We develop a dynamic model of opinion formation in social networks when the information required for learning a parameter may not be at the disposal of any single agent. Individuals engage in communication with their neighbors in order to learn from their experiences. However, instead of incorporating the views of their neighbors in a fully Bayesian manner, agents use a simple updating rule which linearly combines their personal experience and the views of their neighbors. We show that, as long as individuals take their personal signals into account in a Bayesian way, repeated interactions lead them to successfully aggregate information and learn the true parameter. This result holds in spite of the apparent naïveté of agents' updating rule, the agents' need for information from sources the existence of which they may not be aware of, worst prior views, and the assumption that no agent can tell whether her own views or those of her neighbors are more accurate.

Blume and Easley (1992) show that if agents' have the same savings rule, those who maximize the expected logarithm of next period's outcomes will eventually hold all wealth (i.e. are ‘most prosperous’). However, if no agent adopts this rule then the most prosperous are not necessarily those who make the most accurate predictions. Thus, agents who make inaccurate predictions need not be driven out of the market. In this paper, it is shown that, among agents who have the same intertemporal discount factor (and who choose savings endogenously), the most prosperous are those who make accurate predictions. Hence, convergence to rational expectations obtains because agents who make inaccurate predictions are driven out of the market.

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W e argue that large elections may exhibit a moral bias (i.e., conditional on the distribution of preferences within the electorate, alternatives understood by voters to be morally superior are more likely to win in large elections than in small ones). This bias can result from ethical expressive preferences, which include a payoff voters obtain from taking an action they believe to be ethical. In large elections, pivot probability is small, so expressive preferences become more important relative to material self-interest. Ethical expressive preferences can have a disproportionate impact on results in large elections for two reasons. As pivot probability declines, ethical expressive motivations make agents more likely to vote on the basis of ethical considerations than on the basis of narrow self-interest, and the set of agents who choose to vote increasingly consist of agents with large ethical expressive payoffs. We provide experimental evidence that is consistent with the hypothesis of moral bias. I n this article, we provide evidence that voters in large elections tend to vote against their material self-interest and to vote for a morally or ethically appealing alternative. It may seem puzzling that voters might behave differently in small elections than they do in large ones. However, we show that such behavior is a logical consequence of voters having a conflict between obtaining a better material outcome and choosing a moral action. We develop a simple model of this conflict and show that decreasing the probability that a single vote is decisive (i.e., pivot probability) reduces the importance of outcomes relative to actions in voter decision making. Because pivot probability is generally small in large elections, alternatives that are understood by voters to be morally superior are more likely to win in large elections than in small ones. Thus, compared to the preferences of voters, election results will be biased in favor of moral alternatives. 1 The model produces a set of predictions that we test in a laboratory experiment.To clarify ideas, consider a situation in which two outcomes are possible: A and B. Assume that B gives