large ($100,000+) consequences at stake.
For that story see
   http://math.temple.edu/~wds/crv/rangeVborda.html
section 2.
 also point out that another example was the world's only Borda government (Kiribati)
where again such phenomena were immediately observed.
 See p.368 of Benjamin Reilly: Social Choice in the South Seas: Electoral Innovation and the
Borda Count in the Pacific Island Countries, Int'l Political Science Review 23,4 (2002) 355-372.


--As far as "horribly common" by that I meant (as I described on the DH3 page
   http://math.temple.edu/~wds/crv/DH3.html )
that DH3 occurs whenever there are 3 comparable rival good candidates and a bad one.
As I remarked, assuming we can ignore 2-man races (after all, if they were all
we needed to worry about, then plurality would be fine and EM need not exist),
this means essentially every race you are going to have, is fodder for a DH3 disaster.
It is hard to get more common than that.

And since DH3 leads to the worst candidate winning (in the 3 rivals + dark horse 
scenario) it is also "horribly" i.e. maximally, serious.

So, no, I do not think I am prone to "exaggeration" and I do not think something
which actually did happen in the single ranked ballot election for real stakes that 
I have ever actually been in, is  "utterly unlikely".   

What I think is, DH3 is an extremely serious problem faced by Borda and all Condorcet
methods based on strict-ranking ballots.  It also affects many other methods too.
In your judgement of the commonness of Dh3 you have to factor in understanding of
strategy (or lack of understanding of strategy) in that method by either the voters
or you.  That can be tricky.  However, if the voting method is treated as a "black box"
(which I think is a close approximation to what most voters will regard, say,
Schulze beatpaths as) then the obvious intuitive strategic vote that occurs first to
me, is in fact exactly the behavior needed to make DH3 happen.  I therefore
am fairly confident that DH3-type behavior will happen commonly in practice.

This seems to me to be a good reason to dismiss every Condorcet method, including
even MDDA and DMC, form consideration, in favor of range voting which is immune to
the DH3 problem.   Plurality and IRV are also immune.  Note that in this
way Condorcet & Borda methods are actually inferior to plurality voting.
That ought to make you reach for a cool one.  

See, Ossipoff has indicated he felt Range voting was best for the public, but
privately he preferred MDDA.  (I do not know if that is still his stance.)
Anyhow, MDDA and DMC are indeed very neato, and MDDA obeys Ossipoff's favorite
criterion FBC (as does Range), BUT MDDA plausibly will suffer bigtime from
DH3 whereas range will be immune.  That right there seems to me to tip
the balance in favor of Range because DH3 is horribly common and serious,
and that outweighs any advantages MDDA has over range which seem in comparison
minor.

So, that is my view.  If I am forced to go with a ranking-type method and not Range,
then yes, DMC and MDDA or Deluxe MDDA look pretty interesting to me, although
I feel uncomfortable with my (and everybody else's) currnet (lack of) understanding
of them.  The simplicity of range is not only superior for public consumption,
but it is also superior from my personal mental viewpoint of feeling confortable
that I can understand the phenomena that happen in the Range system and that
no humogous GOTCHA (such as DH3 itself, which EM seems to have ignored before I 
started bothering them about it) is going to getcha.  For example, I do not understand
optimal strategy in MDDA and DMC, but do in range voting.  That is an example
of where complexity of the voting system has led to ignorance on a very important 
question.
So MDDA and DMC and many other methods are kind of like dark pools of ignorance
in which monsters may lurk.  It is worrying to base your government on such a thing.

wds