# VOTING POWER IN THE ELECTORAL COLLEGE by ufLjf8W

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```									                             Voting Power and the Electoral College

We learned from last class period that:
 The Electoral College is an example of a weighted voting system.
 The Banzhaf power index is used to quantify the share of power held by each voter in a
weighted voting system.
 In regards to weighted voting systems, it is important to understand that voting power is not
the same as (and is not proportional to) the number of votes; in particular voters with very
similar (but not identical) number of votes may have very different voting power; and
voters with quite different number of votes may have identical voting power.

We could use the Banzhaf power index to measure the relative power of the U.S. states in the Electoral
College. The table below shows the Banzhaf power index for each state (not the power of an
individual from that state).

The Electoral College and The Banzhaf Power Index

Percent of all Electoral
CA                             55                     10.22                       11.41
TX                             34                     6.32                         6.39
NY                             31                     5.76                         5.79
FL                             27                     5.02                         5.01
IL, PA                         21                     3.90                         3.87
OH                             20                     3.72                         3.68
MI                             17                     3.16                         3.12
GA, NC, NJ                     15                     2.79                         2.74
VA                             13                     2.42                         2.37
MA                             12                     2.23                         2.19
IN, MO, TN, WA                 11                     2.04                         2.01
AZ, MD, MN WI                  10                     1.86                         1.82
AL, CO, LA                     9                      1.67                         1.64
KY, SC                         8                      1.49                         1.46
CT, IA, OK, OR                 7                      1.30                         1.27
AR, KS, MS                     6                      1.12                         1.09
NM, NV, UT, WV                 5                      0.93                         0.91
HI, ID, NH, RI                 4                      0.74                         0.73
AK, DE, DC, MT,
ND, SD, VT, WY                 3                      0.56                         0.55
ME, NE                         2                      0.37                         0.36
Congressional
districts (5 in all)           1                      0.19                         0.18
We will look at the power of an individual from a certain state relating to the presidential election.
However, let’s first review the apportionment of electoral votes (i.e. the division and allocation of
Electoral College votes to states) in relation to states’ share of the U.S. population. It is well
known that there is a bias in favor of small states in this apportionment --

For example, consider California (a large state) and Wyoming (a small state).
Population of CA: 36,000,000
Electoral College Votes for CA: 55
A California voter’s share of the state’s electoral votes: 55/36,000,000 = .0000015

Population of WY: 500,000
Electoral College Votes for WY: 3
A Wyoming voter’s share of the state’s electoral votes: 3/500,000 = .000006 (4 times as large)

There is a popular belief that this implies an individual voter in Wyoming has 4 times as much
power as an individual voter in California. However, that is not true. Let’s analyze the situation
carefully and quantitatively. First, we note that the process of electing a president in the U.S. is
actually a two-stage voting system. In the first stage, individual voters from the state vote for
president to find which candidate wins that state. Then (in almost all states), the state uses all of
its electoral votes to vote in the electoral college for the candidate that won the state.

To continue, let’s compare the voting power of an individual voter in California and a voter in
Wyoming. Intuitively:
 In the first stage, the Wyoming voter has a greater chance of being a critical voter, simply
because there are fewer other voters in Wyoming and so that voter has a larger (though still
very small) chance of breaking what would otherwise be a tie in the Wyoming popular
vote.
 On the other hand, while the voter in California has a smaller chance of casting a decisive
vote, if that voter does cast a decisive vote, it is much more likely to determine the outcome
of the Presidential election, because it will tip 55 (rather than 3) electoral votes into one
candidate’s column or the other’s.
The question is, how do these relative advantages and disadvantages balance out?

Because of the huge number of possible coalitions of voters in an individual state, it is impossible
to calculate directly the Banzhaf power index of an individual voter within a state. However,
statistical theory tells us that an individual voter’s “likelihood” of being a critical voter in a
coalition within a state is roughly proportional to 1n , where n is the population of the state.
Because an individual voter’s likelihood of being a critical voter within a state and the likelihood
of that state being a critical voter in the Electoral College are independent events, it can be shown
that the Banzhaf power index of an individual voter in a state with population n is roughly

proportional to 1n times the Banzhaf power index of the state.

So, a quantitative analysis of the voting power of an individual voter in California and a voter in
Wyoming goes as follows.
1.The Banzhaf power index of a voter in California is roughly proportional to:

1
11.41  .0019
36,000,000


2. The Banzhaf power index of a voter in Wyoming is roughly proportional to:

1
 .55  .00078
500,000

3. Since .0019/.00078 = 2.4, the Banzhaf power index of an individual voter in California is
about 2.4 times that of the individual voter in Wyoming.


Choose at least two states other than California and Wyoming with different numbers of electoral
votes. Calculate the Banzhaf power index of an individual voter in each of these states. Consider
how this reflects upon the U.S. Electoral College system. Use this evidence in writing a letter to
the editor (two paragraphs in length) arguing for or against eliminating the Electoral College. Your
letter must include an explanation of the Banzhaf power index. Your calculations of the state’s
Banzhaf power index should be written up on a separate page. State populations can be found by
going to http://quickfacts.census.gov/qfd/. Your letter should be typed.

This assignment will be worth 30 points (10 points for presentation, 10 points for the calculations,
and 10 points for your explanation.)

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