What is the lens model?

The lens model was developed by psychologist Egon Brunswick between 1930 and 1950. He did some research in perceptual psychology and, in particular, did some research on depth perception. A big problem in depth perception is that you have a 3 dimensional world and a 2 dimensional retina that the light from the world impinges upon. How are you able to reconstruct a three dimensional world from this limited two dimensional information?

It turns out that there are are a large number of cues for determining depth that we can glean from 2 dimensional imagery. There are cues such a parallax, stereopsis, occlusion, linear perspective, texture gradients and so on. There are even more cues if we incorporate observer and world motion into the mix.

Egon observed that each cue, under certain circumstances, can provide misleading information about depth (see Ames Room). He also suggested that the importance we assigned to a cue should depend how reliably the cue signals information about depth. The mental leap that Egon took was to say that what is true of perception is true more generally in psychology, namely, that there are often multiple cues that might indicate, for example, what a person's psychiatric diagnosis should be and that we should only put our faith in those cues that have high ecological validities (i.e., are reliably correlated with the criterion we are trying to determine).

Egon proposed the Lens Model as a foundational model that psychology could use for research design and model building. The basic idea is that the real state of the world (the distal stimulus or the criterion to be judged) on the left hand side emits multiple and sometimes redundant cues about the state of world (think depth perception cues). On the right hand side we have the observer who assimilates this cue information to arrive at a decision about the state of the world. The observer never sees the world directly, instead they view the world through a lens. That lens consists of multiple cues that we take to be a proxy for some state of the world (e.g., depth relations among objects).

When we rely upon a cue (e.g., arrival of geese) to inform us about some state of the world (e.g,. whether spring has arrived) we can assign that cue a weight. There are often multiple cues providing us with more or less reliable information about some state of the world and Egon believed that we intuitively assign weights to these various cues, sum the weighted cues, and then infer whether some state of the world is true or not depending on whether some decision threshold is met or not. Our depth perception system would appear to perform such calculations automatically but we can also perform such calculations in other areas in a more controlled way using the lens model.

The final aspect of this model that is worth noting is that on the left hand side we can do research to establish how reliably correlated a given cue (e.g., sleep length) is to some state of the world (e.g., patient has depression) to determine the ecological validity of the cue. On the right had side, we might also use the cue (e.g., sleep length) to arrive at a diagnosis of depression but we might assign it an incorrect weight. We might also be using a cue that is not reliably associated with the criterion (low ecological validity) and arriving at an incorrect assessments as a result. So we need to distinguish between the ecological validities of cues on the left hand side and cue utilization validities on the right hand size (i.e, whether our psychological model is capturing the right cues and assigning them the right weights).

The reason I decided to discuss the lens model is because the Simple Rules book I have been blogging about recently didn't offer up an overall framework for thinking about how Simple Rules relate to the world. In order to use Simple Rules more effectively I would argue that you would benefit from a correspondingly Simple Model of how they relate to the world, why they work, why they don't work, and how they can be improved. I believe the Lens Model provides one such a framework. Simple rules can be understood as weighted cues we use to arrive at particular decisions or actions.

Some interesting research has been done on simple linear models of decision making (which the lens model would be an example of) where you assign a weight to each cue, multiply the measured value of the cue by the weight, sum the terms, and compare the total to some threshold in order to make your decision. For example, the graduate school admission ratings that psychologist Reid Hastie used could be modelled with this equation (from Rational Choice in an Uncertain World, 2nd Ed. 2010, by Reid Hastie & Robin Dawes, p. 49):

Admissibility Rating = 0.012 (Verbal GRE Test Score) + 0.015 (Quantitative GRE Test Score) + 0.25 (Warmth of Recommendations) + 0.410 (College Quality) + Other Factors - 13.280.

Notice that some variables don't have much weight and don't affect the rating much so could be removed. The most heavily weighted cues are "warmth of recommendations" and the "college quality" of the applicants plus, possibly, "other factors" that have non-trivial weights. Using this simple model of graduate admission ratings, Reid Hastie could replace a more complicated screening process with a much simpler screening process and arrive at roughly the same rating. This is one way to arrive at simple rules.

The purpose of today's blog was to talk about the lens model so that I can refer to it in any future blogs I want to. The second reason why I discussed the lens model is because a deficiency of the simple rules book from my perspective is that it didn't offer a simple graphical framework we might use to formally or graphically understand why simple rules work, how the rules can be combined, how they can go wrong, and what can be done to improve them. I believe the lens model provides some general guidance on how to properly think about and use simple rules.

If simple rules work then simple linear models can also be argued to work. Simple linear models have the advantage over more complicated structural models that we can do mental arithmetic with them because they only involve simple additions and multiplications. We can also simplify the weighting scheme so we only use weights that are easy to mentally work with (e.g., -1,0, 1/4, 1/3, 1/2, 2/3, 3/4, 1). If we are bounded in our computational abilities, working memory, and so on then we must find techniques that are sufficiently simple that we stand a chance of using them in the real world. Perhaps the lens model, in its simplest interpretation, is a good starting point.

Here is a lens model handout that you might find useful for exploring the lens model and simple linear modelling further.