[EM] New Criterion
C.Benham
cbenham at adam.com.au
Sat May 17 00:52:48 PDT 2014
Forest,
I consider the problem of the smallest faction winning by truncating
(and perhaps "defecting" from a sincere solid coalition) to be much much
more serious than the problem of the largest faction winning by
truncation (perhaps insincerely).
But in this post you seem to want to put them on the same level. Also
you seem to assume that all sincere pairwise preferences are equally
strong. Probably they aren't and if they aren't then we know the
voters' strongest pairwise preferences are between (on the one side)
candidates
they vote below no other and (on the other) candidates they vote above
no other. But since we are giving the sincere scenarios, we can include
preference-strength information (">" vs ">>" in giving voters' rankings).
> "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."
I'd like the definition (in this context) of "deterred" spelt out. It
is much better if "offensive moves away from sincere ballots" simply
have no chance
of being effective (in as many circumstances as possible) than if the
move is given some (less than 100%) chance of "backfiring" by electing
a candidate
that the offensive strategizers like less than the one who would have
won if they'd voted sincerely.
> "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."
You don't fully answer your own (presumably rhetorical) question. You
don't specify how much more "significantly more" is.
> "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."
Assuming that "strategic equilibrium ballot sets" aren't too difficult
to recognise, this looks interesting and possibly useful.
Chris Benham
On 5/15/2014 9:41 AM, Forest Simmons 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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