An Experimental Comparison of Induced and Elicited Beliefs

Understanding choice under risk requires knowledge of beliefs and preferences. A variety of methods have been proposed to elicit peoples beliefs. The efficacy of alternative methods, however, has not been rigorously documented. Herein we use an experiment to test whether an induced probability can be recovered using an elicitation mechanism based on peoples predictions about a random event. We are unable to recover the induced belief. Instead, the estimated belief is systematically biased in a way that is consistent with anecdotal evidence in the economics, psychology, and statistics literature: people seem to overestimate low and underestimate high probabilities.     

Feddersen and Pesendorfer meet Ellsberg

The Condorcet Jury Theorem formalises the “wisdom of crowds”: binary decisions made by majority vote are asymptotically correct as the number of voters tends to infinity. This classical result assumes like-minded, expected utility maximising voters who all share a common prior belief about the right decision. Ellis (Theor Econo 11(3): 865–895, 2016) shows that when voters have ambiguous prior beliefs—a (closed, convex) set of priors—and follow maxmin expected utility (MEU), such wisdom requires that voters’ beliefs satisfy a “disjoint posteriors” condition: different private signals lead to posterior sets with disjoint interiors. Both the original theorem and Ellis’s generalisation assume symmetric penalties for wrong decisions. If, as in the jury context, errors attract asymmetric penalties then it is natural to consider voting rules that raise the hurdle for the decision carrying the heavier penalty for error (such as conviction in jury trials). In a classical model, Feddersen and Pesendorfer (Am Politi Sci Rev 92(1):23–35, 1998) have shown that, paradoxically, raising this hurdle may actually increase the likelihood of the more serious error. In particular, crowds are not wise under the unanimity rule: the probability of the more serious error does not vanish as the crowd size tends to infinity. We show that this “Jury Paradox” persists in the presence of ambiguity, whether or not juror beliefs satisfy Ellis’s “disjoint posteriors” condition. We also characterise the strictly mixed equilibria of this model and study their properties. Such equilibria cannot exist in the absence of ambiguity but may exist for arbitrarily large jury size when ambiguity is present. In addition to uninformative strictly mixed equilibria, analogous to those exhibited by Ellis (Theor Econo 11(3): 865–895, 2016), there may also exist strictly mixed equilibria which are informative about voter signals.

     

History as a coordination device

Coordination games often have multiple equilibria. The selection of equilibrium raises the question of belief formation: how do players generate beliefs about the behavior of other players? This article takes the view that the answer lies in history, that is, in the outcomes of similar coordination games played in the past, possibly by other players. We analyze a simple model in which a large population plays a game that exhibits strategic complementarities. We assume a dynamic process that faces different populations with such games for randomly selected values of a parameter. We introduce a belief formation process that takes into account the history of similar games played in the past, not necessarily by the same population. We show that when history serves as a coordination device, the limit behavior depends on the way history unfolds, and cannot be determined from a-priori considerations.     

Doxastic Conditions for Backward Induction

The problem of finding sufficient doxastic conditions for backward induction in games of perfect information is analyzed in a syntactic framework with subjunctive conditionals. This allows to describe the structure of the game by a logical formula and consequently to treat beliefs about this structure in the same way as beliefs about rationality. A backward induction and a non-Nash equilibrium result based on higher level belief in rationality and the structure of the game are derived.     

Uncommon Priors Require Origin Disputes

In standard belief models, priors are always common knowledge. This prevents such models from representing agents’ probabilistic beliefs about the origins of their priors. By embedding standard models in a larger standard model, however, pre-priors can describe such beliefs. When an agent’s prior and pre-prior are mutually consistent, he must believe that his prior would only have been different in situations where relevant event chances were different, but that variations in other agents’ priors are otherwise completely unrelated to which events are how likely. Due to this, Bayesians who agree enough about the origins of their priors must have the same priors.     

