minimal defense & SDSC (was Re: [EM] BeatpathWinner doesn't fail Markus' "SDSC".)

[Steve Eppley]

Markus wrote:

> Dear Mike,
> you wrote (4 Feb 2004):
> > Not only does Plurality pass your "SDSC", 
-snip-
> If you mean Steve Eppley's "minimal defense" with "your 'SDSC'"
> then your example doesn't demonstrate a violation of this
> criterion since this majority of the voters doesn't rank
> candidate B "no higher than tied for bottom".
> 
> Steve Eppley wrote (http://www.alumni.caltech.edu/~seppley):
> > Any ordering of the alternatives must be an admissible vote,
> > and if more than half of the voters rank y over x and x no
> > higher than tied for bottom, then x must not be elected.

Markus has taken an excerpt out of context, and in this 
case it is misleading. (Perhaps I should search my election-
methods-list folder to see how often my writing has been 
misrepresented.)  Here's more of what I actually posted at 
the webpage Markus cited, which shows how Markus distorted 
my definition:

   minimal defense:  If more than half of the voters prefer
   alternative y over alternative x, then that majority
   must have some way of voting that ensures x will not 
   be elected and does not require any of them to rank y
   equal to or over any alternatives preferred over y.
   (Another wording is nearly equivalent: Any ordering 
   of the alternatives must be an admissible vote, and 
   if more than half of the voters rank y over x and 
   x no higher than tied for bottom, then x must not 
   be elected.  This criterion, in particular the first
   wording, is promoted by Mike Ossipoff under the name
   Strong Defensive Strategy Criterion. -snip- )

The definitions in that "table of contents" webpage have 
been made brief and simple for the sake of laymen who might 
read the page.  The complete definition of minimal defense 
is in a document two clicks away from that page. (Click on 
"minimal defense" then click on "Strategic Indifference".)

   Minimal Defense:  For all subsets X of the alternatives,
   if there exists an alternative y that more than half 
   the voters prefer over every alternative in X, 
   then there must exist a set of voting strategies 
   for that majority that ensures no alternative in X 
   will be elected and does not require any of them to 
   misrepresent any preferences except possibly lowering
   alternatives in X.

I should add a clause to strengthen that:

   "... and without having to lower any alternative in X
   below a tie for bottom with their least-preferred
   alternative(s)."  

In addition to the obvious reduction of preference 
misrepresentation implied by this clause, I seem to recall 
from years ago that the clause serves to ensure a group 
strategy equilibrium (much more desirable than a Nash 
equilibrium) by preventing the creation of new strategic 
reversal opportunities that could arise if X is lowered 
below other alternatives.  It may be unclear when 
organizing the defensive strategy how popular the other 
candidates will be on election day.  For instance, if some 
supporters of y downrank x below z (rather than tied for 
bottom with z) to deter suporters of x from attempting a 
reversal strategy (x over z over y), then supporters of z 
who prefer z over y over x may be given an opportunity to 
elect z by reversing x over y.

It was near-accidental that I noticed Markus' message.  I 
haven't read the previous messages in the thread, but it's 
clear from the subject line that Mike was referring to some 
(re)definition of SDSC allegedly posted by Markus, not to a 
definition posted by me. 

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