Measuring voting power for dependent voters through causal models

We construct a new measure of voting power that yields reasonable measurements even if the individual votes are not cast independently. Our measure hinges on probabilities of counterfactuals, such as the probability that the outcome of a collective decision would have been yes, had a voter voted yes rather than no as she did in the real world. The probabilities of such counterfactuals are calculated on the basis of causal information, following the approach by Balke and Pearl. Opinion leaders whose votes have causal influence on other voters’ votes can have significantly more voting power under our measure. But the new measure of voting power is also sensitive to the voting rule. We show that our measure can be regarded as an average treatment effect, we provide examples in which it yields intuitively plausible results and we prove that it reduces to Banzhaf voting power in the limiting case of independent and equiprobable votes.

     

The mental representation of causal conditional reasoning: mental models or causal models

In this paper, two experiments are reported investigating the nature of the cognitive representations underlying causal conditional reasoning performance. The predictions of causal and logical interpretations of the conditional diverge sharply when inferences involving pairs of conditionals—such as if P₁then Q and if P₂then Q—are considered. From a causal perspective, the causal direction of these conditionals is critical: are the P_icauses of Q; or symptoms caused byQ. The rich variety of inference patterns can naturally be modelled by Bayesian networks. A pair of causal conditionals where Q is an effect corresponds to a “collider” structure where the two causes (P_i) converge on a common effect. In contrast, a pair of causal conditionals where Q is a cause corresponds to a network where two effects (P_i) diverge from a common cause. Very different predictions are made by fully explicit or initial mental models interpretations. These predictions were tested in two experiments, each of which yielded data most consistent with causal model theory, rather than with mental models.     

Learning to learn causal models

Learning to understand a single causal system can be an achievement, but humans must learn about multiple causal systems over the course of a lifetime. We present a hierarchical Bayesian framework that helps to explain how learning about several causal systems can accelerate learning about systems that are subsequently encountered. Given experience with a set of objects, our framework learns a causal model for each object and a causal schema that captures commonalities among these causal models. The schema organizes the objects into categories and specifies the causal powers and characteristic features of these categories and the characteristic causal interactions between categories. A schema of this kind allows causal models for subsequent objects to be rapidly learned, and we explore this accelerated learning in four experiments. Our results confirm that humans learn rapidly about the causal powers of novel objects, and we show that our framework accounts better for our data than alternative models of causal learning.     

Summarizing information by means of causal sentences through causal graphs

The objective of this work is to propose a complete system able to extract causal sentences from a set of text documents, select the causal sentences contained, create a causal graph in base to a given concept using as source these causal sentences, and finally produce a text summary gathering all the information connected by means of this causal graph. This procedure has three main steps. The first one is focused in the extraction, filtering and selection of those causal sentences that could have relevant information for the system. The second one is focused on the composition of a suitable causal graph, removing redundant information and solving ambiguity problems. The third step is a procedure able to read the causal graph to compose a suitable answer to a proposed causal question by summarizing the information contained in it.     

Interference between cues requires a causal scenario: Favorable evidence for causal reasoning models in learning processes

In an interference-between-cues design (IbC), the expression of a learned Cue A–Outcome 1 association has been shown to be impaired if another cue, B, is separately paired with the same outcome in a second learning phase. The present study examined whether IbC could be caused by associative mechanisms independent of causal reasoning processes. This was achieved by testing participants in two different learning situations. In the Causal Scenario condition, participants learned in a diagnostic situation in which a common cause (Outcome 1) caused two disjoint effects, namely Cues A and B. In the Non-Causal Scenario condition, the same IbC design and stimulus conditions were used. However, instructions provided no causal frame to make sense of how cues and outcomes were related. IbC was only found in the Causal Scenario condition. This result is consistent with Causal Reasoning Models of causal learning and raises important difficulties for associative explanations of IbC.     

The role of causal models in analogical inference

Computational models of analogy have assumed that the strength of an inductive inference about the target is based directly on similarity of the analogs and in particular on shared higher order relations. In contrast, work in philosophy of science suggests that analogical inference is also guided by causal models of the source and target. In 3 experiments, the authors explored the possibility that people may use causal models to assess the strength of analogical inferences. Experiments 1-2 showed that reducing analogical overlap by eliminating a shared causal relation (a preventive cause present in the source) from the target increased inductive strength even though it decreased similarity of the analogs. These findings were extended in Experiment 3 to cross-domain analogical inferences based on correspondences between higher order causal relations. Analogical inference appears to be mediated by building and then running a causal model. The implications of the present findings for theories of both analogy and causal inference are discussed.     

