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Children are surrounded by social structures such as families, schools, and workplaces which are often arranged hierarchically with some people holding more power than others. This dissertation explores how children think about hierarchical relationships and more complex hierarchical structures. In Chapter 2, children were asked to evaluate the traits of people who hold hierarchically dominant and subordinate social roles. With age, 4- to 6-year-olds increasingly inferred that dominant individuals have social power and they deferred to their instructions (Chapter 2, Study 1). Furthermore, 5- and 6-year-olds attributed knowledgeability to individuals with dominant social roles but overall children did not prefer to ask those individuals for information (Chapter 2, Study 2). Chapter 3 extended these studies by presenting children with larger social structures depicting gender and racial inequality and asking children to recognize inequality (Study 1), rectify inequality (Study 2) and create social hierarchies (Study 3). Regardless of age, participants judged hierarchies with more than one woman or Black man in a position of power as fair. However, hierarchies with only one minoritized individual were judged as neutral in gender hierarchies or unfair in racial hierarchies (Chapter 3, Study 1). Children were also asked to rectify inequality by promoting individuals to positions of power in unequal control (arbitrary non-social color groups), gender, and racial hierarchies. Children selected to promote majoritized individuals to positions of power when they were arbitrary groups and children’s gender influenced their responses to gender inequality where girls promoted more women to positions of power than boys (Chapter 3, Study 2). Lastly, children created a social hierarchy without the influence of representations of inequality. In-group gender favoritism drove children’s selections where girls selected more women than men for every tier of the hierarchy but boys were only influenced by gender when selecting someone for the top of the hierarchy. When making racial hierarchies, children selected both White men and Black men equally to be in positions of power (Chapter 3, Study 3). These studies suggest that children can infer power from simple hierarchical structures and that they are motivated to rectify inequalities in more complex social structures.

Cube complexes and hierarchies of cube complexes have been studied extensively by Wise and feature prominently in Agol's proof of the Virtual Haken Conjecture for hyperbolic 3-manifolds. Among hyperbolic groups, Wise characterized hyperbolic virtually compact special groups as the hyperbolic groups that virtually admit a quasiconvex hierarchy terminating in finite groups. The main result of this thesis is that every relatively hyperbolic fundamental group of a virtually compact special non-positively curved cube complex virtually admits a quasiconvex hierarchy terminating in peripheral subgroups, answering a question due to Wise. The proof of the main theorem roughly follows the outline of Agol, Groves and Manning's New Proof of Wise's Malnormal Special Quotient Theorem for hyperbolic groups, but instead uses relatively hyperbolic geometric tools to prove that Wise's double dot hierarchy construction yields a quasiconvex hierarchy. Group theoretic relatively hyperbolic Dehn filling and the main theorem are used in the final chapter to provide a new proof of a relatively hyperbolic analog of Wise's malnormal special quotient theorem.

This dissertation is composed of three essays in microeconomic theory. The first and second essays are in the theory of matching, with hierarchical organizations and complementarities being their respective topic. The third essay is in on electoral competition and political polarization as a result of manipulation of public opinion through social influence networks. Hierarchies are a common organizational structure in institutions. In the first essay, I offer an explanation of this fact from a matching-theoretic perspective, which emphasizes the importance of stable outcomes for the persistence of organizational structures. I study the matching of individuals (talents) via contracts with institutions, which are aggregate market actors, each composed of decision makers (divisions) enjoined by an institutional governance structure. Conflicts over contracts between divisions of an institution are resolved by the institutional governance structure, whereas conflicts between divisions across institutions are resolved by talents' preferences. Stable market outcomes exist whenever institutional governance is hierarchical and divisions consider contracts to be bilaterally substitutable. In contrast, when governance in institutions is non-hierarchical, stable outcomes may not exist. Since market stability does not provide an impetus for reorganization, the persistence of markets with hierarchical institutions can thus be rationalized. Hierarchies in institutions also have the attractive incentive property that in a take-it-or-leave-it bargaining game with talents making offers to institutions, the choice problem for divisions is straightforward and realized market outcomes are pairwise stable, and stable when divisions have substitutable preferences. Complementarity has proved to be a challenge for matching theory, because the core and group stable matchings may fail to exist. Less well understood is the more basic notion of pairwise stability. In a second essay, I define a class of complementarity, asymmetric complements, and show that pairwise stable matchings are guaranteed to exist in matching markets where no firm considers workers to be asymmetric complements. The lattice structure of the pairwise stable matchings, familiar from the matching theory with substitutes, does not survive in this more general domain. The simultaneous-offer and sequential-offer versions of the worker-proposing deferred acceptance algorithm can produce different matchings when workers are not necessarily substitutable. If no firm considers workers to be imperfect complements, then the simultaneous-offer version produces a pairwise stable matching, but this is not necessarily true otherwise. If no firm considers workers to be asymmetric complements, a weaker restriction than no imperfect complements, then the sequential-offer version produces a pairwise stable matching, though the matching produced is order-dependent. In a third essay, I examine electoral competition in which two candidates compete through policy and persuasion, and using a tractable two-dimensional framework with social learning provide an explanation for increasing political polarization. Voters and candidates have policy preferences that depend upon the state of the world, which is known to candidates but not known to voters, and are connected through a social influence network that determines through a learning process the final opinion of voters, where the voters' initial opinions and the persuasion efforts of the candidates affect final opinions, and so voting behavior. Equilibrium level of polarization in policy and opinion (of both party and population) increases when persuasion costs decrease. An increase in homophily increases the equilibrium level of policy polarization and population opinion polarization. These comparative static results help explain the increased polarization in both the policy and opinion dimensions in the United States.

