Most Drastic Falsification?

[Bart Ingles]

Bart Ingles wrote:
> 
> Hugh R. Tobin wrote:
> >
> > I submit that a more drastic form of tactical voting
> > [...]
> > is voting for one's last choice first,
> > and as previously noted this tactic by a minority of the supporters of a
> > candidate can sometimes work quite well in IRO.  The plurality wing
> > tries to get the other (more extreme) wing to run second, so as to use
> > the second choices of the middle to prevail.
> >
> > -- Hugh Tobin
> 
> Not sure I follow -- can you put together an example?
> 
> Bart

Nebmind, I got it:

Initial Preferences
49 AB
26 B
25 CB
--------
C dropped; B beats A,  51:49

Eleven of A's supporters vote for C, in order to force out B (only two
are required, but I want to see how hard this tactic is to counter,
farther down in my message):

Actual Vote
38 AB
26 B
25 CB
11 CA
--------
B dropped; A beats C,  38:36

I don't know if this tactic is more drastic, exactly, but by itself it
certainly favors the FPP winner (unlike the Mike Ossipoff's example,
which seems to favor the Condorcet winner).  In fact these two measures
seem to counter one another (see farther down).

This tactic seems to have more limited application, however.  In the
example above, the initial first choice preferences must meet the
following conditions (I haven't looked at more complex 2nd choice
patterns, or four or more candidates):

1.  A < 50%  	(otherwise A already won)
2.  A > B > C   (basic condition for this tactic to be useful)
3.  A > 33.34%  (implied by #2)
4.  (A-B) > (B-C)+M1+M2  (where M1 is the desired safety margin for A >
C, and M2 is the desired margin for C > B)

In addition to being limited, the tactic doesn't seem very reliable. 
For example, in order to counter A's move, six of C's supporters could
support B instead (note that I made the starting conditions above as
favorable as possible for A's use of the tactic):

38 AB
26 B
6  BC
19 CB
11 CA
---------
C eliminated, B beats A 51:49

Six of C's supporters switching to B were enough to counter the 11
"infiltrators" from A, guaranteeing A's defeat.  If only two of A's
supporters had voted for C, then only only one of C's supporters would
be needed to counter the move.

I'm not sure what all this proved, but it looks like it would be
difficult to use this tactic, and it should be possible to defend
against it if C's supporters are willing to vote for B.

Come to think of it, if C's supporters have reason to expect such a move
from A, some of them may well choose to vote for B defensively.  In
effect, the threat of such a move by A would ultimately tend to favor
the Condorcet candidate (B).

Bart Ingles