The power of causal beliefs and conflicting evidence on causal judgments and decision making

In two experiments, we investigated the relative impact of causal beliefs and empirical evidence on both decision making and causal judgments, and whether this relative impact could be altered by previous experience. Participants had to decide which of two alternatives would attain a higher outcome on the basis of four cues. After completing the decision task, they were asked to estimate to what extent each cue was a reliable cause of the outcome. Participants were provided with instructions that causally related two of the cues to the outcome, whereas they received neutral information about the other two cues. Two of the four cues—a causal and a neutral cue—had high validity and were both generative. The remaining two cues had low validity, and were generative in Experiment 1, but almost not related to the outcome in Experiment 2. Selected groups of participants in both experiments received pre-training with either causal or neutral cues, or no pre-training was provided. Results revealed that the impact of causal beliefs and empirical evidence depends on both the experienced pre-training and cue validity. When all cues were generative and participants received pre-training with causal cues, they mostly relied on their causal beliefs, whereas they relied on empirical evidence when they received pre-training with neutral cues. In contrast, when some of the cues were almost not related to the outcome, participants’ responses were primarily influenced by validity and—to a lesser extent—by causal beliefs. In either case, however, the influence of causal beliefs was higher in causal judgments than in decision making. While current theoretical approaches in causal learning focus either on the effect of causal beliefs or empirical evidence, the present research shows that both factors are required to explain the flexibility involved in human inferences.     

A causal model for causal priority

Recent attempts to fix the direction of causal priority without reference to the direction of temporal priority have begun with an analysis of the causal relation itself. I offer a method, based on causal modelling theory, designed to determine the direction of causal priority while remaining as agnostic as possible about the nature of the causal relation.     

Assessing the theoretical models for sex differences in causal attributions for success and failure

Three basic models of attributional sex differences are reviewed: General Externality, Self-Derogation, and Low Expectancy. Although all of the models predict that women are unlikely to attribute their successes to ability, the models were quite different in other predictions. A meta-analysis of 21 studies examining sex differences in success-failure attributions was done to determine which of these three models had the most empirical support. Wording of attribution questions was also assessed. Results indicated only two consistent sex differences: Men make stronger ability attributions than women regardless of the outcome when informational attributional wording is used; and men attribute their successes and failures less to luck. Empirically, none of the models was well supported.     

Choosing optimal causal backgrounds for causal discovery

In two experiments, we studied the strategies that people use to discover causal relationships. According to inferential approaches to causal discovery, if people attempt to discover the power of a cause, then they should naturally select the most informative and unambiguous context. For generative causes this would be a context with a low base rate of effects generated by other causes and for preventive causes a context with a high base rate. In the following experiments, we used probabilistic and/or deterministic target causes and contexts. In each experiment, participants observed several contexts in which the effect occurred with different probabilities. After this training, the participants were presented with different target causes whose causal status was unknown. In order to discover the influence of each cause, participants were allowed, on each trial, to choose the context in which the cause would be tested. As expected by inferential theories, the participants preferred to test generative causes in low base rate contexts and preventative causes in high base rate contexts. The participants, however, persisted in choosing the less informative contexts on a substantial minority of trials long after they had discovered the power of the cause. We discuss the matching law from operant conditioning as an alternative explanation of the findings.     

Isolating causal effects through experimental changes in parent-child interaction

A distinction is made between functionaland intentionalcontrol in parent-child interaction. These concepts are drawn, respectively, from opérant and cognitive models of interaction process. Experimental evidence is presented that cognitive factors such as expectations or hypotheses indeed affect the relations between parents and their own children. This necessitates a further distinction between long-termand short-termcausal effects: Since changes in parents' expectations for their children may lag behind actual changes in children's behavior, short-term effects inferred from observations of ongoing interactions may not reflect the long-term dynamics of the relationship.     