This report will build up the machinery of special hierarchies by discussing normal surfaces and boundary patterns. Then the report will use this construction to prove the Loop Theorem, following closely the proof presented by Marc Lackenby.

It has been more than twenty years since Duncan Kennedy published his seminal 'Legal Education and the Reproduction of Hierarchy'. In it he called for a radical assault on the hierarchies embedded in American law schools. But that assault failed. Over the past two decades, the hierarchies of legal education have, if anything, become even more fixed, insular, and status-driven, even while the elites of the practicing bar have changed dramatically and become more open to outsiders. It is vastly easier for the graduate of a fourth-tier law school to become a partner at an elite law firm than it is to be hired as a tenure-track assistant professor at even a non-elite American law school. But law school hierarchies may be changing. Not as the result of a critical assault, but because vast changes in communications technologies have seriously eroded the control of information that is necessary for the survival of any non-functional hierarchy. In this paper, written for a symposium on blogging by lawyers and law professors, I revisit the insider world of Kennedy's 'LERH' and contrast it with the outsider-dominated changes being wrought by the Internet.

In the first decades after colonialism, a radical and far-reaching process of social change took place in Cuban society. In the space of four decades, deeply entrenched status hierarchies with regard to race, nation, gender, and religion underwent major transformations. In the present study, I examine this process through a focus on the practice of Catholic marriage, and the changing institutional relationships of the Cuban Catholic church. As one of the most important institutions in colonial society, and a pillar of the old regime, the Catholic Church was deeply implicated in struggles over state and nation, the dynamics of gender and sex, and the construction of race and rank in Cuban society. While the Spanish monarchy was thrown out in 1898, the Church remained. Thus in seeking to break with the past and define a new society, Cubans at all levels were directly or indirectly forced into a series of confrontations and renegotiations with the Catholic Church. What would be the significance of the Church's mandates, institutions and practices in a modern, independent Cuba? What were the legitimate bounds of its influence? In the first section of the dissertation, The 1899 Marriage Law Controversy, I examine a battle over the regulation of marriage that took place during the first U.S. occupation of Cuba. Studying the motivations and ideologies of Catholic Church officials, Cuban statesmen, and U.S. military administrators who were the central protagonists in the controversy, I find that issues of nation, sovereignty, and empire lay at its very core. In the second section of the thesis, the construction of sexual norms and values amongst the rural poor is at the center of focus. I analyze a series of petitions filed on the behalf of couples seeking dispensation of the impediments of consanguinity and affinity in order to marry. These petitions were generated as part of the missionary work of the diocese of Havana, which sought to curb the practice of concubinage in the Cuban countryside, and to retain its waning influence among the local population. In the last section of the study, Sorting God's Children, I conduct quantitative analyses of 14,500 marriage records collected from three historic parishes in the city of Havana between 1902 and 1940. I seek to contribute to the demography of the family in republican Cuba, and to use marriage as a lens through which to elucidate the structure and dynamics of the social construct of race. Particular attention is given to the ways that race was marked and unmarked in parish marital records over time. The study is based on archival research in Cuba and in the U.S.

One common assumption in ecology is that the most abundant plants are the best competitors; however, few theotetical models predict this relationship. For example, models that invoke resource partitioning for plant coexistence assume each species is the superior competitor within their respective niches. Thus, abundance at equilibrium is dependent on niche size, not on competitive ability. Here, I explore the relationship between competitive ability and abundance by using both field and common garden experiments to compare rankings of natural abundance to rankings of competitive ability in old field perennials. I separated competitive ability into competitive effect (ability to suppress neighbors), size-uneven competitive response (ability for seedlings to tolerate or avoid suppression by adult neighbors), and size-even competitive response (ability for seedlings or adults to tolerate suppression by similar-sized individuals). I compared competitive effect using growth and size as performance indicators; I also used germination and survival when comparing competitive response. I generated fourteen independent competitive hierarchies. In each hierarchy, adjacent species commonly overlapped in their 95% confidence intervals but the best and worst competitors generally differed significantly in their competitive abilities. Altogether, rankings of competitive effect were significantly positively correlated with natural abundance, based on a meta-analysis of the distribution of Spearman-rank correlations. A meta-analysis also showed the distribution of correlations for size-uneven competitive response was significantly positive while the distribution for size-even competitive response was not. I found similar results in a literature review of plant competition studies. In addition to determining that some components of competitive ability are correlated with abundance, I found the magnitude of competition varies with the component of fitness measured. In a field experiment, competition significantly reduced growth in four of seven species but showed no effect on germination or survival. Also, based on a four-year removal experiment, the direct competitive effects of neighbors are lessened in the presence of other neighbor species, suggesting that the population-level response to competition is lessened because it integrates across the seedling and adult life stages, or that indirect effects are positive and lessen the negative direct effects of neighbors on targets.