[EM] banzhaf myth

[Warren Smith]

Re Banzhaf myth

the first trouble with Mark Livingston's
Banzhaf-power-computing program cited by Forest

http://www.cs.unc.edu/~livingst/Banzhaf/#results

is it uses an 2^N - time algorithm.
("I ran my implementation on the current (1990) U.S. census distribution of the Electoral College. \
I used 4.29 billion samples in the Monte Carlo estimation of the probability for the states to be c\
ritical by Banzhaf's definition. The program took a little under 25 hours to complete.")

If you instead use my own program (available on my web page
  http://www.math.temple.edu/~wds/homepage/
since 2000) then you will get an exact (not Monte Carlo)
computation running in under 1 second.

The second trouble is the voting-power concept itself.
That idea is, if you have N voters with
different weights W[1], W[2]..., W[N],
then the "voting power" of voter K is defined as the probability that
her vote will swing the election, given that everybody's vote is got by
independent coin tosses (2^N possible voting patterns).

That's fine, but the coin toss assumption is often not realistic.
In a big-vs-small states issue, view the small states (corrssponding to the bottom
50% of the US population) as voting as a bloc vs the big ones.  Then the
small states always win.

Applied to the USA, you can, e.g. say the each state has W[K]=#electoral votes
and ask for its voting power in pickign the president in a 2-way race.
You also can say that each human voter has a certain voting power in swinging
her  state's electoral vote.  Multiply those two powers together and you
get the voting power of Joe Voter in each state.  Lo and behold, large-state
voters (californians) have way more voter power.

Third trouble: the resullting numbers are largely irrelevant to reality.
Because independent coin toss model is bogus in reality.  Bloc voting (dependencies galore)
is more realistic.  In reality the small states are the more powerful.
If every Joe Voter in a small state (100 million) votes A and every Joe in a big
state voted B, then A would win.

And as raphfrk pointed out, the US Senate totally gives the edge to the small states.
The approximation of treating the senate+house as a homogeneous mas and each state
as a W[K]-weight vote, is just bogus.

Finally, this all is proven by the fact the small states
are the ones getting the federal money.

wds
http://rangevoting.org