The purpose of this article is to present a sample from the panoply of formal theories on voting and elections to Statistical Science readers who have had limited exposure to such work. These abstract ideas provide a framework for understanding the context of the empirical articles that follow in this volume. The primary focus of this theoretical literature is on the use of mathematical formalism to describe electoral systems and outcomes by modeling both voting rules and human behavior. As with empirical models, these constructs are never perfect descriptors of reality, but instead form the basis for understanding fundamental characteristics of the studied system. Our focus is on providing a general, but not overly simplified, review of these theories with practical examples. We end the article with a thought experiment that applies different vote aggregation schemes to the 2000 presidential election count in Florida, and we find that alternative methods provide different results.

Most theoretic models of multiparty electoral competition make the assumption that party leaders are motivated to maximize their vote share or seat share. In plurality-rule systems this is a sensible assumption. However, in proportional representation systems, this assumption is questionable since the ability to make public policy is not strictly increasing in vote shares or seat shares. We present a theoretic model in which party leaders choose electoral declarations with an eye toward the expected policy outcome of the coalition bargaining game induced by the party declarations and the parties' beliefs about citizens' voting behavior. To test this model, we turn to data from the 1989 Dutch parliamentary election. We use Markov chain Monte Carlo methods to estimate the parties' beliefs about mass voting behavior and to average over measurement uncertainty and missing data. Due to the complexity of the parties' objective functions and the uncertainty in objective function estimates, equilibria are found numerically. Unlike previous models of multiparty electoral competition, the equilibrium results are consistent with the empirical declarations of the four major Dutch parties.

In an election, voting power---the probability that a single vote is decisive---is affected by the rule for aggregating votes into a single outcome. Voting power is important for studying political representation, fairness and strategy, and has been much discussed in political science. Although power indexes are often considered as mathematical definitions, they ultimately depend on statistical models of voting. Mathematical calculations of voting power usually have been performed under the model that votes are decided by coin flips. This simple model has interesting implications for weighted elections, two-stage elections (such as the U.S. Electoral College) and coalition structures. We discuss empirical failings of the coin-flip model of voting and consider, first, the implications for voting power and, second, ways in which votes could be modeled more realistically. Under the random voting model, the standard deviation of the average of n votes is proportional to $1/\sqrt{n}$, but under more general models, this variance can have the form $cn^{-\alpha}$ or $\sqrt{a-b\log n}$. Voting power calculations under more realistic models present research challenges in modeling and computation.

The 2000 presidential election was the most controversial U.S. election in recent history, mainly due to the disputed outcome of the election in Florida. Elsewhere in this issue, Richard Smith analyzes the high vote for Pat Buchanan in Palm Beach county. As background for his article, we summarize this and other voting-related issues that may have affected the outcome of the election in Florida, such as the undervote in counties that used a punch-card ballot and the overvote in counties that used multicolumn and multipage ballots.

This article presents a statistical analysis of the results of the 2000 U.S. presidential election in the 67 counties of Florida, with particular attention to the result in Palm Beach county, where the Reform party candidate Pat Buchanan recorded an unexpectedly large 3,407 votes. It was alleged that the "butterfly ballot'' had misled many voters into voting for Buchanan when they in fact intended to vote for Al Gore. We use multiple regression techniques, using votes for the other candidates and demographic variables as covariates, to obtain point and interval predictions for Buchanan's vote in Palm Beach based on the data in the other 66 counties of Florida. A typical result shows a point prediction of 371 and a 95% prediction interval of 219--534. Much of the discussion is concerned with technical aspects of applying multiple regression to this kind of data set, focussing on issues such as heteroskedasticity, overdispersion, data transformations and diagnostics. All the analyses point to Buchanan's actual vote as a clear and massive outlier.

Vidyadhar Prabhakar Godambe was born on June 1, 1926, in Pune, India. He received the M.Sc. degree in Statistics from Bombay University in 1950 and the Ph.D. from the University of London in 1958. Between periods of study, from 1951 to 1955, he was a Research Officer in the Bureau of Economics and Statistics of the Government of Bombay. Following a year as Visiting Lecturer at the University of California, Berkeley (1957--1958), and a year as Senior Research Fellow at the Indian Statistical Institute in Calcutta (1958--1959), he became Professor and Head of the Statistics Department at Science College in Nagpur. He was promoted to the position of Professor and Head of the Statistics Department in the Institute of Science, Bombay University, in 1962. In 1964, he left India for North America, becoming for one year a Research Statistician at the Dominion Bureau of Statistics in Ottawa. After subsequent Visiting Professorships at Johns Hopkins University and the University of Michigan, he joined the University of Waterloo Department of Statistics in 1967 and has been at Waterloo ever since.

Professor Godambe is a Fellow of the American Statistical Association, a Fellow of the Institute of Mathematical Statistics, a Member of the International Statistical Institute, and an Honorary Fellow of the International Indian Statistical Association. He is the recipient of the 1987 Gold Medal of the Statistical Society of Canada and is an Honorary Member of that society. Upon his retirement in 1991 he was awarded the title of Distinguished Professor Emeritus at the University of Waterloo.

The following conversation took place in Waterloo in August 2000, mainly by correspondence. Some of the responses are taken from "Briefly about myself,'' an autobiographical piece written by Professor Godambe in 1998--2000.