[EM] Approval Bad Example

[Jameson Quinn]

You are right. It does avoid a favorite betrayal incentive if there is a
sincere Condorcet winner, but not if there isn't.

Jameson

2011/11/9 C.Benham <cbenhamau at yahoo.com.au>

> **
> Jameson,
>
> In response to Forest asking if there was a method that satisfies
> something plus FBC you
> responded:
>
> Yes. 321 voting <http://wiki.electorama.com/wiki/321_voting><http://wiki.electorama.com/wiki/321_voting>
>
>
>
>  321 voting
> From Electowiki
> Jump to: navigation <#1338b9e6e791e9cc_column-one>, search<#1338b9e6e791e9cc_searchInput>
>
> 3-level rated ballots. Of the 3 candidates with the most ratings, take the
> 2 candidates with the most top-ratings, and then take the 1 pairwise winner
> among those.
>
>
> This fails FBC in the same way that ER-IRV(whole) does. From my 2 Nov. EM
> post:
>
> <snip>
>
> Here is Kevin Venzke's example from a June 2004  EM post:
>
> 6: A
> 3: C>B
> 2: C=B  (sincere is C>B)
> 2: B
>
> The method is ER-IRV(whole). If the 2 C=B voters sincerely vote C>B then
> the first-round scores are
> A6,  C5,  B2.   B is eliminated and A wins.
>
> As it is the first-round scores are A6, C5, B4. B is still eliminated
> and A wins.
>
> To meet FBC no voters should have any incentive to vote their sincere
> favourite below equal-top.
>
> 6: A
> 3: C>B
> 2: B>C  (sincere is C>B)
> 2: B
>
> But if those 2 voters (sincere C>B, was C=B) do that and strictly
> top-rank their compromise candidate B, then the first-round scores are
> A6,  B4,  C3.  C is eliminated and B wins: B7, A6.
>
> By down-ranking their sincere favourite those 2 voters have gained a
> result they prefer that they couldn't have got any other way, a clear
> failure of the
> Favorite Betrayal Criterion (FBC).
>
> <snip>
>
> Even if  321 voting met FBC with 3 candidates it  it wouldn't with more,
> because
> sincerely rating your sincere favourite  Top instead of Bottom could mean
> that your
> favourite displaces your compromise candidate from the  top 3 most rated
> candidates and
> goes on to lose when your compromise would have won.
>
> Chris Benham
> .
>
>
> Forest Simmons wrote (9 Nov 2011):
>
> I'm assuming "approval bad example" is typified by the implicit approval
> order in the scenario
>
> 49 C
> 27 A>B
> 24 B
>
> It seems to me that IF we (1) want to respect the Plurality Criterion, (2)
> discourage "chicken"  strategy,
> (3) stick with determinism, and (4) not take advantage of proxy ideas,
> then our method must allow
> equal-rank-top and elect C in the above scenario, but elect B when B is
> advanced to top equal with A in
> the middle faction:
>
> 49 C
> 27 A=B
> 24 B
>
> Then if sincere preferences are
>
> 49 C
> 27 A>B
> 24 B>A,
>
> the B faction will be deterred from truncating A.  While if the B
> supporters are sincerely indifferent
> between A and C, the A supporters can vote approval style (A=B) to get B
> elected.
>
> Do we agree on this?
>
> Note that IRV (=whole) satisfies this, but now the question remains ... is
> there a method that satisfies
> this which also satisfies the FBC?
>
> Forest
>
>
>
>
>
>
>
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