Mathematical Models Of Collective Action 
S06
Robert Page
Why is it that the greater societal good so often gets hijacked by small, special-interest groups? An attempt to answer this question was offered by Mancur Olson in The Logic of Collective Action. His central tenet is that small groups are more likely to succeed in providing a ‘public good’ than are larger groups. Among the first to rigorously connect collective action with game theory was Russell Hardin in Collective Action, which emphasized the dynamic nature of an individual’s decisions toward group action. A result is that truly collective action was recognized as more likely to occur than previously postulated. In The Possibility of Cooperation, Michael Taylor gives an account of the collective action problem and its representation by a range of games such as the Chicken Game, the Game of Assurance, and the Prisoner’s Dilemma game. Through a detailed analysis of the Prisoner’s Dilemma game (which we shall see is the worst-case scenario for collective action success) we will hope to conclude that voluntary cooperation is possible even if individuals only seek to maximize their own payoffs.Statistics, by far the most pervasive application of mathematics in modern society, is a standard analytical tool in such diverse fields as biology, psychology, medicine, business, and marketing, and the determination and manipulation of public opinion. Its apparent mathematical invincibility belies the ease with which it can be abused to assist corporate, political, and even scientific agendas. In addition to critiquing the uses of statistics that we encounter in the media and our professional fields, we will develop an ability to use statistics responsibly to reflect the information implied in data. Specific topics include descriptive statistics, distributions, hypothesis testing and confidence intervals, regression and correlation, and analysis of variance.