a game-theory thought on the popular vote amd a follow-up

Topics: Democracy
10 Nov 2000

From: Ervan Darnell



Many people are now calling for the abolition of the electoral college on
the theory that it doesn't accurately demonstrate the will of the people,
as evidenced by this election if Bush is declared the winner. This
is not an accurate reading of what happened.

Both players knew the game when it started and both played to win
electoral votes, not popular votes. Their campaign strategies, in
terms of ads and appearances, were tailored to this. More
importantly, their policies (at least their claimed policies) were also
tailored to appeal to voters in swing states (even if one doesn't believe
that campaigning per se matters).

Had the election been based on the popular vote instead of electoral
votes, the popular vote would likely have been even closer that it
is. For instance, Bush would not have abandoned California since
extra investment there would have mattered. Instead Bush and
Gore both invested in Florida and other swing states. Given the
dynamic going in, the electoral vote may actually be a better
representation of public desire than the popular vote.


---------------------

I couldn't have chosen a worse election to make my point about the
futility of voting. I still believe the analysis. I think the
only issue is deciding what the real bias factor is. In the case of
FL, it appears to be <0.1%.

The interesting question is: what is the probable biasing factor?
It's a testament to the effectiveness of modern campaigns that the bias
is routinely around 1% and often much less. Pollsters and advisors
are helping candidates ruthlessly seek the middle as a way of maximizing
their vote. They are getting better at doing just that. I
took 0.1% as a historically low bias. So, the value of your vote
mattering depends on the probable distribution of the bias factor as well
as the distribution once it's set.

I've heard several people suggest the electoral college makes your vote
worth more. Stated that way, it's surely false as it cannot be
possible to simultaneously make everyone's vote worth more.
However, it is possible that the chance of being a tie-breaker can be
increased (for instance, if one person is chosen at random and that
person's vote is the only that matters, your chance of being the tie
breaker is 1/n, no matter the bias of everyone else). These are
subtlety different statements.

The electoral college does affect the chance of your being the
tie-breaker, but not much. Take the limiting case of no bias (p=.5
and the candidates are exactly equally preferable), then the collective
decisions of states are random like individuals. For n people and N
states, the probability of being the tie breaker is then Q(N)*Q(n/N)
(using my previous notation) which works out to be 2/(pi*sqrt(n)) versus
sqrt(2/(pi*n)), i.e. your vote is only 20% more likely to matter in one
scenario than the other, hardly significant. A somewhat more
refined analysis reaches the same conclusion [1]. If p != .5, the
assumption that states are random events liked individuals is not
accurate, but I'll leave that analysis to someone else.
------------------------------------
[1]
http://macht.arts.cornell.edu/work/wrm1/fall99/gov317/pdecisive/node1.html





===============================================================

Ervan
Darnell
|"Term limits are not enough.

ervan@iname.com
| We need jail."













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