Optimism in the Face of Despair: Black‐White Differences in Beliefs About School as a Means for Upward Social Mobility*

Objective. This study aims to provide a better understanding of how beliefs about the system of social mobility affect students' schooling outcomes. Previous studies reach conflicting conclusions because they conflate two forms of beliefs about social mobility (i.e., perceived value of school and perceived barriers despite schooling). Methods. The Maryland Adolescence Development In Context Study (MADICS) is used to examine black‐white differences in beliefs about the value of school and barriers to upward mobility despite schooling and how these beliefs predict academic achievement and educational attainment. Results. The analyses show that relative to whites, blacks hold stronger beliefs in both the value of school and barriers to social mobility, and have greater affective attitudes toward schooling. However, belief in barriers to social mobility is not consequential for academic outcomes. Conclusions. Beliefs about upward mobility are mechanisms by which the opportunity structure influences individuals' schooling behaviors and making clear distinctions between various beliefs about the system of social mobility can refine the understanding of this link. This study suggests that individuals make nuanced distinctions about the role of schooling for upward mobility, each with separate effects on academic outcomes.     

Deterring domestic violence: Do criminal sanctions reduce repeat offenses?

This study presents an empirical analysis of domestic violence case resolution in North Carolina for the years 2004 to 2010. The key hypothesis is that penalties at the level set for domestic violence crimes reduce recidivism (re-arrest on domestic violence charges or conviction in 2 years following an index arrest). We use state court data for all domestic violence-related arrests. Decisions to commit an act of domestic violence are based on a Bayesian process of updating subjective beliefs. Individuals have prior beliefs about penalties for domestic violence based on actual practice in their areas. An individual’s experience with an index arrest leads to belief updating. To address endogeneity of case outcomes, we use an instrumental variables strategy based on decisions of prosecutors and judges assigned to each index arrest in our sample. Contrary to our hypothesis, we find that penalities, at least as set at the current levels, do not deter future arrests and convictions.     

Use of data on planned contributions and stated beliefs in the measurement of social preferences

In a series of one-shot linear public goods game, we ask subjects to report their contributions, their contribution plans for the next period, and their first-order beliefs about their present and future partner. We estimate subjects’ preferences from plan data by a finite mixture approach and compare the results with those obtained from contribution data. Controlling for beliefs, which incorporate the information about the others’ decisions, we are able to show that plans convey accurate information about subjects’ preferences and, consequently, are good predictors of their future behavior.     

When learning meets salience

Behavior in one-shot coordination games with common knowledge labels can be described by theories of salience and focal points. Behavior in repeated games, including coordination games, can be explained by theories of learning. This paper considers games in which both theories apply, repeated coordination games with common knowledge labels. The research question asks how players combine the two sources of information—salience and the history of play—when making their choices. We specifically ask whether salience, normally considered as a one-shot strategy, continues to influence players’ actions beyond the first round, even while the player might learn from the history of play. We explore two possible mechanisms for such a continuing effect of salience: via an influence on prior beliefs, and/or via a bias, given beliefs. Regression analysis of individual-level choices shows that salience, normally considered only in the context of one-shot games, does exert a lasting effect, with the precise mechanism depending on the details of the game.     

On Stalnaker's Notion of Strong Rationalizability and Nash Equilibrium in Perfect Information Games

Counterexamples to two results by Stalnaker (Theory and Decision, 1994) are given and a corrected version of one of the two results is proved. Stalnaker's proposed results are: (1) if at the true state of an epistemic model of a perfect information game there is common belief in the rationality of every player and common belief that no player has false beliefs (he calls this joint condition strong rationalizability), then the true (or actual) strategy profile is path equivalent to a Nash equilibrium; (2) in a normal-form game a strategy profile is strongly rationalizable if and only if it belongs to C , the set of profiles that survive the iterative deletion of inferior profiles.     

