We are interested in Effect (and more generally, Effectiveness) for many reasons - we might want to discuss whether some input can, or could, or did have any Effect at all on some output; and we are often interested in the size or magnitude of the Effect, the influence of one Variable on another:

• can a Difference in one Variable can be totally or partially attributed to some Difference in another
• how much of a contribution (exhaustive? partial?) does one influence Variable make to some consequence Variable;
• and all of these questions are all the more interesting and tricky in the presence of other influence Variables;
• in particular Variables which are controlled by our peers, because we distinguish in ordinary language between additional “natural” factors and factors which we can imagine controlling as an Agency. We distinguish between root Variables which are a) subject to our Intervention, b) subject to intervention by peers, c) subject to random noise.

## Definitions

Attribution and contribution are words which are involved in some considerable polemic in evaluation theory. We could start by looking at how they are defined.

Unfortunately they don’t seem to have very well accepted definitions. Can we fix that?

Lets look at various ways of contrasting the two words.

### Total versus partial

Often we hear the two contrasted in this kind of way:

" Outcome Mapping assumes only that a contribution has been made, and never attempts attribution" (Earl, Carden, and Smutylo 2001, 12)

“Attribution … caused the observed outcomes; Contribution … helped to cause the observed outcomes” (Almquist 2011, my italics).

““Attribution” is the idea that a change is solely due to your intervention. If I run a humanitarian programme dedicated to handing out buckets, then the gift of a bucket is ‘attributable’ to my programme. I caused it, and nobody can say otherwise. “Contribution” is the idea that your influence is just one of many factors which contribute to a change.” (Aidleap 2015)

I’ve not managed to find any canonical sources for this contrast but it seems really widespread, for example in the Outcome Mapping community.

But basically, using the word “contribution” emphasises that only partial (perhaps also indefinite, under-determined, fuzzy, emergent, whatever) causal links are involved, whereas “attribution” is often (but not always) used to imply that causal links are total.

(Aidleap 2015) however points out that in real evaluations, “Any change (except for the most simple) is caused by many things”.

### Different directions

But there is also a clear syntactical distinction which often gets lost: in ordinary English, attribution and contribution go in different directions:

you attribute an effect on a child variable to an input on a parent variable whereas you say an input on the parent variable contributes to an effect on the child variable. For example, we say the political situation contributed to the famine, and that the famine can be partially attributed to the political situation.

### Contribution excuses you from estimating the counterfactual

This idea is well debunked in (Aidleap 2015). As (Davidson 2010) says, evaluators are not interested in accidents.

### Attribution is the whole process

On the other hand, sometimes “attribution” used to refer to the whole process of establishing (partial) causal links, whereas “contribution” is reserved for something more specific, as in (Mayne J 2001).

### Contribution is not necessarily quantifiable

I found this again in (Aidleap 2015). But this seems like a red herring; why shouldn’t both “attribution” and “contribution” refer to effects which may or may not be numerically quantifiable, as required?

## Solution

So here’s my suggested solution.

We will try to avoid various ideological debates by basing the definitions on the concept of effect and leave that undefined. Just plug in whatever definition / understanding of “effect” you like the most.

To make things much simpler, we will restrict ourselves for now to understandings of “effect” which are specified just for the factual settings of the other parent Variables. Remember, our definition of Effect explicitly takes into account the influence one Difference would have on another for all the different combinations of settings of the other parent Variables. So we can focus on our contribution given that the other NGO delivered its training manual on time (which in fact was indeed the case), etc etc.

The Contribution of d on V is the Effect of d on V relative to V. We can write this in Soft Arithmetic as Effect of d on V // V, whereby the // in Soft Arithmetic is only like normal division in special, numerical cases, but serves as a fuzzy analogue of division in more general, i.e. non-numerical cases.

We defined Effect first for simple Theories and then we showed how to build up the idea of, and “calculate”, an Effect further downstream by combining the composite Effects. In the same way we can “calculate” Contribution also for composite Theories.

### Attribution: the reverse direction, and not necessarily partial.

If the effect of U on V is c, c can be attributed to U.

So attribution is just contribution back-to-front, and without being set in relation to the whole.

## Contribution described for different kinds of Rules

### Rules with only propositional (Boolean) Variables

Children more tolerant and resistant (Rule: AND) ((no,yes))

Training delivered ((no,yes))

Schools supported ((no,yes))

Ministry supportive ((no,yes))

In these type of functions, all the Variables are propositions which take Boolean values (true / false), and the rules are completely deterministic. Project planning frameworks usually assume this kind of logic and explicitly or implicitly use the idea of a “development hypothesis”, e.g.:

If the teacher training courses are delivered (intervention) and the schools are continuously supported (intervention) and if the Ministry of Education provides a supporting environment (assumption) then children will be more tolerant and resistant to radicalisation (outcome).

The use of the word “hypothesis” is perhaps a little misleading here because there is nothing hypothetical about the Theory taken as a whole, which is asserted to be true. It does not mean that we are hedging our bets or are open to alternative Theories. It simply means: there is a Mechanism such that if and when the influence Variables are manipulated, there will be this particular effect in the consequence Variable. The only hypothetical is whether or not the influence Variables will actually be manipulated.

This kind of model has a lot of advantages and disadvantages … xx

#### INUS causes (Mackie, 1974) within propositional Mechanisms

This kind of Mechanism has received a lot of attention in the literature on causation …. TBC

### Words in Capitals: Thin contributions

The effect of one Variable on another in a given context, is thin if it only provides a small part of the effects (or of the humanly influence-able effects) on the downstream Variables.

Judea Pearl (Pearl 2000) and others have argued that the kind of simple directed graph such as those displayed by Theory Maker drives the way we understand, predict, explain and try to control the world around us.

In particular, and this is absolutely central to project and programme evaluators, within this basic model we can get a good understanding of the contribution which one influence Variable makes - in the context of any other influence Variables - to a consequence Variable. Contribution is the defining question of evaluation: how much does our project intervention contribute to changes we desire?

If we can understand contribution in the context of one simple building block, and then we can show how to build up more complex Theories using these blocks, we should be able to understand contribution within these more complex Theories too.

There are many other interesting templates for building up explanations of how the world changes and how we can intervene, from system dynamics to chaos Theory. But I believe any Theory expressed with any of these alternative models can also be expressed using the kind of basic building block we deal with here: a single-step functional model linking parent and consequence Variables. I discuss this claim in more detail later.

Attribution and contribution concern calculating or at least estimating or desribing the effects of individual influence Variables within Theories with multiple influence Variables.

### References

Earl, S, F Carden, and T Smutylo. 2001. Outcome mapping. IDRC (International Development Research Centre). http://www.idrc.ca/en/ev-26586-201-1-DO{\_}TOPIC.html.

Almquist, Anne. 2011. “Attribution versus contribution.”