A comparison of the belief-adjustment model and the quantum inference model as explanations of order effects in human inference (original) (raw)
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Order effects in belief updating with consistent and inconsistent evidence
Journal of Behavioral Decision Making, 1993
The current study tests for the presence of differential order effects in evaluation tasks with consistent and inconsistent evidence as predicted by the Hogarth and Einhorn (1992) belief-adjustment model. The results, based on both betweensubjects and within-subjects experiments, demonstrate that there were significant recency effects with inconsistent evidence as predicted, larger recency effects when the inconsistent evidence was farther apart in subjective value as predicted, and significant recency effects even when subjects were given training designed to both help them understand the task as completely as possible and to be better able to assess the pieces of evidence. By including a within-subjects design, we were able to demonstrate that the difference in subjective value between two pieces of evidence is the primary factor influencing the magnitude of the recency effect, regardless of whether the evidence is consistent or inconsistent. This latter finding is unique and contrary to previous research and theory.
A Quantum Probability Account of Order Effects in Inference
Cognitive Science, 2011
Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains order effects by transforming a state vector with different sequences of operators for different orderings of information. We demonstrate this process by fitting the quantum model to data collected in a medical diagnostic task and a jury decision-making task. To further test the quantum inference model, a new jury decision-making experiment is developed. Using the results of this experiment, we compare the quantum inference model with two versions of the belief-adjustment model, the adding model and the averaging model. We show that both the quantum model and the adding model provide good fits to the data. To distinguish the quantum model from the adding model, we develop a new experiment involving extreme evidence. The results from this new experiment suggest that the adding model faces limitations when accounting for tasks involving extreme evidence, whereas the quantum inference model does not. Ultimately, we argue that the quantum model provides a more coherent account for order effects that was not possible before.
Order effects in human belief revision
1998
Abstract The order effect, a phenomenon in which the final belief is significantly affected by the temporal order of information presentation, is a robust empirical finding in human belief revision. This paper investigates how order effects occur on the basis that human belief has a coherence foundation and a probability/confidence distinction. Both the experimental results and the UEcho modeling suggest that confidence play an important role in human belief revision.
Order effects in belief updating: The belief-adjustment model
Cognitive Psychology, 1992
Much literature attests to the existence of order effects in the updating of beliefs. However, under what conditions do primacy, recency, or no order effects occur? This paper presents a theory of belief updating that explicitly accounts for order-effect phenomena as arising from the interaction of information-processing strategies and task characteristics. Key task variables identified are complexity of the stimuli, length of the series of evidence items, and response mode (Step-by-
Human belief revision and the order effect
2000
Abstract The order effect, a phenomenon in which the final belief is significantly affected by the temporal order of information presentation, is a robust empirical finding in human belief revision. This paper investigates how order effects occur, on the basis that human belief has a coherence foundation and a probability/confidence distinction. Both the experimental results and the UEcho modeling suggest that confidence plays an important role in human belief revision.
Learning from examples does not prevent order effects in belief revision
Thinking & Reasoning, 2010
A common finding is that information order influences belief revision (e.g., Hogarth & Einhorn, 1992). We tested personal experience as a possible mitigator. In three experiments participants experienced the probabilistic relationship between pieces of information and object category through a series of trials where they assigned objects (planes) into one of two possible categories (hostile or commercial) given two sequentially presented pieces of probabilistic information (route and ID), and then they had to indicate their belief about the object category before feedback. The results generally confirm the predictions from the Hogarth and Einhorn model. Participants showed a recency effect in their belief revision. Extending previous model evaluations the results indicate that the model predictions also hold for classification decisions, and for pieces of information that vary in their diagnostic values. Personal experience does not appear to prevent order effects in classification decisions based on sequentially presented pieces of information and in belief revision.
