[EM] Re: Burying and defection with the "defeat-droppers".

Mon Mar 21 10:01:34 PST 2005

James G-A,
Referring to this example,

46 abc
44 bca (sincere is bac)
05 cab
05 cba

I asked you why you "reccomend methods that elect b",
and you replied (Mon.Mar.21):

> Do I?

As far as I can tell from your website, with some
beating about the bush, yes. If pressed as to which
you think is the best plain ranked-ballot method for
public political elections, I gather you reccomend
using Winning Votes with either  Beat Path, Ranked
Pairs or River.
You say your Cardinal-Weighted Pairwise method is only
"marginally preferable to Condorcet methods which only
use ranking information".

I  went on to ask some questions about certain
criteria and this example. Perhaps I should have
specified that I was only referring to plain
ranked-ballot methods, and not ones that incorporate
ratings information or offer the voters explicit
strategy devices.

> I suggest that this would be an unrealistic winning
votes example, because I expect that in a real wv
election of this type, most of the A>B>C voters would
truncate before B, and most of the B voters would
truncate before A. 

I agree that in a public political election with
reasonably well-informed voters and truncation
allowed, this is an unrealistic example if  any method
that fails absolute
Later-no-harm is used.  But we can imagine an election
(for something much smaller than the US presidency)
where the B voters are much better informed than the
A voters.
In my opinion DD(WV)'s vulnerability to this type of 
burial/defection sits very badly with its 0-info.
random-fill incentive.Suppose that the  A voters have
a very small sincere
ratings gap between B and C, and they have some
suspicion/paranoia that the B voters will try some
strategy. In WV, if they truncate and their
expectations about how others
vote turns out to be completely wrong, then on average
they have harmed their favourite's chances.  If on the
other hand the method is SCRIRVE (which also elects B
in this
example) the A voters (or any other voters) could
truncate without, in the 0-info.case, on average
harming their favourite.  So in situations where this
scenario might arise, it would be somewhat less likely
with SCRIRVE than with DD(WV).

I suggested this criterion:
"Weak Defection Resistance: If  winning candidate x is
the CW and the FPW, and xy are a solid coalition with
more than 2/3 of the votes; and afterwards  some
ballots that rank y above x and z are changed so that
z's ranking relative to x is raised while keeping y
ranked above both; then if there is a new winner it
cannot be y."
("FPW" means "first-preferences winner".)

You responded:

> A proof? 

Maybe not quite, but  this example is highly
suggestive and convinces me:
34 xyz
33 yzx  (was yxz)
16 zxy
16 zyx
99 ballots.
While conforming with the situation described in the
criterion, x here is as weak as possible with this
number of voters. The defection fails and x wins.
x>y 50-49,  y>z 67-32,  z>x 65-34.   z has the lowest
gross score in any pairwise comparison and so is
eliminated.

"Weak Burial Resistance: If winning candidate x is the
CW and FPW while z is the CL and FPL , and afterwards 
some ballots that rank any y above x and z are changed
so that z's ranking relative to x is raised while
keeping y ranked above them both; then if  there is a
new winner it cannot be y."

(CL is "the candidate pairwise-beaten by all other
others"; FPL is "the candidate with the fewest
first-preferences".)

You asked:

> Does anything interesting meet this criterion? 

"CNTT,AV" (Smith,IRV) is in my view a good method that
meets it.

"CNTT,AV: Elect the CW if there is one. Otherwise,
working with the original ballots, commence a normal
IRV count and when all-but-one members of the Smith
set has been eliminated, elect the one remaining."

Unfortunately, Raynaud(GL) fails this criterion.
12 abc
04 acb
14 bca  (was bac)
06 cab
07 cba
43 ballots.
FPs: a16,  b14, c13.
a>b 22-21,  b>c 26-17,  c>a 27-16
a is eliminated and b wins.