Learning the form of causal relationships using hierarchical bayesian models

People learn quickly when reasoning about causal relationships, making inferences from limited data and avoiding spurious inferences. Efficient learning depends on abstract knowledge, which is often domain or context specific, and much of it must be learned. While such knowledge effects are well documented, little is known about exactly how we acquire knowledge that constrains learning. This work focuses on knowledge of the functional form of causal relationships; there are many kinds of relationships that can apply between causes and their effects, and knowledge of the form such a relationship takes is important in order to quickly identify the real causes of an observed effect. We developed a hierarchical Bayesian model of the acquisition of knowledge of the functional form of causal relationships and tested it in five experimental studies, considering disjunctive and conjunctive relationships, failure rates, and cross-domain effects. The Bayesian model accurately predicted human judgments and outperformed several alternative models.     

The role of causal models in multiple judgments under uncertainty

Two studies examined a novel prediction of the causal Bayes net approach to judgments under uncertainty, namely that causal knowledge affects the interpretation of statistical evidence obtained over multiple observations. Participants estimated the conditional probability of an uncertain event (breast cancer) given information about the base rate, hit rate (probability of a positive mammogram given cancer) and false positive rate (probability of a positive mammogram in the absence of cancer). Conditional probability estimates were made after observing one or two positive mammograms. Participants exhibited a causal stability effect: there was a smaller increase in estimates of the probability of cancer over multiple positive mammograms when a causal explanation of false positives was provided. This was the case when the judgments were made by different participants (Experiment 1) or by the same participants (Experiment 2). These results show that identical patterns of observed events can lead to different estimates of event probability depending on beliefs about the generative causes of the observations.     

Active power and causal flow in aristotle's theory of vision

Aristotle's theory of vision has been characterized as naive, incommensurate with his theory of audition, and of historical interest only. This view is based on an analysis which fails to acknowledge the role of the concepts acting upon and active power in the theory. The meaning of these terms and the role Aristotle assigned them in vision and in sensation generally is demonstrated. It is argued that with the inclusion of these concepts (1) the theory of vision is sufficiently sophisticated and modern to be more than comparable with more recent perceptual theorizing, and (2) the overall integrity of Aristotle's sensory philosophy is preserved. It is further argued that given the cohesiveness and comprehensiveness of Aristotle's psychological works, more attention should be given them by modern psychologists.     

A test of causal sequences in two models for development of career-orientation in women

To evaluate the tenability of two causal orderings of variables in the development of career-orientation, responses of 92 college senior women to Need Achievement, Dating Frequency, and Career-Orientation items were analyzed. The postulated orderings were derived from two models: a compensatory model implying that failure in a woman's heterosexual affiliation leads to high nAch which, in turn, produces high C-O; an enrichment model suggesting that a woman's high nAch may lead to high C-O which, in turn, decreases heterosexual affiliation. Criteria for temporal sequences as per the Simon-Blalock correlational procedures rendered the enrichment model more tenable.     

ConceptBuilder: An open-source software tool for measuring,depicting, and quantifying causal models

Measurements of people’s causal and explanatory models are frequently key dependent variables in investigations of concepts and categories, lay theories, and health behaviors. A variety of challenges are inherent in the pen-and-paper and narrative methods commonly used to measure such causal models. We have attempted to alleviate these difficulties by developing a software tool, ConceptBuilder, for automating the process and ensuring accurate coding and quantification of the data. In this article, we present ConceptBuilder, a multiple-use tool for data gathering, data entry, and diagram display. We describe the program’s controls, report the results of a usability test of the program, and discuss some technical aspects of the program. We also describe ConceptAnalysis, a companion program for generating data matrices and analyses, and ConceptViewer, a program for viewing the data exactly as drawn.     

Statistical power analysis for growth curve models using SAS

Power analysis is critical in research designs. This study discusses a simulation-based approach utilizing the likelihood ratio test to estimate the power of growth curve analysis. The power estimation is implemented through a set of SAS macros. The application of the SAS macros is demonstrated through several examples, including missing data and nonlinear growth trajectory situations. The results of the examples indicate that the power of growth curve analysis increases with the increase of sample sizes, effect sizes, and numbers of measurement occasions. In addition, missing data can reduce power. The SAS macros can be modified to accommodate more complex power analysis for both linear and nonlinear growth curve models.