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## Bayesian Analyses of Political Decision Making

Bayes’ theorem is a relatively simple equation but one of the most important mathematical principles discovered. It is a formalization of a basic cognitive process: updating expectations as new information is obtained. It was derived from the laws of conditional probability by Reverend Thomas Bayes and published posthumously in 1763. In the 21st century, it is used in academic fields ranging from computer science to social science. The theorem’s most prominent use is in statistical inference. In this regard, there are three essential tenets of Bayesian thought that distinguish it from standard approaches. First, any quantity that is not known as an absolute fact is treated probabilistically, meaning that a numerical probability or a probability distribution is assigned. Second, research questions and designs are based on prior knowledge and expressed as prior distributions. Finally, these prior distributions are updated by conditioning on new data through the use of Bayes’ theorem to create a posterior distribution that is a compromise between prior and data knowledge. This approach has a number of advantages, especially in social science. First, it gives researchers the probability of observing the parameter given the data, which is the inverse of the results from frequentist inference and more appropriate for social scientific data and parameters. Second, Bayesian approaches excel at estimating parameters for complex data structures and functional forms, and provide more information about these parameters compared to standard approaches. This is possible due to stochastic simulation techniques called Markov Chain Monte Carlo. Third, Bayesian approaches allow for the explicit incorporation of previous estimates through the use of the prior distribution. This provides a formal mechanism for incorporating previous estimates and a means of comparing potential results. Bayes’ theorem is also used in machine learning, which is a subset of computer science that focuses on algorithms that learn from data to make predictions. One such algorithm is the Naive Bayes Classifier, which uses Bayes’ theorem to classify objects such as documents based on prior relationships. Bayesian networks can be seen as a complicated version of the Naive Classifier that maps, estimates, and predicts relationships in a network. It is useful for more complicated prediction problems. Lastly, the theorem has even been used by qualitative social scientists as a formal mechanism for stating and evaluating beliefs and updating knowledge.

## Using Online Experiments to Study Political Decision Making

The field of political science is experiencing a new proliferation of experimental work, thanks to a growth in online experiments. Administering traditional experimental methods over the Internet allows for larger and more accessible samples, quick response times, and new methods for treating subjects and measuring outcomes. As we show in this chapter, a rapidly growing proportion of published experiments in political science take advantage of an array of sophisticated online tools. Indeed, during a relatively short period of time, political scientists have already made huge gains in the sophistication of what can be done with just a simple online survey experiment, particularly in realms of inquiry that have traditionally been logistically difficult to study. One such area is the important topic of social interaction. Whereas experimentalists once relied on resource- and labor-intensive face-to-face designs for manipulating social settings, creative online efforts and accessible platforms are making it increasingly easy for political scientists to study the influence of social settings and social interactions on political decision-making. In this chapter, we review the onset of online tools for carrying out experiments and we turn our focus toward cost-effective and user-friendly strategies that online experiments offer to scholars who wish to not only understand political decision-making in isolated settings but also in the company of others. We review existing work and provide guidance on how scholars with even limited resources and technical skills can exploit online settings to better understand how social factors change the way individuals think about politicians, politics, and policies.

## Social Network Influence on Political Behavior in Religious Contexts

As the most common form of voluntary association in America, houses of worship remain an unquestionably critical component of American civil society. Major approaches to studying religion and politics in the United States are described, and the authors present an argument for focusing more attention on the organizational experience provided by religious contexts: studying how individuals’ social networks intersect with their associational involvements (i.e., studying religion from a “interpersonal” perspective) may actually shed new light on intrapersonal, psychological constructs like identity and religiosity. Evidence is presented from two nationally representative data sets that suggests considerable variance in the degree to which individuals’ core social networks overlap with their houses of worship. This variance exists within and between individuals identifying with major religious traditions, and such networks are not characterized solely by agreement (as theories of self-selection might suggest).