We study the issue of polarization in society through a model of opinion formation. We say an opinion formation process is polarizing if it results in increased divergence of opinions. Empirical studies have shown that homophily, i.e., greater interaction between like-minded individuals, results in polarization. However, we show that DeGroot's well-known model of opinion formation based on repeated averaging can never be polarizing, even if individuals are arbitrarily homophilous. We generalize DeGroot's model to account for a phenomenon well known in social psychology as biased assimilation: When presented with mixed or inconclusive evidence on a complex issue, individuals draw undue support for their initial position, thereby arriving at a more extreme opinion. We show that in a simple model of homophilous networks, our biased opinion formation process results in polarization if individuals are sufficiently biased. In other words, homophily alone, without biased assimilation, is not sufficient to polarize society. Quite interestingly, biased assimilation also provides a framework to analyze the polarizing effect of Internet-based recommender systems that show us personalized content.T he issue of polarization in society has been extensively studied and vigorously debated in the academic literature as well as the popular press over the last few decades. In particular, are we as a society getting more polarized? If so, why, and how can we fix it? Different empirical studies arrive at different answers to this question depending on the context and the metric used to measure polarization.Evidence of polarization in politics has been found in the increasingly partisan voting patterns of the members of Congress (1, 2) and in the extreme policies adopted by candidates for political office (3). McCarty et al. (4) claim via rigorous analysis that America is polarized in terms of political attitudes and beliefs. Phenomena such as segregation in urban residential neighborhoods (5-7), the rising popularity of overtly partisan television news networks (8, 9), and the readership and linking patterns of blogs along partisan lines (10-13) can all be viewed as further evidence of polarization. On the other hand, it has also been argued on the basis of detailed surveys of public opinion that society as a whole is not polarized, even though the media and the politicians make it seem so (14, 15). We adopt the view that polarization is not a property of a state of society; instead it is a property of the dynamics through which individuals form opinions. We say that opinion formation dynamics are polarizing if they result in an increased divergence of opinions.It has been argued using empirical studies that homophily, i.e., greater interaction between like-minded individuals, results in polarization (12,16,17). This argument has been used to claim that the rise of cable news, talk radio, and the Internet has contributed to polarization: the increased diversity of information sources coupled with the increased ability to narrowly ta...

We study the issue of polarization in society through a model of opinion formation. We say an opinion formation process is polarizing if it results in increased divergence of opinions. Empirical studies have shown that homophily, i.e., greater interaction between like-minded individuals, results in polarization. However, we show that DeGroot's well-known model of opinion formation based on repeated averaging can never be polarizing, even if individuals are arbitrarily homophilous. We generalize DeGroot's model to account for a phenomenon well known in social psychology as biased assimilation: When presented with mixed or inconclusive evidence on a complex issue, individuals draw undue support for their initial position, thereby arriving at a more extreme opinion. We show that in a simple model of homophilous networks, our biased opinion formation process results in polarization if individuals are sufficiently biased. In other words, homophily alone, without biased assimilation, is not sufficient to polarize society. Quite interestingly, biased assimilation also provides a framework to analyze the polarizing effect of Internet-based recommender systems that show us personalized content.T he issue of polarization in society has been extensively studied and vigorously debated in the academic literature as well as the popular press over the last few decades. In particular, are we as a society getting more polarized? If so, why, and how can we fix it? Different empirical studies arrive at different answers to this question depending on the context and the metric used to measure polarization.Evidence of polarization in politics has been found in the increasingly partisan voting patterns of the members of Congress (1, 2) and in the extreme policies adopted by candidates for political office (3). McCarty et al. (4) claim via rigorous analysis that America is polarized in terms of political attitudes and beliefs. Phenomena such as segregation in urban residential neighborhoods (5-7), the rising popularity of overtly partisan television news networks (8, 9), and the readership and linking patterns of blogs along partisan lines (10-13) can all be viewed as further evidence of polarization. On the other hand, it has also been argued on the basis of detailed surveys of public opinion that society as a whole is not polarized, even though the media and the politicians make it seem so (14, 15). We adopt the view that polarization is not a property of a state of society; instead it is a property of the dynamics through which individuals form opinions. We say that opinion formation dynamics are polarizing if they result in an increased divergence of opinions.It has been argued using empirical studies that homophily, i.e., greater interaction between like-minded individuals, results in polarization (12,16,17). This argument has been used to claim that the rise of cable news, talk radio, and the Internet has contributed to polarization: the increased diversity of information sources coupled with the increased ability to narrowly ta...

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Credit networks are an abstraction for modeling trust among agents in a network. Agents who do not directly trust each other can transact through exchange of IOUs (obligations) along a chain of trust in the network. Credit networks are robust to intrusion, can enable transactions between strangers in exchange economies, and have the liquidity to support a high rate of transactions. We study the formation of such networks when agents strategically decide how much credit to extend each other. We find strong positive network formation results for the simplest theoretical model. When each agent trusts a fixed set of other agents and transacts directly only with those it trusts, all pure-strategy Nash equilibria are social optima. However, when we allow transactions over longer paths, the price of anarchy may be unbounded. On the positive side, when agents have a shared belief about the trustworthiness of each agent, simple greedy dynamics quickly converge to a star-shaped network, which is a social optimum. Similar star-like structures are found in equilibria of heuristic strategies found via simulation studies. In addition, we simulate environments where agents may have varying information about each others’ trustworthiness based on their distance in a social network. Empirical game analysis of these scenarios suggests that star structures arise only when defaults are relatively rare, and otherwise, credit tends to be issued over short social distances conforming to the locality of information. Overall, we find that networks formed by self-interested agents achieve a high fraction of available value, as long as this potential value is large enough to enable any network to form.

We study a market for private data in which a data analyst publicly releases a statistic over a database of private information. Individuals that own the data incur a cost for their loss of privacy proportional to the differential privacy guarantee given by the analyst at the time of the release. The analyst incentivizes individuals by compensating them, giving rise to a privacy auction. Motivated by recommender systems, the statistic we consider is a linear predictor function with publicly known weights. The statistic can be viewed as a prediction of the unknown data of a new individual, based on the data of individuals in the database. We formalize the trade-off between privacy and accuracy in this setting, and show that a simple class of estimates achieves an order-optimal trade-off. It thus suffices to focus on auction mechanisms that output such estimates. We use this observation to design a truthful, individually rational, proportional-purchase mechanism under a fixed budget constraint. We show that our mechanism is 5-approximate in terms of accuracy compared to the optimal mechanism, and that no truthful mechanism can achieve a 2 − ε approximation, for any ε > 0.