[EM] (1) The fact of an objectively meaningless vote

[Michael Allan]

Dear Juho and Fred,

Thanks again for your thoughtful replies.  Here I fall back to the
premise section of the thesis, where you both have questions.
Although this section is still undrafted, it boils down to a simple
assertion of emprirical fact that is relatively easy to summarize [1].
Here again (with corrections) is the relevant section of the abstract:

   An individual vote in a general election has no meaningful effect
   in the objective world, and no effect whatsoever on the official
   outcome of the election; whether the vote is cast or not, the
   outcome is the same regardless.  Beneath this fact lies a
   structural fault that emerges here and there in society as a series
   of persistent discontinuities between facts and norms, or contents
   and forms. ... [2]

Juho Laatu wrote:
> This is not a "flaw", but I wouldn't say "extensive structural
> fault" but something milder.

I agree thanks, and I corrected it.

> > The value 1/N [power of vote] appears to be erroneous.  It is
> > refuted by empirical evidence that measures the value at exactly
> > zero.  Again, the experimental method is:
> > 
> >  1. Take the last election in which you voted, and look at its
> >     political outcome (P).  Who got into office?
> >  2. Subtract your vote from that election.
> >  3. Recalculate the outcome without your vote (Q).
> >  4. Look at the difference between P and Q.
> >  5. Repeat for all the elections you ever participated in.

> Maybe we should make a difference between the technical analysis of
> the method and the real life impact of voting. Maybe terms
> "technical outcome" and "political outcome" could be used (although
> I note that you used the latter term in a different meaning few
> lines before this line). The first term refers to the method as a
> formally defined function. The latter terms may covers all aspects
> of the society, the impact of campaigns, impact of the numeric
> result of this election on the next election etc.

So the "political outcome" is the consequence for political power in
general.  The vote's effect on that power, or equivalently its share
of the political outcome, is its own "power", or "electoral power".
These seem to be good definitions.

I would argue that the numerical effects of the vote (a 7 vs. 6 in the
least significant digits) has no significant effect on political
power.  The only potential path for significant electoral power from
the vote appears to be its influence over who gets into office.  This
comes as no surprise, because it's the purpose of the electoral system
to staff offices.  I propose to call this the "official outcome".
Barring any other effects, the vote's share of the political outcome
can be taken as its share of the official outcome.

Where you say "real life impact of voting", I would say "real life
impact of the individual vote".  We may speak of voting in general,
but the premise speaks only of the individual vote.  The assertion of
its powerlessness cannot be refuted, of course, by the fact of the
election's overall power, so probably we needn't consider generalized
voting in this part of the argument. [3]

> True [of the abstract], if one considers only the formal output of
> the election and says "with high probability no effect in large
> elections if changed". I don't agree with "no effect whatsoever on
> the political outcome". Only the technical outcome [who wins] is
> unlikely to change if one vote changes in large elections.

I was thinking probabilities don't apply, because the actual results
are available.  Those results may include tie breaker/maker elections.
One option for dealing with those is to dismiss them altogether as
outliers or meaningless abnormalities.  I could leave it as a
challenge for others to gather evidence to the contrary.  I think this
is a valid approach, because it admits another point of fallability.

But how likely is the argument to fail on this point?  It seems
misleading to qualify the abstract "with high probability" or "except
once every 12,000 years or so", thus implying that tie breakers/makers
are likely to have significance.  There is probably no evidence for
this, and no reason to expect any.

Fred wrote:
> If only one person votes in an election, that person's vote decides
> the election.  As more people vote, their votes dilute the
> significance of the single deciding vote as expressed by 1/N.  As
> the electorate grows, the significance of an individual vote
> diminishes but does not reach zero (although it gets very close).
> ... It is proper to say the value of an individual's vote is
> effectively zero, but it is not mathematically so.

