[EM] New Criterion

[C.Benham]

> "The 2nd one, as you said, seems closely-related to FBC. Having just 
> now read of it, I don't now know how it differs.You say it's somewhat 
> weaker. Then it could be useful for comparing methods that don't meet 
> the more demanding FBC."

Mike,

I don't see how they are similar.

49 C
27 A>B
24 B


> "A method satisfies the Semi-Sincere Criterion if and only if each 
> sincere ballot set can be modified without any order reversals into a 
> strategic equilibrium ballot set that preserves the sincere winner."

If  Forest's criterion's "sincere ballot sets" allow truncation, then it 
seems to me that it isn't compatible with both of Plurality and Chicken 
Dilemma.  A method meeting Plurality and CD
must elect C in the above "sincere ballot set", but (assuming the method 
meets Majority Favourite) it doesn't seem to be in "strategic 
equilibrium"  (because there is no "deterrent" to the
A>B  voters electing B by voting B>A or B).

Or I could be wrong.

49 C
27 A>B
24 B=C

Is this a "strategic equilibrium ballot set" for a method that meets all 
of Condorcet, Plurality and CD?   It seems odd to see some virtue in a 
faction being able to rescue the sincere
method winner... at the expense of its favourite!


Chris


On 5/16/2014 12:42 AM, Michael Ossipoff wrote:
> Interesting two criteria. For the first one, would the magnitude of a 
> change be measured by the total number of half-reversals of 
> candidate-order (the matter of which is voted over which), where a 
> half-reversal is a move from voting X over Y, to voting nether over 
> the other?
> The 2nd one, as you said, seems closely-related to FBC. Having just 
> now read of it, I don't now know how it differs.You say it's somewhat 
> weaker. Then it could be useful for comparing methods that don't meet 
> the more demanding FBC.
> Do you know how MAM, Benham, Woodall, MMLV(erw)M and your sequence 
> based on covering and approval do,  by those two new criteria?
> Michael Ossipoff
>
> On Wed, May 14, 2014 at 8:11 PM, Forest Simmons <fsimmons at pcc.edu 
> <mailto:fsimmons at pcc.edu>> wrote:
>
>     Every reasonable method that takes ranked ballots has the
>     following problem: not every sincere ballot set represents a
>     strategic equilibrium.
>
>     In other words, no matter the method there is some scenario where
>     a loser can change to winner through unilateral insincere voting.
>
>     For example, consider the following two sincere scenarios:
>
>     34 A>B
>     31 B>A
>     35 C
>
>     and
>
>     34 X>Y
>     31 Y
>     35 Z>Y
>
>     All of the methods that we currently consider reasonable (except
>     perhaps IRV) , make A win in the ABC scenario, and make Y win in
>     the XYZ, scenario.
>
>     Now suppose that the B supporters unilaterally truncate A in the
>     first scenario, and the Z supporters unilaterally truncate Y in
>     the second scenario.  The resulting insincere ballot sets are
>
>     34 A>B
>     31 B
>     35 C
>
>     and
>
>     34 X>Y
>     31 Y
>     35 Z .
>
>     By neutrality, if our method must pick corresponding winners in
>     the two scenarios, i.e. either A and X, or B and Y, or C and Z.
>
>     But plurality rules out A and X, while the chicken dilemma
>     criterion  rules out B and Y.  Therefore our method must pick C and Z.
>
>     That's fine for the first scenario; it means that sincere votes in
>     that scenario could well be a strategic equilibrium.  But making z
>     the winner in the second scenario means that sincere ballots were
>     not a strategic equilibrium position.  The unilateral defection of
>     the Z faction was rewarded by the election of Z.
>
>     The purpose of this example is to illustrate why sincere votes
>     cannot always be a strategic equilibrium position.
>
>     Sometimes a faction can take advantage of this problem by making a
>     move (away from sincere ballots) that (if not countered) would
>     improve the outcome from their point of view.  Let's call such a
>     move an offensive move.  Any move by another faction that would
>     make an offensive move unrewarding can be called a defensive move.
>
>     Now here's the criterion:
>
>     A method satisfies the Economical Defense Criterion (EDC) if and
>     only if every potential unilateral offensive move away from
>     sincere ballots can be deterred by a smaller unilateral defensive
>     move.
>
>     How should we measure the size of a move?
>
>     It should be by the total number of order changes over all changed
>     ballots.  An order reversal of the type X>Y to Y>X should count
>     significantly more than a collapse of the type X>Y to X=Y or the
>     reverse process from X=Y to X>Y.
>
>     Here's another criterion:
>
>     A method satisfies the Semi-Sincere Criterion if and only if each
>     sincere ballot set can be modified without any order reversals
>     into a strategic equilibrium ballot set that preserves the sincere
>     winner.
>
>     This SSC criterion is similar to the FBC, but easier to satisfy. 
>     I think it is just as good as the FBC for practical purposes,
>     since rational voters will always aim at strategic equilibria.
>
>
>     Gotta Go!
>
>     Forest
>
>
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>
>
>
>
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