[EM] Are voters in larger or smaller states more powerful?

Rob LeGrand honky1998 at yahoo.com
Fri Jun 15 12:12:09 PDT 2001

Blake wrote:
> The province populations are 48%, 48% and 4%.  The give 48, 48, and 4
> votes respectively.  So, winning any two provinces wins the election.
> A candidate is as concerned about winning the small province as either
> of the larger ones.  So, the small province is disproportionately
> influential.  I don't think that the advantage for large states in
> your example can be generalized.

There are two ways generally used to measure actual power in this kind of case:
the Shapley-Shubik index and the Banzhaf index.  See Weighted Voting Systems at
http://www.ctl.ua.edu/math103/POWER/wtvoting.htm .  Usually the two give very
similar results; in the case above, they both correctly assign equal power to
all three provinces, showing that voters in the smallest province are much,
much more powerful than the others.  I've never seen a power analysis of the
U.S. Electoral College, but I'd be willing to bet that voters in smaller states
are almost always more powerful than those in larger states.  Unfortunately,
giving states power even roughly proportional to their populations is difficult
in most cases, which is only one reason I see the Electoral College as
ridiculous.  Also see http://www.russp.org/electionmethods.org/college.htm .

Rob LeGrand
honky98 at aggies.org

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