The notion of  proportionality was introduced into the philosophical literature by Yablo 1992. To use one of his examples, consider a pigeon, Sophie, who has been trained to peck at red and only red targets. Suppose Sophie is presented with a scarlet target and pecks. Contrast the following two claims

(1) The red color of the target caused Sophie to peck

(2) the scarlet color of the target caused Sophie to peck

Yablo claims that (1) is (at least) preferable to (2) and, more strongly, that in this particular case (1) is true and (2) false. He describes the cause cited in (1) as more proportional to its effect than the cause cited in (2). Intuitively, in comparison with (1), (2) is overly specific since it fails to communicate the information that Sophie would have pecked if the target had been some non-scarlet shade of red. Yablo provides a more precise characterization of proportionality (which I will not discuss) but the intuitive idea is that causes are proportional to their effects when they “do not contain too little” in the sense of being inappropriately narrow and omitting crucial elements as (2) does and also “do not contain too much” in the sense of being overly broad and containing superfluous elements. (The claim (4) that Sophie pecked because the target was some color or another is overly broad).

The suggestion that Causal claims should satisfy a proportionality requirement has been criticized by a number of philosophers. Usually the target is an interpretation according to which satisfaction of a proportionality requirement is a necessary condition for a causal claim to be true. For example,  Shapiro and Sober (2012) target a formulation of proportionality according to which “a statement of the form ‘C caused E’ obeys the constraint of proportionality precisely when C says no more than is necessary to bring about E”.  They then consider a candidate causal relation  between two quantitative variables, X and Y, that is described by a function  F that is not 1-1– e.g., F maps two different values of X, 3 and 22, into the same value of Y (6). In such a case

(3)  X=3  caused Y = 6  

does not give us a description of the cause that is necessary for Y=6 (since X=22 would have sufficed) but (Sober and Shapiro claim, and I agree) that it does not seem plausible to dismiss (3) as false on these grounds. Other writers criticize the imposition of  proportionality requirement on the grounds that, at best, this is a “pragmatic constraint” deriving from “general features of language use rather than the causal relation itself” (Bontly, 2005).

This discussion of proportionality raise a number of interesting issues, both normative and descriptive. First, is there a way of formulating a proportionality condition that avoids problems like those described by Sober and Shapiro and is normatively defensible — defensible in the sense, as before, of  making sense in terms of goals associated with causal cognition? Second, to what extent do lay people (and other groups such as scientists) conform to a proportionality requirement (however this is understood) and value proportionality in the assessment of causal claims?

After considering several alternative ways of formulating a proportionality condition, CHF proposes a normative constraint that is organized around the following two ideas. (I will not give the exact formulation of the constraint since it requires too much background explication for a post of this length.) 

First, a causal claim might falsely claim that some  intervention-supporting dependency relationship is present when it is not. Call this falsity.   

Violations of falsity are ruled out by standard interventionist requirements on causation according to which causal claims must truly describe how the cause variable responds to interventions. For example, (4) violates this requirement because it is false that Sophie will peck any colored target

Second, a causal claim might fail to represent one or more dependency relations   that are present in the system of interest and that should be represented. Call this omission.

 It is omission that is, so to speak, the distinctive feature contributed by proportionality. This consideration is violated by (2) since (2) fails to represent dependency relations present in the example– that Sophie will peck at non-scarlet red targets. As explained in CHF, the extent to which omission is satisfied is a matter of degree. Proportionality is thus not conceptualized a as a necessary condition for causal claims to be true but rather as a condition that can be satisfied to a greater or lesser extent, with  greater conformity to the condition being a prima-facie desideratum in causal claims. (CHF presents arguments for this normative claim.)  The extent to which proportionality is satisfied is thus another example of a distinction within causation.   

Following the methodology laid out in previous posts there is also the question of the extent to which, as an empirical matter, proportionality considerations influence people’s causal judgments. If I am right that the most plausible formulation of proportionality takes its satisfaction to be a matter of degree, the right verbal probe for addressing this question will be a graded one, such as some version of a causal strength probe, with the expectation being that more proportional causal clams will receive higher strength ratings. Although there are a number of scenarios in the philosophical literature which are used to prompt intuitive judgments relevant to the role of proportionality, there is to the best of my knowledge very little systematic empirical investigation of how people in general judge with respect to these scenarios or regarding the factors which influence their judgments. For example, there do not seem to be  empirical investigations of how people judge regarding claims like (1) and (2), even though it seems it would be easy to do this. The one  exception I know is an elegant series of experiments by Lien and Cheng, 2000 which does indeed find a strong influence of proportionality like considerations on judgments, although these authors do not use the word “proportionality”. In part for this reason, CHF makes a number of suggestions about possible experiments that might probe the role of proportionality considerations. 

Bontly, T.  (2005) “Proportionality, Causation and Exclusion” Philosophia 32: 331-348. 

Lien, Y. and Cheng, P. (2000) “Distinguishing Genuine from Spurious Causes: A Coherence Hypothesis” Cognitive Psychology 40: 87-137.  

Shapiro. L. and Sober, E. (2012) “Against Proportionality” Analysis 72: 89-93.  

Yablo, S. (1992) “Mental Causation” Philosophical Review 101: 245-280.

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