The topics of microfoundations and causal mechanisms have come up frequently in this work. The microfoundations thesis maintains that social attributions and explanations based on macro-level entities and structures depend upon pathways at the level of the individual actors through which the entities and processes are maintained. The causal mechanisms thesis maintains that the best way of understanding causal assertions linking A to B is to identify the concrete causal mechanisms through which the powers of A bring about the properties of B.
Is there a relation between these two bodies of philosophical theory about the social world? There is, in a fairly obvious way. When we ask for the microfoundations of a hypothesized social process, we are really asking about the lower-level social mechanisms that bring the process about.
For example: What is it about an extended population that creates the observed features of the spread of rumor or panic? Or in other words, what are the social mechanisms through which socially interacting actors spread rumors or contribute to a broader occurrence of panic and fear? When we provide an account of the ways in which individuals communicate with each other and then demonstrate how messages diffuse through the given network structure, we have identified one of the social mechanisms of the social process in question.
Asking for the microfoundations of X is asking for an answer to two related questions: What is X (at the micro level)? And how does X work (also at the micro level)? The latter question can be paraphrased as: what are the sub-level mechanisms through which the X-level processes work? The first question is not so clearly a question about mechanisms; it is rather a question about composition. What is it about the substrate that gives rise to (constitutes) the observed macro-level properties of X? But in their book In Search of Mechanisms: Discoveries across the Life Sciences Craver and Darden argue that mechanisms play both roles. Mechanisms can be invoked to account for both process and structure (link). Here is their diagram illustrating the role that mechanisms can play with respect to higher-level structures and processes:
So here is a preliminary answer to the question of whether microfoundations and mechanisms are related. In the most immediate sense, we might say that the search for microfoundations is a search for a group of lower-level social mechanisms, to account for both the constitution and the causal dynamics of the higher-level structure. Searching for microfoundations involves learning more about the substrate of a given level of structure and process, and the causal mechanisms that occur at that lower level. Microfoundations is the question and mechanisms is the answer.
This response is not fully satisfactory, however, for several reasons.
First, there is an implication in this analysis that mechanisms live at the substrate level -- in the case of the social world, at the level of individual social actors. This is clearly assumed in the analytical sociology literature (Hedstrom, Dissecting the Social: On the Principles of Analytical Sociology). But this is an unnecessary and narrow stipulation about causal mechanisms. It is plausible to maintain that there are causal mechanisms at a range of levels (link); for example, at the cognitive level, the motivational level, the organizational level, or the system level (link).
Second, we might also observe that various social mechanisms themselves possess microfoundations. There are processes in the causal substrate that constitute the causal necessity of a specified mechanism. A spark in the presence of methane and oxygen brings about an explosion. This is a mechanism of combustion. The substrate is the chemical composition of methane and oxygen and the chemical processes that occur when an electrical spark is introduced into the environment. So the question of "level" is a relative one. A given set of objects and causal processes has its own substrate at a lower level, and simultaneously may serve as the substrate for objects and processes at higher levels.
We might also consider the idea that the two concepts have a different grammar. They play different roles in the language of science. The microfoundations conceptual scheme immediately invokes the idea of level and substrate. It brings along with it an ontological principle (the higher level is constituted by the properties of the substrate), and a partial methodological principle (the generative strategy of showing how higher-level processes come about as a consequence of the workings of the substrate). The mechanisms conceptual scheme does not inherently presuppose higher-level and lower-level structures; instead, a mechanism is something like a unit of causation, and it may be found at any level from molecular biology to organizational change.
(In an earlier post I considered a similar question, the relation between powers and mechanisms. There I argued that these two concepts are symmetrical: mechanisms lead us to powers, and powers lead us to mechanisms.)