[EM] The Electoral College (was Interesting use of Borda count)

Forest Simmons fsimmons at pcc.edu
Fri Jan 25 09:42:24 PST 2002

On Thu, 24 Jan 2002, Anthony Simmons wrote:


> [Forest wrote in part]
> >> See the discussion of this result at the URL
> >> http://www.cs.unc.edu/~livingst/Banzhaf/#results
> Hmmm, I'm a bit short on time presently, so I haven't worked
> this out, but it would seem that by the same criteria, when
> states are considered individual voters in the EC, that
> smaller states have more power, per voter, than larger
> states.  This at the same time that individuals in the small
> states have less power than their counterparts in large
> states.
> Of course, while this might be peculiar, there's nothing
> about it that requires that the power of a state be the sum
> of the power of the individual voters.

As Markus once pointed out, there are cases where block voting gives
disproportionate power to small blocks, and other cases where block voting
gives disproportionate power to large blocks. It's not always obvious in
any particular case whether the members of small or the members of large
blocks are the ones with the relative advantage. That's why the
simulations at the above URL are interesting and important. 

It turns out (in the current EC case) that even though the small states
have super proportional representation in the EC, that factor is not
enough to make up for the disproportionate power of the larger blocks
relative to the smaller blocks.

In the original configuration (immediately after the constitutional
convention) the smaller states probably had disproportionate power, at
least that was the intention.

Setting the EC aside, here are two simple examples showing that (1) small
blocks can have disproportionate power, and (2) large blocks can sometimes
have disproportionate power.  It just happens that the current EC is more
like the second example than the first.

(1) There are three voting blocks with votes of 48, 49, and 3,
respectively.  The block with three votes has just as much power as either
of the others (assuming a 50+ majority is the quota for passing a

(2) There are two voting blocks with votes of 51 and 49, respectively. The
block with 49 has nearly half the votes, but no voting power in deciding
any measure.

Suppose that in this last example, the block with 51 votes actually had 51
voters in it and that the block with 49 votes had only one voter in it
because of some special dispensation of voting rights.  

We might think that the voter with 49 votes had a relative advantage to
the typical voter with only one vote in the other block. 

Not so. The single voter with 49 votes has no influence on the outcome of
any election, while the voter with only one vote has approximately one
chance in nine of making a difference in the outcome of a randomly chosen

As Richard mentioned, block voting not only tends to give some voters
unfair advantage over others, it also dilutes the average voting power, so
that the typical voter has less influence in a block voting system than
he/she would have in a non-block system. 

It is ironical indeed that the small states are the ones most dead set
against getting rid of the EC system.

By the way, some states don't require their electors to vote as a block.
It would help a lot if the states were required to allocate their votes as
proportional as possible.  But the large states would never go for this,
since they would lose a relative advantage.


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