Hear No Evil, See No Evil? Associations of Gender, Trauma History, and Values with Believing Trauma Vignettes

Attitudes and beliefs about sexual assault in general influence judgments about the veracity of specific sexual assault reports and disclosures ( Taylor, 2007 ). The present study investigated the impact of gender, personal trauma history, and beliefs about gender and child sexual abuse (CSA) on judgments of the veracity of CSA disclosures. The study also examined judgments about other kinds of trauma disclosures using a variety of different types of trauma vignettes. Men were found to be more skeptical than women, and those who reported no trauma history were less likely than those who reported a trauma history to believe disclosures. Overall, all participants were more skeptical about CSA disclosures than disclosures about other kinds of trauma. Sexism and belief in CSA myths (CSAMs) were negatively related to believing adults' retrospective CSA disclosures. In a series of regression analyses, we observed that belief in CSAMs moderated the negative association between sexist attitudes and believing disclosures. Implications for educating professionals are discussed .     

Gender differences in ambiguity aversion under different outcome correlation structures

This paper studies the impact of different outcome correlation structures on gender differences in ambiguity aversion. We conducted an investment game with two separate treatments. In the uncorrelated treatment, the outcomes of the investment game were determined individually. In the correlated treatment, the outcomes of the investment game were determined collectively within a reference group. From an evolutionary perspective, men should be more concerned about relative outcomes, because their reproductive success mainly depended on their relative standing within society. Women, by contrast, should be more concerned about absolute outcomes, because their reproductive success was mainly linked to their access to resources for themselves and their children. Therefore, we predict that the type of outcome correlation structure has a larger impact on men than on women. In particular, we hypothesize that men are less ambiguity averse under an uncorrelated outcome structure. In this situation, the ambiguous alternative should be more attractive, because it potentially reduces inequality and thereby improves men’s relative standing within society. Women’s choices should not be significantly affected by different outcome correlation structures. Both hypotheses are supported by evidence from laboratory experiments.     

The Developmental Progression of Understanding of Mind during a Hiding Game

In this longitudinal study, 52 typically developing preschoolers engaged in a hiding game with their mothers when children were 42‐, 54‐, and 66‐months old. Children's understanding of mind, positive affect, and engagement with the task were rated, and mothers' utterances were coded for role and content. Analyses confirmed that some facets of children's understanding of mind developed sequentially; specifically, they expressed an understanding of knowledge access before an understanding of deception and false beliefs, and expressed an understanding of deception before an understanding of false beliefs. Children's understanding of mind increased across visits and positively correlated with false belief task performance. Results suggest that mothers may tailor the content of their utterances to the child's growing expertise, but the role of mothers' utterances did not change. Observing preschoolers engaged in a playful hiding game revealed that children's understanding of mind not only increased with age but also developed sequentially.     

Perceptron versus automaton in the finitely repeated prisoner’s dilemma

We study the finitely repeated prisoner’s dilemma in which the players are restricted to choosing strategies which are implementable by a machine with a bound on its complexity. One player has to use a finite automaton while the other player has to use a finite perceptron. Some examples illustrate that the sets of strategies which are induced by these two types of machines are different and not ordered by set inclusion. Repeated game payoffs are evaluated according to the limit of means. The main result establishes that a cooperation at almost all stages of the game is an equilibrium outcome if the complexity of the machines the players may use is limited enough and if the length T of the repeated game is sufficiently large. This result persists when more than T states are allowed in the player’s automaton. We further consider a variant of the model in which the two players are restricted to choosing strategies which are implementable by perceptrons and prove that the players can cooperate at most of the stages provided that the complexity of their perceptrons is sufficiently reduced.     

Belief elicitation in the presence of na?ve respondents: An experimental study

It is often of interest to elicit beliefs from populations that may include na?ve participants. Unfortunately, elicitation mechanisms are typically assessed by assuming optimal responses to incentives. Using laboratory experiments with a population that potentially includes na?ve participants, we compare the performance of two elicitation mechanisms proposed by Karni (Econometrica 77(2):603-606, 2009). These mechanisms, denoted as “declarative” and “clock,” are valuable because their incentive compatibility does not require strong assumptions such as risk neutrality or expected utility maximization. We show that, theoretically and empirically, with a sufficient fraction of na?ve participants, the clock mechanism elicits beliefs more accurately than the declarative. The source of this accuracy advantage is twofold: the clock censors na?ve responses, and participants are more likely to employ dominant strategies under the clock. Our findings hold practical value to anyone interested in eliciting beliefs from representative populations, a goal of increasing importance when conducting large-scale surveys or field experiments.     

