states in an electoral college of 100 votes. The states have 49, 48, and 3
electoral votes. To compute the BPI of the 3-vote state, we count the losing
coalitions that become winning ones once the 3-electoral-vote state joins
it. By itself, the 49-vote state is a losing coalition, but if the 3-vote state
joins it, the 52-vote total assures victory. Similarly, by itself the 48-vote
state loses, but if the 3-vote state joins it, the coalition is a winning one.
This computation shows that the 3-vote state has a BPI of 2, as does each
of the other states. The small state has tremendous clout in this election,
far out of proportion to its actual electoral total, and the candidates should
be working just as hard to win this state as either of the big ones.
The opposite side of this picture is that a state with an apparently sizable
number of electoral votes may actually be powerless to swing an election.
If there are three states, each with 26 electoral votes, and a fourth state
with 22 electoral votes (again, the electoral vote total is 100), whichever
candidate wins two of the large states wins the election; it makes no dif-
ference how the small state votes. There is no losing combination of states
the small state can join that will turn that combination into a winner; the
small state has a BPI of 0. Each of the big states has a BPI of 4, as it can
join either of the other big states, or an alliance of a big state plus the
small state, and turn a losing combination into a winning one. The voters
of the small state are effectively disenfranchised.
Power index analyses have been done that show that a California voter is
almost three times as likely to swing a presidential election as a voter
from the District of Columbia.^2 So everyone knows that the Electoral Col-
lege is not a truly democratic way to decide a presidential election—but
how we measure this depends upon the mathematics one chooses to use
to analyze the situation.
In an ideal democracy, each vote should have equal weight, so we might
decide to give each voter a total of 100 points, and ask him to distribute
those points among the various candidates. Called the preference inten-
sity method, a variation of this was used for more than a century in deter-
mining the members of the Illinois House of Representatives.^3 A simple
example shows that there are potential problems with this method. Con-
sider an election with two candidates, A and B, and three voters (we could
as easily be discussing larger groups of people as well as individuals). The
first voter allocates 100 points to A and none to B, whereas the other two
voters allocate 70 points to B and 30 points to A. A majority prefers B to A,
but the lone voter that prefers A to B carries the day, as A wins the elec-
tion by 160 points to 140. Are we content with an election process that al-
lows a vocal minority to outshout the majority?
The investigation of the problems in determining which voting
Cracks in the Foundation 207