VOTING POWER, COOPERATIVE GAMES, AND THE COURTS

PAUL EDELMAN

Vanderbilt University

April 22, 4:15pm
2-105

ABSTRACT 


In 1964, state and local legislative bodies were, for the first time,
required by law to meet the "one person, one vote" standard.  Rather than
reapportion themselves, a number of such bodies introduced alternative
methods of representation, such as allowing certain legislator's votes to
carry more weight than others, or to have multiple representatives from
the same district.  The question then arose, was this sufficient to meet
the constitutional requirement "one person, one vote."  And what does "one
person one vote" even mean in this context?

To answer these questions, techniques from cooperative game theory are
brought to bear, principally the Banzhaf index, which measures voting
power in these voting system.  I will introduce these ideas and show what
they tell us about a mathematical interpretation of "one person, one
vote."

These techniques have rather broad application, including to the Electoral
College, and the Supreme Court, itself.  In addition I will describe how
the mathematical arguments fared in the courts.  A number of open
problems, both mathematical and jurisprudential, will be discussed, as
well.




Return to Applied Math Colloquium home page