[EM] vulnerability to compromise?

[Markus Schulze]

Dear participants,

Steve wrote (17 May 2000):
> Markus wrote (16 May 2000):
> > 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.

I think that Steve should always read whole sentences before
he replies to them.

******

Steve wrote (17 May 2000):
> In scenarios where direct burying strategies exist, the
> existence of indirect strategies in addition should not be
> considered a problem.

In my opinion, that's a bad idea. Steve suggests we utterly
neglect the possibility of IBCM's manipulability when we
compare manipulability.

But if Steve believes that only burying should be considered,
then he should introduce some criteria to measure the
vulnerability to burying.

******

Steve wrote (17 May 2000):
> 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.

I claim that this example shows that Tideman violates beat
path GMC. The name of that thread is "Tideman and GMC" and not
"Tideman and burying."

******

Steve wrote (17 May 2000):
> 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.)

I didn't deny that Schulze is vulnerable to burying and
compromising. Actually, I wrote (10 May 2000): "Every Condorcet
method can be manipulated by burying [=lower a candidate with
respect to sincere placement in the hopes of defeating it] and
compromising [=raise a candidate with respect to sincere
placement in the hopes of electing it]." In so far as the
Schulze method meets the Condorcet criterion, the statement
above is also valid for the Schulze method.

Steve wrote (17 May 2000): "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." I don't agree with
Steve's conclusion. I can add candidates (E,F,G,...) to that
example such that candidate B isn't the favorite of this
group any more and such that the candidates E,F,G,... are
not elected. Therefore the question is: What is
Steve's criterion to decide whether a given strategy is
"near-drastic"?

Markus Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de