Three ways of thinking about linearity

Describing change in "linear" terms is seen as bad form these days. But what does this term linear mean? Or perhaps more usefully, what could it mean?

In its simplest sense it just means one thing happening after another, as in a Theory of Change that describes an Activity leading to an Output leading to an Outcome leading to an Impact. Until time machines are invented, we can't escape from this form of linearity.

Another perspective on linearity is captured by Michael Woolcock's 2009 paper on different kinds of impact trajectories. One of these is linear, where for every x increase in an output there is a y increase in impact. In a graph plotting outputs against impacts, the relationship appears as a straight line. Woolcock's point was that there are many other shaped relationships that can be seen in different development projects. Some might be upwardly curving, reflecting an exponential growth arising from the existence of some form of feedback loop, whereby increased impact facilitates increased outputs. Others may be must less ordered in their appearance as various contending social forces magnify and moderate a project's output to impact relationship, with the balance of their influences changing over time. Woolcock's main point, if I recall correctly, was that any attempt to analyse a project's impact has to give some thought to the expected shape of the impact trajectory, before it plans to collect and analyse evidence about the scale of impact and its causes.

The third perspective on linearity comes from computer and software design.Here the contrast is made between linear and parallel processing of data. With linear processing, all tasks are undertaken somewhere within a single sequence. With parallel processing many tasks are being undertaken at the same time, within different serial processes. The process of evolution is a classic example of parallel processing. Each organism in its interactions with its environment is testing out the viability of a new variant in the species' genome. In development projects parallel processing is also endemic, in the form of different communities receiving different packages of assistance, and then making different uses of those packages, with resulting differences in the outcomes they experience.

In evaluation oriented discussion of complexity thinking a lot of attention is given to unpredictability, arising from the non-linear nature of change over time, of the kind described by Woolcock. But it is important to note that there are various identifiable forms of change trajectories that lie in between simple linear trajectories and chaotic unpredictable trajectories. Evaluation planning needs to think carefully about the whole continuum of possibilities here.

The complexity discussion gives much less attention to the third view of non-linearity, where diversity is the most notable feature. Diversity can arise from both intentional and planned differences in project interventions but also from unplanned or unexpected responses to what may have been planned as standardized interventions. My experience suggests that all too often assumptions are made, at least tacitly, that interventions have been delivered in a standardized manner. If instead the default assumption was heterogeneity, then evaluation plans would need to spell out how this heterogeneity would be dealt with. If this is done then evaluations might become more effective in identifying "what works in what circumstances", including identifying localized innovations that had potential for wider application.