[EM] vulnerability to compromise?

[Steve Eppley]

Markus S wrote:
> Steve wrote (13 May 2000):
> > Markus wrote (12 May 2000):
> > > Steve wrote (11 May 2000):
> > > > Markus wrote (10 May 2000):
> > > > > It can be argued that -in the Schulze method- if some
> > > > > voters uprank D ahead of A or downrank A behind D then
> > > > > this means that candidate A becomes less popular and that
> > > > > it is therefore legitimate when candidate A loses the
> > > > > elections.
> > > >
> > > > That's a flawed argument. Candidate A is not really less 
> > > > popular; it merely appears that way if one trusts the
> > > > sincerity of the votes.
> > > 
> > > Mike wrote (12 May 2000):
> > > > But (rhetorical question) if compromising means insincerely
> > > > voting someone higher to make him win, then how could that be
> > > > considered something that shouldn't work, or something that
> > > > means that a method has a vulnerability fault if it works?
> > > > If "vulnerability to compromise" means that, with a method,
> > > > it can sometimes be necessary for a voter to insincerely vote
> > > > someone higher in order to prevent the election of someone
> > > > worse, then "vulnerability" seems the wrong word.
> > > 
> > > I have to agree with Mike.
> > > 
> > > It is understandable that if some voters rank a candidate
> > > higher then this candidate might win ("compromising"). And
> > > it is understandable that if some voters rank a candidate
> > > lower then this candidate might lose ("burying").
> >
> > I agree with Mike too.  Mike's statement and mine are not 
> > contradictory.  
> >
> > And Mike's statement does not support Markus' argument shown at 
> > the top of this message.  The voters manipulating Markus' Feb 3 
> > 2000 example, if the Schulze method were employed, would be 
> > electing their favorite, not a compromise.
> 
> Mike's statement and mine are not contradictory. And Mike's
> statement does not support Steve's argument.

I didn't claim that Mike and Markus' statements above are 
contradictory; I said that Mike, Markus, and I are agreed on 
Mike's point.  And I didn't claim Mike's argument "supports" 
mine.  Mike's argument is unrelated to mine and therefore does 
not contradict (or support) mine.

The truth of my argument (i.e., that Markus' first argument 
above is flawed) is self-evident, if true popularity is defined 
by sincere preferences, which seems a reasonable definition.

> As far as I have understood Mike correctly, he says that
> (1) burying and compromising are problems, 

Markus has obviously misunderstood Mike, who wrote that 
compromising should not be viewed as a problem.  This can easily 
be seen by rereading Mike's words above, and from the next 
paragraph Mike wrote (which Markus didn't copy in his reply):

   If "vulnerability to compromise" means that, with a method,
   it can sometimes be necessary for a voter to insincerely vote
   someone higher in order to prevent the election of someone
   worse, then "vulnerability" seems the wrong word. I'd instead
   just say that, with that method, compromise can be needed.

Saying that vulnerability is the wrong word means that 
compromising should not be viewed as a problem.

>                                         but (2) that it isn't
> wrong if voting someone higher can make him win or if voting
> someone lower could make him lose and (3) that it would be
> therefore more problematic if the winner could be changed
> with other strategies and (4) that it is therefore not a
> "vulnerability fault" when an election method can be manipulated
> by burying or compromising.
> 
> Therefore Mike's statement is in drastic contrast to Steve's
> claim that the existence of a "direct" strategy (e.g. burying
> or compromising) is worse than the existence of an "indirect"
> strategy (e.g. changing the winner from candidate A to candidate
> B by ranking candidate C insincerely ahead of candidate D).

I never claimed that existence of a so-called "direct" strategy 
is worse.  Markus frequently misquotes me.  What I said was that 
in scenarios where direct strategies exist, the existence of 
indirect strategies in addition should not be considered a 
problem.  My argument can be further refined, in light of the 
discussion that compromise is not a problem, to the following:

   In scenarios where direct burying strategies exist, the
   existence of indirect strategies in addition should not be
   considered a problem.

My only reference to a direct strategy being worse was not a 
general statement, but specific to the example which Markus 
claimed showed Tideman to be worse than Schulze.  In that 
example, the direct burying strategy usable given Schulze 
would elect the favorite of the strategizers.  In contrast, 
the indirect strategy usable given Tideman would elect the 
next-to-last choice of the strategizers and also require the 
strategizers to drastically misrepresent their preference for 
their favorite.  Thus I view the direct burying strategy as 
worse than the indirect strategy in that example.

Markus also misrepresents the example.  The manipulation of 
Schulze in his example involved burying, not compromising.  This 
is why Mike's comment is obviously totally unrelated.  In the 
example, the voters who upranked D over A to defeat the sincere 
Schulze winner A are not electing "compromise D", they are 
electing "favorite C."  For reference, I repeat Markus' example 
along with some of my comments from my May 9 message:

   26 voters vote:  C>A>B>D
   20 voters vote:  B>D>A>C
   18 voters vote:  A>D>C>B
   14 voters vote:  C>B>A>D
    8 voters vote:  B>D>C>A
    7 voters vote:  D>A>C>B
    7 voters vote:  B>D>(A=C)

   What Markus apparently neglected to notice is that voters can
   easily manipulate Schulze in this scenario too, to change the 
   Schulze winner from A to C.  Some of the voters who prefer C 
   to A and A to D (the 26 "C>A>B>D" voters and the 14 "C>B>A>D" 
   voters) can uprank D ahead of A or downrank A behind D, which 
   would reverse the A>D majority to D>A.  Since the ADC58
   beatpath depends on the A>D majority, the ADC58 beatpath
   would be destroyed and Schulze would elect C.

   Here's a second consideration, but less important:  Markus' 
   Tideman strategizers (some of the 20 "B>D>A>C" voters) need
   to suppress the expression that B is their favorite -- which
   we may be consider a drastic or near-drastic strategy -- in
   order to improve the outcome from their least preferred
   alternative to their second least preferred alternative.  
   By contrast, the Schulze strategizers would not have to
   suppress the expression of their favorite, and would change
   the outcome to their favorite, and a smaller percentage of
   the relevant faction(s) need to strategize.

   So it seems to me we should not accept the argument that the
   example shows Tideman(majoritarian) to be more manipulable
   than Schulze.  (Tideman(margins) is more manipulable, though.)


---Steve     (Steve Eppley    seppley at alumni.caltech.edu)