[EM] Approval Bad Example

[C.Benham]

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>



>   321 voting
>
>
>       From Electowiki
>
> Jump to: navigation <#column-one>, search <#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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