[EM] Anti-defection strategy device for IBIFA

[C.Benham]

I'm afraid that I am now aware that this method fails FBC, so I withdraw 
this method suggestion.

20: F=C >> B
07: F > C=B
25: B
48: W

We are looking at this from the perspective of  the 20 F=C >> B voters  
who are top-rating F and C and
only giving "conditional approval" to B.  (The candidates full names 
could be Favourite, Compromise,
Bad, Worst).

Top Ratings scores:   W48 >  F27 > B25 > C20.

Because F's  TR score is higher than B's, the 20 F=C voters 
"conditional" approval of B doesn't count,
so IBIFA elects W.

But if the 20 F=C voters drop F from Top Rating F then the conditional 
approval of B would count the same
as normal approval and so then IBIFA  would elect B, a candidate those 
voters prefer to W, so the method fails
FBC.

Chris Benham


On 11/3/2016 11:23 PM, C.Benham wrote:
> 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
>
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