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

[matt welland]

On Sat, 2011-08-27 at 16:22 -0400, Michael Allan wrote:
> > > But not for voting.  The voting system guarantees that my vote
> > > will have no effect and I would look rather foolish to suppose
> > > otherwise.  This presents a serious problem.  Do you agree?
> 
> Dave Ketchum wrote:
> > TRULY, this demonstrates lack of understanding of cause and effect.
> > 
> > IF the flask capacity is 32 oz then pouring in 1 oz  will:
> > . Do nothing above filling if the flask starts with less than 31 oz.
> > . Cause overflow if flask already full.
> > 
> > In voting there is often a limit at which time one more would have
> > an effect.  If the act were pouring sodas into the Atlantic the
> > limit would be far away.
> 
> Please relate this to an election.  Take an election for a US state
> governor, for example.  Suppose I am eligible to vote.  I say my vote
> cannot possibly affect the outcome of the election.  You say it can,
> under certain conditions.  Under what conditions exactly?

The meaning of an individual vote is mostly irrelevant and pointless to
discuss. If a barge can carry 10 tons of sand then of course at any
point in time while loading the barge no single grain of sand matters,
but will *you* get on that barge for a 300 mile journey across lake
Superior if it is loaded with 10.1 tons of sand? Probably not. Votes in
any election with millions of voters are like this, individually
irrelevant, but very meaningful as an aggregate. If there are ten
thousand people who share your values and will vote as you vote then
together you have a shot at influencing the outcome of the election with
20 thousand voters.

For single winner elections in the US we need the simplest system that
can force politicians to be accountable to aggregates of voters.
Plurality voting creates a situation where the force on the candidates
from these smaller groups is a small fraction of the natural or real
force. In my opinion this is *the* key issue to fix at this point in
history.

I noticed something interesting in that some polling I heard reported on
the radio for the Republican nominee candidate sounded like approval. It
was reported as a per candidate vote ("when asked, 20% of likely voters
would vote for X)". It really is a very natural way to vote and because
it is *aggregates* that matter a single vote for each candidate is all
that is needed to accurately articulate the will of the people. So back
to meaning of a vote. Well, in approval, if N is the number of
candidates and V the number of voters I guess you get a maximum of
(N*1/N)/V worth of influence. With plurality you get (1/N)/V for
influence so to really stretch the sand analogy, if you fill your barge
with plurality sand your 10.1 tons of sand might actually only weigh one
or two tons and you can sally forth on your 300 mile journey with nary a
worry.

A final analogy ...

I remember a science fiction story (maybe a Harry Harrison book?) where
a prison was constructed of a massive stone disc set in a stone recess.
The cells were along the edge of the disk such that the prisoners could
push on the outer stone wall but the gap was too small to escape. If
enough prisoners pushed on that wall the disk would move a few
centimeters. The only way out of the prison was to get the disk to make
a full rotation where the cell was exposed to an exit. If on a
particular day a prisoner didn't push on the wall you probably could not
measure the reduction in distance moved that day. The individual vote
(prisoner pushing on the wall) is irrelevant, but the aggregate is
meaningful.

This idea is so much a part of life it baffles me when people make the
claim that their vote is meaningless. It is blindingly obvious to me
that the only meaningful context for discussing a vote is as an
aggregate and using thus you must use statistical notions.

> Note my critique of Warren's proof in the other sub-thread:
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-August/028266.html
>