I come from an economics background where people often written explicit mathematical models for their theories. To be clear, the vast majority of economic models are not useful quantitatively — the functional forms, etc, tend to be way off. However, the models are useful in disciplining the qualitative predictions from the theory. Human intuition is faulty. If we just rely on intuition in building theories, we almost always miss something until we write them out using models.

When I read psychological theories, I find that most of them are not expressed in explicit models. This makes me worried that my understanding of the theories can be incomplete and different from what the original authors intended.

Why is this the common practice? Would we gain anything to make psychological theories mathematically explicit, or will that be a waste of time?

  • $\begingroup$ I believe it is mostly due to the lack of overlap in people working in the two fields i.e. lack of development in math theory in psychology. The involvement of math is to better understand the data and model predictions. So mathematical models might provide some insights which are easy to overlook otherwise. But still, when it comes to some field like behavioral psychology, I would say mathematical models might not help us as such due to the difficulty in expressing certain things quantitatively. $\endgroup$ – Notwen Dec 30 '20 at 21:11
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    $\begingroup$ What does "explicit mathematical model" mean to you? How is the intuition used in developing these models distinct from intuition used in theory in psychology? Can you be more specific about the areas of psychology you are reading about that are not using explicit mathematical models? $\endgroup$ – Bryan Krause Dec 30 '20 at 21:21
  • $\begingroup$ @BryanKrause literally all of them. For instance, take the idea of “cognitive dissonance”. A mathematical model will begin with specifying the initial beliefs, and then formally defining what does it mean for some beliefs to be contradictory, and then predict which beliefs will be “distorted”, in what specific ways, to reconcile the cognitive dissonance. $\endgroup$ – J Li Dec 31 '20 at 9:12
  • $\begingroup$ This question is soliciting opinion-based answers. I am not sure how to edit it to promote evidence-based answers, but if you have some ideas about what sort of evidence can be used to support an answer, then it would likely benefit from adding that. $\endgroup$ – Arnon Weinberg Jan 4 at 7:32

Come read some cognition! It's a wide open field with angles on all kinds of psychology stuff, and we're having a great time throwing greek letters around like confetti. I think you might like it!

One of my favorite recent pro-model rants is this one psyarxiv.com/rybh9/ Although, to be fair they do argue for 'computational' rather than 'mathematical'. I would argue these both mean 'explicit formalism', which is what you're after here?

There's a whole journal of mathematical psychology www.journals.elsevier.com/journal-of-mathematical-psychology

or Computational Brain and Behavior www.springer.com/journal/42113 is full of cool stuff on a surprisingly wide range of psych topics united by a common theme of awesome mathy-ness

Psych is very broad, but whatever corner of it you're interested in, there's almost certainly a math-y cognitive/computational version of it (as well). Those mathpsych folks definitely get around. Probably the most math-resistant corner of psych is social psych, emergent behavior of groups type stuff is absolutely vicious to model, as you would know, coming from econ... but see eg. cogsci.mindmodeling.org/2019/papers/0172/0172.pdf

Explicit formalism is the future of psych, and quite a lot of the future is here already

  • $\begingroup$ Thank you for the helpful references! $\endgroup$ – J Li Jan 4 at 7:26

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