Re: Our supermajority requirement has changed !

[Ian Jackson <ian@davenant.greenend.org.uk>]

Raul Miller writes ("Re: Our supermajority requirement has changed !"):
> If you approve of two options but like one better than another, you're
> not being penalized if the "liked, but not liked as much" option wins
> over your favorite.  Instead, you're being rewarded -- there weren't
> enough votes to get you your favorite, but there were enough to get you
> your alternate.

Let us suppose that:

 * There are two voters X and Y, whose real utilities are
    Voter X:  A=+10 (`Good')    Voter Y:  B=+10
              B=  0 (`OK')                A=  0
	     FD= -5                      FD= -5
   (Let us neglect the quorum for the moment as I want to have just
   two voters to simplify the situation.)

 * The chairman is abstaining but when they cast their vote they
   will agree either with X or Y, with 50% probability each (and
   neither X or Y know how the chairman will jump).

 * Each voter chooses between voting Good:OK:FD and Good:FD:OK.
   (Ie, let's avoid considering strategies involving other ballots.)

Here are the possible outcomes seen from X:

  Payoffs for X    Y votes B:A:FD `cooperate'   Y votes B:FD:A `defect'
    X cooperates        +5 (50% of +10)            0
    X defects          +10                        -5

Whether X's best strategy is cooperate depends on whether Y
cooperates, and X's outcome is mainly controlled by whether Y
cooperates or not.  If X knows that Y is going to defect then X should
cooperate.

This is a strange and dysfunctional game if what we want is for people
to discuss and vote honestly.


The alternative voting system, with the word `strictly' removed, works
like this:

  Payoffs for X    Y votes B:A:FD `cooperate'   Y votes B:FD:A `defect'
    X cooperates        +5                        +5 *
    X defects           +5 *                      +5 *

This is much more sensible.  (Entries marked * are ones where the
chairman could choose FD too.)


Ian.