[EM] Anti-defection strategy device for IBIFA

[C.Benham]

I normally don't like explicit strategy devices, and (beyond considering 
it desirable to elect from the
voted Smith set) don't care very much about the "center squeeze" effect.

(I like truncation resistance, so I'm happy with some of the methods 
that meet the Chicken Dilemma criterion.)

Nonetheless here is  version of  IBIFA with a device aimed at addressing 
the Chicken Dilemma scenario.

* Voters mark each candidate as one of  Top-Rated, Approved, 
Conditionally Approved, Bottom-Rated. Default is Bottom-Rated.

A candidate marked "Conditionally Approved" on a ballot is approved if 
hir Top Ratings score is higher than the highest
Top Ratings score of any candidate that is Top-Rated on that ballot.

Based on the thus modified ballots, elect the 3-slot IBIFA winner.*

("Top-Rated"  could be called 'Most Preferred' and "Bottom-Rated" could 
be called 'Unapproved' or 'Rejected').

To refresh memories, IBIFA stands for "Irrelevant-Ballot Independent 
Fall-back Approval", and the 3-slot version goes thus:

*Voters rate candidates as one of  Top, Middle or Bottom. Default is 
Bottom.  Top and Middle is interpreted as approval.

If any candidate X  is rated Top on more ballots than any non-X is 
approved on ballots that don't top-rate X, then the X
with the highest Top-Ratings score wins.

Otherwise the most approved candidate wins.*

http://wiki.electorama.com/wiki/IBIFA

35: C
33: A>B
32: B (sincere might be B>A)

In the scenario addressed by the Chicken Dilemma criterion, if all  (and 
sometimes less than all) of A's supporters only "conditionally"
approve B then the method meets the CD criterion.  Otherwise it meets 
the Minimal Defense criterion.

http://wiki.electorama.com/wiki/Chicken_Dilemma_Criterion

http://wiki.electorama.com/wiki/Minimal_Defense_criterion

Of course it meets the Plurality criterion and doesn't have any 
random-fill incentive.

The downside is that the use of  Conditional Approval can cause a 
vulnerability to Push-over strategy.

48: C
27: B
25: A>>B

The A supporters are all only conditionally approving B, but that has 
the same effect as normal approval because B has a higher Top Ratings score
than A.  But now if 3 to 22 of the C voters change to C=A  then A's  Top 
Ratings score rises above B's so the "conditional" approval is switched off
and then C wins.

I dislike this "at the same time"-no-help failure, but the new result 
doesn't look terrible and of course if the B voters really prefer A to C 
then
they were foolish not to conditionally approve A. If they'd done that 
then the attempted Push-over would have just elected A.

(It crossed my mind to try to make Push-over strategising  more 
difficult and riskier with the same mechanism I suggested a while ago 
for IRV
or Benham that allows above-bottom equal-ranking, but that would have 
broken compliance with FBC.)

Chris Benham