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 