# [EM] New Criterion

Forest Simmons fsimmons at pcc.edu
Thu May 15 20:34:06 PDT 2014

```I'm hopeful that some of our recent proposals including both of Benham's
methods might satisfy these two criteria;  I haven't any proof, but I have
no counter example either.

I can show that IRV fails Economical Defense:

Sincere ballots:
34 X>Y
31 Y
35 Z>Y
The sincere IRV winner is Z.

Offensive Threat by the X faction to support Y which they prefer over the
sincere winner Z:

34 Y>X
31 Y
35 Z>Y

The Z supporters have no deterrent at all, let alone an economical one.

Now here's an example of Benham employing an economical defense:

Same sincere scenario:
34 X>Y
31 Y
35 Z>Y

The Benham winner is Y.

The Z faction threatens to truncate Y, which would get Z elected under
Benham:

34 X>Y
31 Y
35 Z

But the X faction defends the sincere CW by raising Y:

34 X=Y
31 Y
35 Z

Now the threat is empty.

The threat involved truncating Y on 35 ballots.  The deterrence involved
raising Y on 34 ballots.  The defense involved fewer (half) reversals than
the threat.  The defense was indeed economical.

Here's another example involving Enhance Majority (equal top minus equal
bottom):

Sincere
34 A>B
31 B>A
35 C

The B faction threatens truncation of A on all 31 ballots, which if
unopposed, would change the winner from A to B.

In turn the A faction announces that they intend to vote as in the nearest
strategic equilibrium: they will truncate B on 28 ballots (all except 6).

28 A
6  A>B

As long as two B voters refuse to truncate A, the sincere winner A will be
saved.  Otherwise, C wins.

Since the threat involves at least 30 truncations, and the deterrent
involves only 26 truncations, the defense is economical.

The rationale for this defense criterion is that in general it is easier to
convince 28 voters than to convince 30 voters to do a semi-sincere
truncation.

Note that in these examples (except for the case of IRV) semi-sincere
modifications were sufficient to reach the nearest strategic equilibrium
position.

FBC is much stronger because it is an unconditional guarantee (regardless
of strategic equilibria) that raising your favorite to equal top must
change the winner to your favorite unless the winner doesn't change at all.

The semi-sincere criterion entails that you never have to lower your
favorite below another candidate in order to reach the strategic equilibrium

On Thu, May 15, 2014 at 8:12 AM, Michael Ossipoff <email9648742 at gmail.com>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
>>
>>
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list
>> info
>>
>>
>
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