Splash Biography

America's democracy is broken. That, at least, is a conclusion many seem to have reached. The culprit? According to some, it's a voting system that discourages people from voting their consciences and pushes candidates toward extreme ends of the political spectrum. Many reforms have been proposed, from instant run-off voting to increasing the number of congressional districts, and from requiring people to vote to using nonpartisan committees to redraw congressional districts. But will these reforms accomplish their goals? And if so, will there be unintended consequences? For voting rules at least -- such as instant-runoff voting, Borda's count, Copeland's method, and others -- it is possible to make mathematically precise definitions of desirable properties and prove whether or not they hold. For example, if I vote for candidates in instant-runoff voting in a way that doesn't match my true preferences, is it possible to secure an outcome I like better? (the answer is yes!) Using analysis of these voting rules as a jumping-off point, we will explore the mathematical advantages and disadvantages of many voting reforms proposed in the United States.