Bidirectional Reasoning

astar_4_bidirectionalThe idea of bidirectional reasoning seems to have really got going by way of a 1999 paper entitled: “Bidirectional Reasoning in Decision Making by Constraint Satisfaction” written by Keith J. Holyoak and Dan Simon that was  published in the Journal of Experimental Psychology. 1999, Vol 128, No. 1, pages 3-31.

The researchers wrote that one of the most deep-rooted assumptions about human reasoning is that the flow of inference is inherently unidirectional, moving from premises to be accepted as given to inferred conclusions. Unidirectionality is most apparent in deductive inference, but is generally assumed to hold also for inductive inference.  The unidirectionality assumption rules out “reverse” inferences, from conclusions to premises.

Holyoak et al posited that there is an alternative conception of reasoning and decision making in which inferences are inherently bidirectional, so that the distinction between premises and conclusion is blurred. Bidirectional inferences are inherent in the operation of models of thinking based on parallel constraint satisfaction.  The writers state that such models are typically formulated as networks of units representing possibilities (e.g., possible beliefs or actions), interconnected by excitatory and inhibitory links representing positive and negative support relations between pairs of possibilities. Holyoak et al wrote:

Constraint satisfaction models operate by applying a relaxation algorithm, which settles the network into a stable state in which the asymptotic activation levels of the units define a set of “winning” possibilities (those with relatively high activation), which have succeeded in mutually supporting one another and collectively inhibiting their rivals. The bidirectional influences between related possibilities play a critical role in allowing the system to impose a coherent interpretation on an initially ambiguous set of inputs.

The researchers note that the interactive activation model of letter and word perception was the prototype for computational constraint satisfaction models.  At a more qualitative level, the constraint satisfaction approach has it roots in consistency theories developed in social psychology under the Gestalt influence. These consistency theories, which were applied to attitude and belief revision, included balance theory, dissonance theory, and symbolic psycho-logic. According to Holyoak et al, the early consistency theories waned in influence over the years, in part because they were unable to specify how consistency could be reliably attained, and were generally limited to networks that included just two or three elements. This problem has been solved by constraint satisfaction algorithms, which for networks of any size will adjust activations so as to reach an asymptotic state that maximizes the internal consistency (i.e., coherence) of the set of winning hypotheses. As an early 1970s student of social psychology, I had since wondered why dissonance theory did not seem to be in the picture any more, but apparently fancy math and computers have brought such theories part way back.

Holyoak et al did not deny that some inferences are strongly directional. For example, given that it is raining we can securely conclude that the lawn will be wet; but given that the lawn is wet, it would be unwise to conclude that it is raining. Their claim was simply that natural human decision making does not exclusively depend on strictly directional inferences.

Holyoak et al in this 1999 paper suggested that In the domain of politics, the generation of patterns of coherent beliefs through the creation of constraint networks may help explain the emergence of political ideologies.  The authors suggested, for example, current American conservatism often combines favoring free access to guns with favoring restricted access to abortion, whereas liberalism tends to combine the opposite views; yet it is unclear what the two points of dispute have to do with one another. They agreed with the idea that conservatism and liberalism are respectively grounded in two alternative analogical extensions of the family, and that an analogy can provide a potent basis for a set of interrelated inferences. Beyond that, however, coherence-based reasoning provides a yet broader conception of how “coalitions” of beliefs and attitudes can arise. An analogy may provide the core; but more generally, factors that cohere with favorably-viewed outcomes will tend to come to cohere with each other.  The latter inference was not directly based on the analogy, but rather cohered with a decision that in turn cohered with the favored analogy. Such indirect connections may foster the emergence of loosely connected attitudes that cohere to form a stable cluster.  Human understanding appears less like a serial process of logical deduction, moving rigidly from established premises to new conclusions, and more like the solution to a complex puzzle in which the individual pieces must be reorganized and transformed to form a coherent whole.  (Note: this idea seems connected to Kahan’s Cultural Cognition.)

My reason, at least initially, for providing some background on bidirectional reasoning was a 2010 exchange of comments between Julian Marewski and Andreas Glockner and Tilmann Betsch in response to a paper by Glockner and Betsch all in the Journal of Behavioral Decision Making.  Everyone agreed that bidirectional reasoning exists.  Glockner and Betsch suggested that Fast and Frugal Heuristics are not bidirectional and cannot account for coherence shifts, while Marewski disagreed.

According to Glockner and Betsch, Marewski refers to the Reconstruction after Feedback with Take The Best (RAFT) model. Basically, the RAFT model assumes that people update their cue values from an original response to a later response after receiving feedback. An example  is a person judging whether cake or pie has more cholesterol. For this task, the decision maker might rely on information about saturated fat, calories, and protein as cues. Suppose that the person does not initially know whether cake or pie has more saturated fat: after making a decision and receiving feedback that cake has more cholesterol than pie, the person might update her cue knowledge concerning unknown cues and subsequently assume that cake has more saturated fat than pie. Glockner and Betsch acknowledge that Marewski is correct in stating that, according to RAFT, cue values could be modified. However, they state, this modification obviously takes place after a decision has been made.

Gigerenzer and Goldstein suggest a case where the RAFT heuristic might be considered bidirectional. For instance, in a blind taste test, most people preferred a jar of high-quality peanut butter over two alternative jars with low-quality peanut butter. Yet when one familiar and two unfamiliar brand labels were randomly assigned to the jars, preferences changed. When the high-quality product was in a jar with an unknown brand name, it was preferred only 20% of the time, whereas the low-quality product in the jar with the familiar brand name was chosen 73% of the time. When the exact same peanut butter was put into three jars, one showing a familiar brand name and two showing unfamiliar brand names, the (faux) familiar product won the taste test 75% of the time. The taste cues themselves might be changed by name recognition—people “taste” the brand name.  Although Gigerenzer is good at creating persuasive examples, it seems a quite specific case.

I must agree with Glockner and Betsch that Fast and Frugal Heuristics do not hold together as a general cognitive model of memory and perception on their own.  However, Glockner and Betsch note that implementations of production rules in ACT-R, as suggested by Marewski  might be another interesting trajectory to scientific progress. This is Marewski’s cognitive niche model which will be explored in a later post.  Although, I have not seen comments by Glockner and Betsch on Marewski’s cognitive niche work since it was published, it seems they were acknowledging that heuristics could be hung on the framework of ACT-R and create a bidirectional model.

Gigerenzer, G., & Goldstein, D.G. (2011). “The recognition heuristic: A decade of research,” Judgment and Decision Making, Vol. 6, No. 1, January 2011, pp. 100–121.

Glockner, A., Betsch, T., & Schindler, N. (2010). “Coherence shifts in probabilistic inference tasks,” Journal of Behavioral Decision Making, Vol 23, Issue 5, p 439-462, December 2010.

Glockner, A., Betsch, T., (2010). “Accounting for Critical Evidence While Being Precise and Avoiding the Strategy Selection Problem in a Parallel Constraint Satisfaction Approach: A Reply to Marewski,” Journal of Behavioral Decision Making, Vol 23, Issue 5, p 468-472, December 2010.

Holyoak, K., & Simon, D., (1999). “Bidirectional Reasoning in Decision Making by Constraint Satisfaction,” Journal of Experimental Psychology. 1999, Vol 128, No. 1, pages 3-31.

Marewski, J., (2010). On the Theoretical Precision and Strategy Selection Problem of a Single-Strategy Approach:  A Comment on Glockner, Betsch, and Schindler,” Journal of Behavioral Decision Making, Vol 23, Issue 5, p 463-467, December 2010.

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