FPTP family theory, REDLOG shadowing

[Bart Ingles]

Markus Schulze wrote:

> You wrote (10 Dec 1999):
> > I do not know if the AV is passed or failed by the participation
> > axiom. It will be passed in the 3 candidates case. An interesting
> > question could be: assuming (P1) and/or the "participation axiom",
> > deduce the values of quotas, for a AV method that was modified so
> > that it used quotas (for losers). Some easy inductive argument
> > maybe, or a computer simulation done in a day if it takes more
> > than a few hours to solve the problem. Lord Alexander wasn't
> > impressed with the method, and nor was Winston Churchill.
> 
> It has already been proven by Fishburn and Brams that Alternative
> Voting violates the participation criterion even in the 3 candidate
> case.
> 
> Example:
> 
>   7 voters vote A > B > C.
>   6 voters vote B > A > C.
>   8 voters vote C > B > A.
> 
>   If Alternative Voting is used, then candidate A is elected.
>   But if three of the eight CBA voters didn't go to the polls,
>   then candidate B would be elected.


Stranger still, if three of the eight CBA voters raise A to first choice
(changing their vote to ACB), A is defeated, and their new last choice
(B) wins.


The claim under AV/IRV that your second choice will never harm your
first choice is also false -- the six BAC voters can attempt to coerce
some of the ABC voters into supporting B, either by truncating or by
order reversal (announcing their plans publicly before the election.

If all six vote only for B, then A can never win, and the ABC voters
should instead vote BAC to insure C's defeat.

Alternatively, just three of the BAC voters could switch to BCA with the
same effect.  The three who choose to switch might have
lower-than-average ratings for A, and not mind much if the strategy
fails with A losing to C.  They can engage in this strategy over the
objection of the remaining three BAC voters, who have
higher-than-average ratings for A.


I believe similar strategies are possible with any ranked method;
certainly with Borda and the Condorcet methods.