Truncation Resistance #2 criterion (was Re: First Choices tiebre

[Steve Eppley]

Demorep wrote:
>After rethinking the problem of Condorcet circular ties, I note
>that such ties occur because any tiebreaker method using additional
>rankings beyond the first choice ranking has the potential for
>strategic voting
-snip-

The Gibbard-Satterthwaite theorem points out that *any* method has 
the potential for strategic voting.  Demorep's proposed new method
is even worse than Condorcet and Smith//Condorcet.  

I suggest that when people think about a new method they should
first test them on the following two examples:

     46:ABC                          46:A
     10:BAC                          10:BAC
     10:BCA                          10:BCA
     34:CBA                          34:CBA
     ------                          ------
     MUST ELECT B                    MUST NOT ELECT A

In the example on the left, it should elect B (the compromise
centrist who would beat any other in a head to head matchup).  In
the example on the right, it should not elect A, else the supporters
of A have a clear incentive to strategize.  If truncation would
elect A, the method has a serious problem.

We may as well call this two-example test a criterion: the
"Truncation Resistance #2" criterion, perhaps.  Do we have a
consensus that any method which fails TR-2 should not be posted 
here in EM, unless it's accompanied by a solid explanation why it's
better than Condorcet or Smith-Condorcet on some other criterion we
should respect?  Such a consensus would save us all a lot of time.

If I understand it right, Demorep's new "First Choices tiebreaker"
method fails TR-2.  Though it passes the left example (elects B), 
it fails the example on the right: the circular tie is resolved by 
eliminating B (which has fewest first choices), then A beats C. 

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