A Local-Dominance Theory of Voting Equilibria

It is well known that no reasonable voting rule is strategyproof. Moreover, the common Plurality rule is particularly prone to strategic behavior of the voters and empirical studies show that people often vote strategically in practice. Multiple game-theoretic models have been proposed to better understand and predict such behavior and the outcomes it induces. However, these models often make unrealistic assumptions regarding voters' behavior and the information on which they base their vote. We suggest a new model for strategic voting that takes into account voters' bounded rationality, as well as their limited access to reliable information. We introduce a simple behavioral heuristic based on \emph{local dominance}, where each voter considers a set of possible world states without assigning probabilities to them. This set is constructed based on prospective candidates' scores (e.g., available from an inaccurate poll). In a \emph{voting equilibrium}, all voters vote for candidates not dominated within the set of possible states. We prove that these voting equilibria exist in the Plurality rule for a broad class of local dominance relations (that is, different ways to decide which states are possible). Furthermore, we show that in an iterative setting where voters may repeatedly change their vote, local dominance-based dynamics quickly converge to an equilibrium if voters start from the truthful state. Weaker convergence guarantees in more general settings are also provided. Using extensive simulations of strategic voting on generated and real preference profiles, we show that convergence is fast and robust, that emerging equilibria are consistent across various starting conditions, and that they replicate widely known patterns of human voting behavior such as Duverger's law. Further, strategic voting generally improves the quality of the winner compared to truthful voting

On the convergence of iterative voting: how restrictive should restricted dynamics be?

We study convergence properties of iterative voting procedures. Such procedures are defined by a voting rule and a (restricted) iterative process, where at each step one agent can modify his vote towards a better outcome for himself. It is already known that if the iteration dynamics (the manner in which voters are allowed to modify their votes) are unrestricted, then the voting process may not converge. For most common voting rules this may be observed even under the best response dynamics limitation. It is therefore important to investigate whether and which natural restrictions on the dynamics of iterative voting procedures can guarantee convergence. To this end, we provide two general conditions on the dynamics based on iterative myopic improvements, each of which is sufficient for convergence. We then identify several classes of voting rules (including Positional Scoring Rules, Maximin, Copeland and Bucklin), along with their corresponding iterative processes, for which at least one of these conditions hold

Approval-Based Shortlisting

Shortlisting is the task of reducing a long list of alternatives to a (smaller) set of best or most suitable alternatives from which a final winner will be chosen. Shortlisting is often used in the nomination process of awards or in recommender systems to display featured objects. In this paper, we analyze shortlisting methods that are based on approval data, a common type of preferences. Furthermore, we assume that the size of the shortlist, i.e., the number of best or most suitable alternatives, is not fixed but determined by the shortlisting method. We axiomatically analyze established and new shortlisting methods and complement this analysis with an experimental evaluation based on biased voters and noisy quality estimates. Our results lead to recommendations which shortlisting methods to use, depending on the desired properties

Three Puzzles on Mathematics, Computation, and Games

In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear programming. The second puzzle is about errors made when votes are counted during elections. The third puzzle is: are quantum computers possible?Comment: ICM 2018 plenary lecture, Rio de Janeiro, 36 pages, 7 Figure

Path dependence or convergence? The evolution of corporate ownership around the world

We offer a theory that sheds light on the current debate over whether the form of corporate ownership converges to the Berle-Means image. Our analytical results are threefold. First, legal rules and firm-specific protective arrangements are complementary. Secondly, corporate ownership patterns can be convergent or path dependent depending on the relative importance of these protective arrangements. We predict, for example, diffuse stock ownership in countries that impose legal limits on blockholders’ power to expropriate minority investor rights. Thirdly, we find that convergence toward diffuse share ownership is a movement towards the social optimum. Our empirical results suggest a case for the co-existence of path dependence and functional convergence (convergence to the diffuse form of share ownership through cross-listings on U.S. stock exchanges that impose more stringent disclosure and listing requirements). These results have implications for the design of executive compensation, the case for institutional investor activism and the proposal to increase shareholder power

Why the Voting Gap Matters

Over the last half-century, affluent Americans have turned out to vote at significantly higher rates than lower-income Americans

All Together Now: Collaboration and Innovation for Youth Engagement

Each new generation must become active, informed, responsible, and effective citizens. As a teacher we surveyed for this report said, civic education "is essential if we are to continue as a free democratic society. Not to educate the next generation will ensure the destruction of our American way of life as we know it."Data show that many young Americans are reasonably well informed and active. For instance, 45% of citizens between the ages of 18 and 29 voted in the 2012 election. In a national survey conducted for this Commission, 76% of people under the age of 25 who voted could correctly answer at least one (out of two) factual questions about where the presidential candidates stood on a campaign issue and state their own opinion on that issue.On the other hand, more than half of young people did not vote. And on some topics, most young people were misinformed. A majority (51.2%) of under 25-year olds believed that the federal government spends more on foreign aid than on Social Security, when in fact Social Security costs about 20 times more. (Older adults have also been found to be misinformed on similar topics.) Our research, like many other studies, finds that young people from disadvantaged backgrounds are far less likely to be informed and to vote.These shortcomings cannot be attributed to the schools alone, since families, friends, political campaigns, election officials, the mass media, social media, and community-based organizations are among the other important influences on young people. In fact, our research shows that while schools matter, civic education must be a shared responsibility.The outcomes are acceptable only when all the relevant institutions invite, support, and educate young people to engage in politics and civic life. Improving the quality and quantity of youth participation will require new collaborations; for example, state election officials and schools should work together to make voting procedures understandable and to educate students about voting rules