Has online dating increased social integration? The aim of this paper is to analyze the interdependent relationship between matching and the network in which the matching takes place. In a highly clustered network, the expected probability of a match between agents belonging to two different clusters is low. On the other hand, a high number of matches between agents belonging to different clusters will contribute to the integration of the clusters in the following period. I develop a model of meeting and matching that sheds light on the patterns of ethnic homophily observed in the marriage market. The model is a two-stage game: in the first stage, agents engage in a population game to strategically increase their set of acquaintances, with the objective of maximizing their expected indirect utility in the second stage. In the second stage, the actual matching occurs, with the restriction that agents can only match with individuals they are connected to in the network. The model is then used to investigate how changes in the meeting technology, such as the introduction of online dating, affect matching frequencies and couples’ assortativeness. In particular, the model is used to explain three empirical patterns of romantic relationships: (i) all ethnic groups are biased toward same-ethnicity partners, (ii) couples who meet online are more likely to be in an interracial relationship than those who meet offline, (iii) minorities who meet their partner online are significantly more likely to be in a relationship with a white person, but equally likely to be in a relationship with a member of another minority group other than their own. The model is estimated and the network effect is disentangled from the effect of preferences on matching probabilities. The estimates show that online dating has increased exposure of white people to minorities and viceversa, but it has not increased integration among minorities. Finally, the model estimates are used to form a prediction on the evolution of the clustering of the network over time with and without online dating.

In this paper we investigate the relationship between stability, optimality, and inequality in matchings with aligned preferences. We develop a definition of inequality that allows us to draw a comparison between different feasible matchings. We define a compatible ranking of pairs as a complete order over pairs that agrees with individual preferences. We prove that when preferences are aligned, a compatible ranking of pairs exists. From such ranking, we define the max-max-lexalgorithm that converges to a stable matching, and we prove the matching thus obtained coincides with the outcome of the Gale and Shapley algorithm. We show such a matching outcome causes more inequality than other Pareto-efficient matchings, and we propose an algorithm whose matching outcome minimizes inequality.

The choice correspondence properties of gross substitutability and irrelevance of rejected contracts are sufficient conditions for the existence of an equilibrium in a one-to-many matching setting. These properties are pervasive in the literature of decision theory, and have been formulated in many different ways by different authors. This work is aimed at reconciling all different formulations of substitutability and irrelevance of rejected contracts and relating these concepts to other properties of choice correspondences, such as rationalizability. The properties are investigated both at a primitive level of preferences and in the case in which preferences are representable by a function. In the latter case, I explore how both of these two conditions are present in matroid-based valuations and how the assumption of quasi-linearity in wages can be relaxed, while still satisfying gross substitutability and irrelevance of rejected contracts.

The aim of this paper is to quantify the long-term effects on exposure to different races and ethnicities caused by the “separate but equal” doctrine. *De jure *segregation applied to a range of public facilities, including transportation, hospitals, theaters and most importantly schools. The state of California led the way by being the first state to declare the "separate but equal” doctrine in the educational system unconstitutional, 7 years before it was declared unconstitutional at a federal level in 1954. Similarly, anti-miscegenation laws were outlawed at a federal level in 1967, but different states outlawed them at different times. In the state of California, laws banning interracial marriages where declared unconstitutional in 1948, while in the state of New York such laws were never in place. Through a comparison of historical data on married couples in the states of California and New York and exploiting the difference in legal decisions timelines in these two states, I am able to derive information on the structure of the social network in which those marriages took place. Through the analysis, I am able to estimate the probabilities of a connection existing between a white person and a minority group member in California and New York respectively. With these estimates, I am able to show how such probability has been impacted by the early abolition of “separate but equal” in California and how it has evolved over time.

An Allocation of Gale and Shapley to the City of New York

This paper is an exploration of multiple algorithms that can be applied in a geographical matching setting. There are two sides of the market, and each element of each side is fully described by their geographical coordinates. Each element on either side of the market has a preference ranking over possible matches. Individual preferences are dictated by a negative transformation of the distance that exists between the geographical coordinates of the individual and the geographical coordinates of their potential match. Three allocations are explored in this setting. A stable allocation, that arises from the application of a generalized version of the Gale and Shapley algorithm. An efficient allocation, which is obtained by minimizing the average distance between matched individuals. A bottleneck allocation, obtained by minimizing the maximum distance between matched individuals. The algorithms are applied to the case of students and schools in the New York City territory. Using data from the NYC Department of Education, I obtain the precise location and capacity of all public kindergartens, elementary, middle and high schools in New York City. Using Census data, I obtain the number of kids in the age range of interest in each Census tract in the city. Combining these data, I then apply a generalized version of the Gale and Shapley algorithm to explore the characteristics of the stable allocation. The stable allocation thus obtained causes inequality of treatment among students. It does indeed dictate that some students travel a short distance to go to the school they are assigned to, while others need to travel an unreasonably long one. It also has students living in the same Census tract going to different schools. This suggests that other allocations need to be explored in order to reduce inequality.

Octavia Ghelfi

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