Maybe you are looking to the future here, because (like Juho above)
you are thinking in terms of probabilities.  But the empirical method
(1-5 above) measures the actual power of your vote *in past elections*
at exactly zero; unless you happen to get a different result for one
of your votes.  In either case, no probability enters into it because
the actual values are known.  Nor could a value ever be close to zero
*even in theory*, except when it was exactly zero. [1]

The reason is the rounding procedure that translates the vote count
into the official outcome (who gets into office).  In that rounding
procedure, either the effect of each vote is nullified, or (once every
12,000 years or so) the effect of each is made decisive.

I might be wrong, but I think the premise is strong.  A friend warned
me of the possibility that it might become a red herring, blinding
people to the rest of the thesis, but fortunately that hasn't happened
yet.  You gents raise questions about other sections, and I'll reply
to those separately.


 [1] For a more complete summary of the emprirical basis of the
     premise, please see this response to Juho:
     http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-October/028732.html

 [2] http://zelea.com/project/autonomy/a/fau/fau.xht

 [3] Elsewhere, the unexpected contrast between individual electoral
     power (zero) and collective election power (non-zero) can be
     taken as another manifestation of the structural fault that
     extends through society.

-- 
Michael Allan

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


Juho Laatu wrote:
> On 22.10.2011, at 1.42, Michael Allan wrote:
> 
> > Here is my latest attempt at a brief
> > summary with conclusions: [2]
> > 
> >  An individual vote in a general election has no meaningful effect in
> >  the objective world, and no effect whatsoever on the political
> >  outcome of the election; whether the vote is cast or not, the
> >  outcome is the same regardless.
> 
> True, if one considers only the formal output of the election and says "with high probability no effect in large elections if changed". I don't agree with "no effect whatsoever on the political outcome". Only the technical outcome is unlikely to change if one vote changes in large elections.
> 
> >  Beneath this fact lies an extensive
> >  structural fault
> 
> This is not a "flaw", but I wouldn't say "extensive structural fault" but something milder.
. . .

> >> - 1/N is maybe a better (although not perfect) estimate of the power
> >>  that one voter holds than 0
> > 
> > The value 1/N appears to be erroneous.  It is refuted by empirical
> > evidence that measures the value at exactly zero.  Again, the
> > experimental method is:
> > 
> >  1. Take the last election in which you voted, and look at its
> >     political outcome (P).  Who got into office?
> >  2. Subtract your vote from that election.
> >  3. Recalculate the outcome without your vote (Q).
> >  4. Look at the difference between P and Q.
> >  5. Repeat for all the elections you ever participated in.
> 
> Maybe we should make a difference between the technical analysis of the method and the real life impact of voting. Maybe terms "technical outcome" and "political outcome" could be used (although I note that you used the latter term in a different meaning few lines before this line). The first term refers to the method as a formally defined function. The latter terms may covers all aspects of the society, the impact of campaigns, impact of the numeric result of this election on the next election etc.
> 
> Juho


Fred Gohlke wrote:
> Good Morning, Michael
. . .
 
> re:  Comment to Juho Laatu, 20 Oct 2011:  "Recall that we already
>       discussed the power of one's vote.  Didn't we measure it at
>       zero, not 1/N?  The vote has no effect on the political
>       outcome of the election, therefore it has no power."
> 
> If only one person votes in an election, that person's vote decides the 
> election.  As more people vote, their votes dilute the significance of 
> the single deciding vote as expressed by 1/N.  As the electorate grows, 
> the significance of an individual vote diminishes but does not reach 
> zero (although it gets very close).
> 
> As Juho pointed out, interest groups form to attract votes to one side 
> of an issue or another.  As the interest groups grow in size, the effect 
> of their members' votes increases.  However, and this is the critical 
> point, for individuals that reject interest groups and vote their own 
> beliefs, the significance of their vote decreases as the size of the 
> electorate grows.  Thus, the value of the individual's vote approaches 
> zero (but never actually reaches it) because it is swamped by the votes 
> of special-interest groups.  It is proper to say the value of an 
> individual's vote is effectively zero, but it is not mathematically so.
> 
> Fred Gohlke