Endogenizing the order of moves in matrix games

Players often have flexibility in when they move and thus whether a game is played simultaneously or sequentially may be endogenously determined. For 2 × 2 games, we analyze this using an extended game. In a stage prior to actual play, players choose in which of two periods to move. A player moving at the first opportunity knows when his opponent will move. A player moving at the second turn learns the first mover's action. If both select the same turn, they play a simultaneous move subgame.If both players have dominant strategies in the basic game, equilibrium payoffs in the basic and extended games are identical. If only one player has a dominant strategy or if the unique equilibrium in the basic game is in mixed strategies, then the extended game equilibrium payoffs differ if and only if some pair of pure strategies Pareto dominates the basic game simultaneous play payoffs. If so, sequential play attains the Pareto dominating payoffs. The mixed strategy equilibrium occurs only when it is not Pareto dominated by some pair of pure strategies.In an alternative extended game, players cannot observe delay by opponents at the first turn. Results for 2×2 games are essentially the same as with observable delay, differing only when only one player has a dominant strategy.     

The Foreign Policy Beliefs of Political Campaign Contributors: A Post-Cold War Analysis

Objective. In this article we address two questions raised by the literature on the structure of foreign policy beliefs. First, has the end of the Cold War brought about any major changes in these belief systems? Second, how do ideology and economic interests shape these beliefs? Methods. We analyze data from a 1996 survey of U.S. presidential campaign contributors conducted by the Ray Bliss Center to determine the foreign policy belief systems of contributors. We then compare those results to the belief systems found in a 1988 survey of contributors. Results. We find that Cold War belief systems are quite durable. There was surprisingly little change in the structure or content of contributors' foreign policy beliefs between 1988 and 1996. We also find that both ideology and economic interests help shape these beliefs and examine the circumstances under which each of these two considerations appears to have the most important effects. Conclusions. Policymakers face new challenges since the end of the Cold War, but domestic political elites still approach foreign policy with a Cold War perspective. Also, although ideology is very important in determining how individuals think about foreign policy, material interests also make a difference for campaign contributors.     

Age Differences in Perceptions of Rich and Poor People: Is It Skill or Luck?

To gain new perspective on the development of understandings and perceptions of income inequality, this study compared the reactions of six, eight, and 10‐year‐olds to a rich man and a poor man and the winners and losers of a contest of skill and a game of chance. Age differences in attributions for outcomes reflected a strengthening with age of the skill–luck distinction and of equity thinking about wealth. Although men with good outcomes were generally perceived more positively than men with bad outcomes, and likeability was affected only by outcome, 10‐year‐olds differentiated most sharply among different types of ‘winners’ or ‘losers’, viewing the rich and poor men as more like the winner and loser of a contest of skill than like the winner and loser of a game of chance. Overall, the findings suggest that differential evaluation of rich and poor people may begin as affective tagging based on good or bad life outcomes and later be associated with justifications grounded in an equity perspective on income inequality that emphasizes the role of personal qualities such as ability in wealth accumulation.     

宗教与信仰的双重社会化——当代中国宗教—信仰的基本变迁

中国宗教与信仰近30年的变迁,始终围绕着宗教与信仰的双重社会化问题。这些问题主要有:信仰自由与宗教自由、"宗教危机"的社会意义、私人信仰与中国法制建设、宗教消费方式对中国宗教—信仰的影响、"宗教民族主义"的抬头"、执政党信仰"的建构与认同等。解决这些问题,对使"宗教危机"转为"宗教转机"具有重要意义。