In many theories of group choice a dominance relation expressing the ability of alternatives to "defeat" or replace others is the central object on which various solutions are based. I present and argue for the use of a particular sub-relation of the dominance relation called the ultimate challenges relation as a basis for solutions in abstract systems. This derived relation is the largest sub-relation with the property that all win-sets are "self-consistent" with the ultimate challenges relation itself. When a group collectively and iteratively considers alternatives and compares them to possible replacements, the challenges relation is a useful and appropriate device for reasoning about stable outcomes. It reflects a form of iterated reasoning about the replaceability of a status quo by another alternative. Based on this new relation I propose a new solution in abstract systems. I apply it to cooperative majority voting which results in a modification to the tournament equilibrium set, potentially addressing some issues in the original solution.

Strategic abstentions are a poorly understood feature of legislative voting records. This paper discusses a spatial model for legislators revealed preferences that accounts for abstentions driven by competing principals. A particularly appealing feature of our model is its ability to identify legislators that consistently engage in strategic abstentions, as well as bills for which the position of the legislator in policy space is a key driver of abstentions. We illustrate the performance of our model through the analysis of two datasets, one from the period leading to the Second Reform Act of 1867 in the UK House of Commons, and one from the second session of the 108th U.S. Senate.

Moser et al. (2009) provide one formalization of heresthetics - the art of political strategy - in collective choice settings. In doing so they introduce the heresthetically stable set as the set of outcomes least susceptible to manipulation of issue dimension. In this paper we examine the heresthetically stable set as a tournament solution, establishing some basic properties it possesses. In addition, we relate the heresthetically stable set to other tournament solutions, notably the Weak Uncovered and refinements thereof.

In this article we consider a model where boundedly rational agents choose both which coordination game to play and what action to take in that game, when their information and mobility are limited and changes over time. We completely characterize both short-run and long-run outcomes. There are multiple types of short-run predictions in which agents may be at different locations, taking different actions. In the long-run, however, all agents are at the same location and take the same action in that game. The long-run prediction is unique and globally efficient most of the time.

We present a formal model of international bargaining between two states in which one government must negotiate with a domestic opposition faction to secure tax revenue to fund military spending. It examines how robust the international order is to random domestic political crises that activate a stark tradeoff to a governing coalition: fiscal relief to stave off domestic revolution can simultaneously undermine the larger international political order via sizable shifts in the relative distribution of military power between states. We find that the likelihood of preventive war is shaped by two key domestic conditions: the distribution of income within an economy and the relative economic stake that opposition groups possess in international settlements.

Supplemental Information here.

The Second Reform Act ushered in the age of democratic politics in the UKs by expanding the voting franchise to include the working classes and providing new representation to industrialized cities. The circumstances of its passage provide an opportunity to analyze mechanisms of electoral reform. Explanations of democratic electoral reform often focus on constituency-level and elite partisan behavior. Using unsupervised topic model analysis of parliamentary debates and quantitative analysis of roll call votes, we investigate why electoral reform successfully passed the House of Commons in 1867. Specifically we consider why reform passed under a Conservative government while a similar bill failed under a Liberal government despite no election or change in membership of the House of Commons. We find that party, not constituency, is responsible for explaining votes on reform and that, ultimately, it was the reduction in the number of aspects in the debate over reform that allowed Conservatives to pass bill.

Supporting Information here.

``Binary Relations from Tournament Solutions, and Back Again'' (with Daniel Allcock )

(working paper)

We present a generalization of an abstract model of group choice in which the process of collective choice is modeled as a cooperative process of consideration and reconsideration of alternatives. We develop a general framework for studying choice from a finite set of alternatives, using the idea that one alternative may challenge or displace from consideration another in the course of a group choosing. From this binary relation the challenges relation new tournament solutions are obtained, the limit of which is the central object of the present study. The model presented generalizes that of contestation [Schwartz, 1990] and we characterize the set of alter- natives that can be chosen in a collective choice setting when the process of collective choice is viewed as cooperatively considering and reconsidering alternatives. Basic properties of the family of tournament solutions studied are given as well.

This paper introduces new methods for ranking alternatives in collective choice situations. The new methods reflect aspects of robustness of alternatives when voters vote strategically, and discriminate among elements of the Banks set [Banks, 1985]. The new scoring methods are compared to traditional scoring methods and related to the amount of intransitivity (specifically, the size of the top-cycle and the size of the Banks set) in collective choice settings. The new scores are shown to measure important aspects of alternatives not captured by extant scoring methods.

This note introduces a family of new tournament solutions based on the contestation relation [Schwartz, 1990] and relates them to existing refinements of the Banks set. Additionally, the connection between the contestation relation and general tournament solutions is discussed.

``Informational Consequences of Agenda Procedures'' -- 2009 (last updated July 2011)

(working paper)

Agenda procedures are an important aspect of political decision making in legislatures. This paper compares different agenda forms and evaluates them on their ability to amalgamate information. I model voters with private information, but subject to party pressures, voting in a common value environment and use this model to compare different agenda forms. Special attention is paid to two agenda forms commonly used in practice: the amendment agenda and the sequential elimination agenda. I find that amendment agendas select superior outcomes more often than sequential elimination agendas when there is much ex-ante uncertainty; that the amendment agenda is better able to extract information from votes, but this information can be to the detriment of a group if information is of poor quality.

``The Structure of Heresthetical Power'' (with John W. Patty and Elizabeth Maggie Penn)
Journal of Theoretical Politics, 21(2): 139-159, 2009.
doi:10.1177/0951629808100761

(This version corrects the typos printed in the appendix)

This article considers manipulation of collective choice in such environments, a potential alternative is powerful only to the degree that its introduction can affect the collective decision. Using the Banks set (Banks, 1985), we present and characterize alternatives that can, and those that can not, affect sophisticated collective decision-making. Along with offering two substantive findings about political manipulation and a link between our results and Riker's concept of heresthetic, we define a new tournament solution concept that refines the Banks set, which we refer to as the heresthetically stable set.

Remarkable levels of coordination are observed among social agents; yet the exact mechanisms by which such agents coordinate are not well understood. Here we examine the role of communication in achieving coordination--in particular, does endowing agents with the ability to communicate lead to more favorable outcomes? To pursue this question we employ an adaptive model of strategically communicating agents (Miller et al., 2002) playing the Stag Hunt game. We find that communication plays a key role in the ability of agents to reach and maintain superior coordination. In the absence of communication, agents tend to get trapped at the inferior coordination point. However, once agents reach a particular strategic threshold, sending even a priori meaningless messages serves to increase the likelihood that the population will coordinate on the superior outcome. While the system spends the majority of its time with well-coordinated behavior, it is not static--such periods are often punctuated by brief transitions in which the system switches to the alternative coordination point. We analyze the various mechanisms that account for this dynamic behavior and find that there are a few critical pathways by which the system transitions from one coordination point to another. Communication plays a critical, yet short-lived, role in one key pathway. Our analysis suggests that giving agents the ability to communicate even a priori meaningless messages may promote the emergence of a rich, and often robust, ``ecology'' of behaviors that allows agents to achieve new, and in this case superior, outcomes.