Additionally, it is highly unlikely that any California voter would have
knowledge of how the other voters would cast their ballots; but once
again, in small elections such as committee chairmanships or nominat-
ing conventions, it is not at all unlikely that there would be voters possess-
ing such knowledge. Voting in the United States Senate also seems
subject to insincere voting; there is a time frame established for many
votes, and the running tabulation is openly displayed. As a result, even
though the Gibbard-Satterthwaite theorem is far less widely known than
Arrow’s celebrated result, it is nonetheless not only a significant contribu-
tion to the social sciences, but also one with considerable real-world rami-
fications.Fair Representation
In an ideal democracy, everyone who wishes to participate in the decision-
making process would be able to do so by casting a vote. However, the
Founding Fathers recognized that most people were too occupied with
their lives—with such essentials as farming, shopkeeping, or manufac-
turing—to be constant participants, and opted for a republic rather than
a democracy. In a republic, the voters elect their representatives, who
make the decisions.
Unfortunately, under a republican system, it is impossible for all the fac-
tions to be fairly represented. A simple example of this might be some
political body with five different subgroups, but only three leadership po-
sitions. At least two of those subgroups must necessarily be excluded
from the leadership.
The American republic has a similar problem. Election to each of our
houses of Congress is done on a state-by-state basis. The Senate has two
members from each state, so in that house every state has an equal share
of leadership positions. Membership in the House of Representatives is a
little trickier. The House has a fixed number of representatives (435); the
allocation of representatives to each state is done on the basis of the cen-
sus, which is performed every ten years. It doesn’t seem like such a diffi-
cult job to determine how many representatives each state should get: if a
state has 8 percent of the total population, it should receive 8 percent of
the representatives. A quick calculation shows that 8 percent of 435 is
34.8, so the question is whether to round off that .8 of a representative to
34 or 35.
Most elementary school students learn the following algorithm for
rounding numbers to whole numbers: round to the nearest integer un-
less the number to be rounded is midway between two integers (such as
The Smoke- Filled Rooms 227