[EM] Approval Margins example

Forest Simmons fsimmons at pcc.edu
Wed May 14 15:08:03 PDT 2014

> ----------------------------------------------------------------------
> Date: Thu, 15 May 2014 02:01:13 +0930
> From: "C.Benham" <cbenham at adam.com.au>
> To: election-methods at lists.electorama.com
> Subject: Re: [EM] Approval Margins example
> Message-ID: <53739A51.9050505 at adam.com.au>
> Content-Type: text/plain; charset="iso-8859-1"; Format="flowed"
> Forest,
> Originally I conceived Approval Margins as using ballots with an
> approval  cutoff/threshold, but since then I've largely gone off
> allowing voters to rank among unapproved candidates (and the somewhat
> more complicated ballot).
> But I agree that with that type of ballot Approval Margins is  a good
> method.
> Still, in the example the chicken dilemma is to some extent revived.
> Maybe the A voters can be scared into approving B, in which
> case maybe the B voters can again get their favourite elected by
> "defecting".  Arguably it's better for the method to have a kind
> of  (Strangegloveian)  "doomsday machine"  defection deterrence.

I used to think the same thing, but because of the following example I have
changed my mind:

34 A>B
31 B
35 C

The CD criterion requires that C be the winner.

That's great when the above ballot set arises from a chicken defection,
i.e. when it comes from an insincere truncation of A by the B faction.

Sincere scenario I:

34 A>B
31 B>A
35 C

But what if the ballot set comes from an insincere truncation of B by the C

Sincere scenario II:

34 A>B
31 B
35 C>B

The problem is that it is impossible for both sincere ballot sets to
represent strategic equilibria.

If a method elects C from the ballot set

34 A>B
31 B
35 C,

then sincere scenario II is not an equilibrium.

If it elects B, then sincere scenario I is not an equilibrium.

When a sincere scenario is not a strategic equilibrium position, then the
supporters of the sincere winner have to take defensive action.

In sincere scenario I how can the A supporters take defensive action
against a chicken attack?  By announcing their intent to truncate B on some
of their ballots:

(More Later)

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