[EM] New Criterion

Forest Simmons fsimmons at pcc.edu
Wed May 14 17:11:15 PDT 2014

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


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


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!

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