Interference effects of choice on confidence: Quantum characteristics of evidence accumulation
Decision-making relies on a process of evidence accumulation which generates support for possible hypotheses. Models of this process derived from classical stochastic theories assume that information accumulates by moving across definite levels of evidence, carving out a single trajectory across these levels over time. In contrast, quantum decision models assume that evidence develops over time in a superposition state analogous to a wavelike pattern and that judgments and decisions are constructed by a measurement process by which a definite state of evidence is created from this indefinite state. This constructive process implies that interference effects should arise when multiple responses (measurements) are elicited over time. We report such an interference effect during a motion direction discrimination task. Decisions during the task interfered with subsequent confidence judgments, resulting in less extreme and more accurate judgments than when no decision was elicited. These results provide qualitative and quantitative support for a quantum random walk model of evidence accumulation over the popular Markov random walk model. We discuss the cognitive and neural implications of modeling evidence accumulation as a quantum dynamic system. confidence | Markov | decision-making | cognitive model | random walk D ecisions in a wide range of tasks (e.g., inferring the presence or absence of a disease, the guilt or innocence of a suspect, and the left or right direction of enemy movement) require evidence to be accumulated in support of different hypotheses. Arguably, the most successful theory of evidence accumulation in humans and other animals is Markov random walk (MRW) theory (and diffusion models, their continuous space extensions) (1, 2). MRWs can be viewed as psychological implementations of a first-order Bayes-ian inference process that assigns a posterior probability to each hypothesis (3). MRWs can account for choices, response times, and confidence for a variety of different decision types (2, 4). Moreover, these models of the accumulation process have been connected to neural activity during decision-making (5, 6). According to MRW models, when deciding between two hypotheses , the cumulative evidence for or against each hypothesis realizes different levels at different times to generate a single particle like trajectory of evidence levels across time (Fig. 1). At any point in time, the decision-maker has a definite level of evidence, and choices are made by comparing the existing level of evidence against a criterion. Evidence above the criterion favors one option, and evidence below it favors the alternative. Other responses are modeled in a similar manner; for example, confidence ratings are modeled by mapping evidence states onto one or more ratings (4). However, this idea that judgments and decisions are simply read out from the existing level of evidence—henceforth referred to as the " read-out " assumption—is inconsistent with the well-established idea that preferences and beliefs are constructed rather than revealed by judgments and decisions (7). We present an alternative model of choice and judgment based on quantum random walk (QRW) theory (8–11), which posits that preferences and beliefs are constructed when a judgment or decision is made. Note that this work does not make the assumption that the brain is a quantum computer; instead, we simply use the mathematics of quantum theory to explain and predict human behavior. According to QRW theory, at any point in time before a decision, the decision-maker is in a superposition state that is not located at a single level of evidence. Instead, each level of evidence has a potential to be expressed, formalized as a probability amplitude (Fig. 1). New information changes the amplitudes, producing a wavelike process that moves the amplitude distribution across time. In some ways the QRW is like a second-order Bayesian model (12). According to the latter, the decision-maker assigns a probability (rather than an amplitude) to each level of evidence for each hypothesis. However, like the MRW model, second-order Bayesian models are perfectly compatible with the read-out assumption, and as an optimal model, this would suggest that a decision should not change the probability assigned to each evidence level. In contrast, a QRW, like all quantum models of cognition (13), treats a judgment or decision as a measurement process that constructs a definite state from an indefinite (superposition) state. When a decision is made, the indefinite state collapses onto a set of evidence levels that correspond to the observed choice, producing a definite choice state. Confidence ratings work similarly, with the indefinite state collapsing onto a more specific set of levels corresponding to the observed rating. These different theories of choice and judgment have strong implications for sequences of responses. Consider the situation when decision-makers have to make a choice (e.g., decide that hypothesis A or B is true) and later rate their confidence that a given (usually the chosen) hypothesis is true. According to the read-out assumption, a choice is reported on the basis of existing evidence that does not change the internal state of evidence itself. This applies to the MRW, a second-order Bayesian model, and many other accumulation models as well. Thus, after pooling across a person's choices, the distribution of confidence ratings should be identical to conditions in which the person makes no choice at all. By contrast, the state of the system in a QRW Significance Most cognitive and neural decision-making models—owing to their roots in classical probability theory—assume that decisions are read out of a definite state of accumulated evidence. This assumption contradicts the view held by many behavioral scientists that decisions construct rather than reveal beliefs and preferences. We present a quantum random walk model of decision-making that treats judgments and decisions as a constructive measurement process, and we report the results of an experiment showing that making a decision changes subsequent distributions of confidence relative to when no decision is made. This finding provides strong empirical support for a parameter-free prediction of the quantum model.
Updating beliefs in light of uncertain evidence: Descriptive assessment of Jeffrey's rule
2010
Jeffrey (1983) proposed a generalisation of conditioning as a means of updating probability distributions when new evidence drives no event to certainty. His rule requires the stability of certain conditional probabilities through time. We tested this assumption (���invariance���) from the psychological point of view. In Experiment 1 participants offered probability estimates for events in Jeffrey's candlelight example.
Many studies have shown that inferential behavior is strongly affected by access to real-life information about premises. However, it is also true that both children and adults can often make logically appropriate inferences that lead to empirically unbelievable conclusions. One way of reconciling these is to suppose that logical instructions allow inhibition of information about premises that would otherwise be retrieved during reasoning. On the basis of this idea, we hypothesized that it should be easier to endorse an empirically false conclusion on the basis of clearly false premises than on the basis of relatively believable premises. Two studies are presented that support this hypothesis.