[EM] New Criterion
Forest Simmons
fsimmons at pcc.edu
Mon May 19 10:51:22 PDT 2014
Chris,
good example showing the incompatibility of CD with Semi-Sincerity!
It may be that some weaker (but adequate) version of CD is compatible with
Semi-sincerity.
Forest
On Sun, May 18, 2014 at 9:20 AM, C.Benham <cbenham at adam.com.au> wrote:
> "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> 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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