# [EM] Vote Management

Alex Small asmall at physics.ucsb.edu
Thu Apr 17 11:23:12 PDT 2003

```Forest Simmons said:
> How about groups of three.  Then every sub decision would be made by a
> two thirds majority.

One could make a good technical argument (not necessarily a good
political argument) for an electoral college that has Sqrt(N) members,
where N is the number of voters.  Here's a sketch of the argument:

Say that we have some measure of "voting power" p(n), where n is the
number of people voting in the election.  The voting power of an
individual would be the voting power he exercises in picking an elector,
multiplied by the voting power of the elector.  If d is the number of
districts and N is the total number of voters across all districts, then
an individual's net voting power P(d) is:

P(d) = p(d)*p(N/d)

The logarithm of P(d) is symmetric about the point d = Sqrt(N), so d =
Sqrt(N) is either a minimum or maximum of P(d).  Whether it's a minimum
or maximum depends on the form of p(n), but we can draw a reasonable
conclusion without trying to precisely define p(n).

If d = 1 or N we have the standard popular vote.  The only time an
individual has much clout is in a close election.  But, in a districted
election, even if the popular result isn't close (in 2000 the margin was
statistically significant) the districted result can still be close, so
a voter in a closely contested district can be pivotal.  It is hence
reasonable to assume that P(d) takes on a local maximum at d = Sqrt(N).

This is not a political argument in favor of an electoral college,
especially not our current one (with 100 million people voting in 2000,
the optimal size would be 10,000 districts of 10,000 people), but since
Josh raised the question of intermediate bodies I thought it was worth
throwing out as a thought.

Alex

```