[EM] The meaning of a vote (or lack thereof)

[Michael Allan]

Kristofer, Fred and Jameson,

Kristofer Munsterhjelm wrote:
> This can also be used to validate Warren's proof. Say that we have
> one set of ballots X_a, where A is the unique winner, and another
> set of ballots X_b, where A is not the unique winner. Then by
> permuting X_a into X_b one vote at a time, there will be a set of
> "adjacent" ballot sets (differing only by a single vote). Call these
> X_a', and X_a'', where X_a' has A as the unique winner, but X_a''
> does not. Then if there was an election, and the submitted ballots
> just happened to form X_a', then the alteration or addition of a
> single ballot could turn X_a' into X_a'', and then that would prove
> that a single ballot could alter the outcome.

I think I see the intent of Warren's proof.  This also generalizes on
the tie-breaking situation proposed by Dave Ketchum.  I agree this is
correct.

> You might say that these voting situations are very rare indeed, so
> that a single vote *most of the time* does not affect the
> outcome. However, "most of the time" is not the same thing as
> "always".

This suggests that the critique in regard to the meaning of a vote
must be a matter of probabilities, and not absolutes.  I try to
restate it in a more correct form:

   It is probable that the course and outcome of the election will
   affect the voter, yet improbable that the voter will affect the
   course and outcome of the election.  This imbalance amounts to a
   fault in the electoral method, because the individual ought not to
   be subject to a power over which she (or he) has no corresponding
   influence.  This fault bears upon the human rights of the
   individual and the moral legitimacy of state power.

Fred Gohlke wrote:
> I believe (and I think Michael shares this view) an electoral method
> that embodies the concept of the former, giving every member of the
> electorate an opportunity to participate in the electoral process to
> the full extent of their desire and ability, is possible, practical
> and necessary.

Jameson Quinn replied:
> ... I agree. But I do not think that you can thereby conclude that
> any method which does not reach all those goals is thereby
> useless. In fact, I think that such imperfect methods are necessary
> stepping stones to your vision.

I agree too, it's necessary that we reach that goal.  I also agree
that imperfections can be useful as stepping stones.  Consider a novel
interpretation of this in the situation of a mainstream political
party:

  (a) The party has a maximum of freedom and influence in the election
      of state officials without infringing on the equal freedom of
      other parties.

  (b) The party has a maximum of freedom and influence in the
      promulgation of state laws, again without infringing on the
      equal freedom of other parties.

  (c) The political power and laws of the state that bear upon the
      party are legitimized in the eyes of the party by corresponding
      political freedoms (a, b).  Insofar as the sovereignty of the
      state depends upon the loyalty of the party, that sovereignty is
      secure.

  (d) The party employs a primary electoral method and system that has
      decisive effect within its scope.  Where the winner of the
      general election is a party member, that member was previously
      the winner of the primary.

  (e) The political freedoms of the party (a, b) are enabled by the
      decisiveness of the primary electoral method (d), without which
      the party would have none of those freedoms.

  (f) The party chooses its own primary electoral method independently
      of other parties' choices.  In freely and independently making
      this choice, the party is the author of its own liberty (a, b,
      d, e).

The individual has the same goal.  To reach this goal, it would be
sufficient to follow in the footsteps of the party.  Replace "party"
by "individual" in the statements above, and then identify what is
needed to make each statement true for the individual as it is true
for the party.  *

The crucial thing to note is that (f) requires all electoral methods
to be treated equally; the political liberty of the individual depends
on the technical liberty of the experts who design, deploy and
administer those electoral methods.  Where a method is discovered to
be imperfect, the experts need not petition or agitate in order to
correct the problem; they need only deploy the solution.


  * Maybe the toughest thing is to reconcile the decisiveness of the
    primary electoral method (d) with the freedom of the individual to
    choose her own method (f).  Thomas von der Elbe's invention of
    vote mirroring offers one possible solution.  It is based on the
    translation of votes, a practice that depends upon a detailed
    knowledge of the differences among the various electoral methods.

    See: Vote mirroring as a counter-monopoly measure.
    http://listserv.aoir.org/pipermail/air-l-aoir.org/2011-July/024104.html

-- 
Michael Allan

Toronto, +1 416-699-9528
http://zelea.com/


Kristofer Munsterhjelm wrote:
> (Resubmitting to the list as Michael Allan suggested :-)
> 
> Michael Allan wrote:
> > Warren Smith wrote:
> >> --no. A single ballot can change the outcome of an election. This 
> >> is true in any election method which is capable of having at least 
> >> two outcomes.
> >> Proof: simply change ballots one by one until the outcome changes. 
> >> At the moment it changes, that single ballot changed an election 
> >> outcome. QED.
> > 
> > Your proof is flawed, of course. It assumes the election method would
> >  allow one to "change ballots one by one until the outcome changes". 
> > Such gross manipulations are not permitted by the rules of any 
> > election method. The rules grant to the voter a single vote, and that
> >  is all.
> 
> I haven't been following the list all that closely of late because I
> have been busy with other things, therefore I'm replying here instead of
> to list. If you think my mail would be of use on list even given the
> time delay, just say so and I'll put it up there, too :-)
> 
> Anyway, to prove that a single ballot can change the outcome of an
> election, it is sufficient to find a single example where this is the
> case. Such a case is easy to construct for most methods. For instance,
> this will do in every method that passes Majority:
> 
> 50: A > B
> 50: B > A
> 
> which is a tie. Now add a single A>B vote, or alter an B>A vote to
> become A>B, and A wins. Hence a single vote altered the outcome of the
> election.
> 
> This can also be used to validate Warren's proof. Say that we have one
> set of ballots X_a, where A is the unique winner, and another set of
> ballots X_b, where A is not the unique winner. Then by permuting X_a
> into X_b one vote at a time, there will be a set of "adjacent" ballot
> sets (differing only by a single vote). Call these X_a', and X_a'',
> where X_a' has A as the unique winner, but X_a'' does not. Then if there
> was an election, and the submitted ballots just happened to form X_a',
> then the alteration or addition of a single ballot could turn X_a' into
> X_a'', and then that would prove that a single ballot could alter the
> outcome.
> 
> You might say that these voting situations are very rare indeed, so that
> a single vote *most of the time* does not affect the outcome. However,
> "most of the time" is not the same thing as "always".