Reducibility means that the statements of one scientific discipline should be logically deducible from the truths of some other "more fundamental" discipline. It is sometimes maintained that the truths of chemistry ought in principle be derivable from those of quantum mechanics. A field of knowledge that is not reducible to another field R is said to be "autonomous with respect to R". Philosophers sometimes further distinguish "law-to-law" reduction, "type-to-type" reduction, "law-to-singular-fact" reduction, and "type-to-token" reduction.
Are social sciences such as economics, sociology, or political science reducible in principle to some other more fundamental field--perhaps psychology, neurophysiology, or the theory of rationality?
To begin to answer this question we must first decide what items might be reduced: statements, truths, laws, facts, categories, or generalizations. Second, we need to distinguish several reasons for failure of reduction: failure in principle, because events, types, and laws at the social level are simply not fixed by states of affairs at "lower" levels, and failure for reasons of limits on computation. (The motions of a five-body system of stars might be determined by the laws of gravitation even though it is practically possible to perform the calculations necessary to determine future states of the system.)
So now we can consider the question of social reduction in a reasonably clear form. Consider first the "facts" that pertain to a domain of phenomena--whether these facts are known or not. (I choose not to concentrate on laws or generalizations, because I am doubtful about the availability of strong laws of social phenomena.) Do the facts of a hypothetically complete theory of human psychology "fix in principle" the facts of economics or sociology, given appropriate information about boundary conditions?
One important approach to this problem is the theory of supervenience (Jaegwon Kim, Physicalism, or Something Near Enough). A level of description is said to supervene upon another level just in case there can be no differences of state at the first level without there being a difference of state in the second level. The theory is first applied to mental states and states of neurophysiology: "no differences in mental states without some difference in neurophysiology states." Supervenience theory implies an answer to the question of whether one set of facts "fixes in principle" the second set of facts. (It has been taken as obviously true that social facts supervene upon facts about individuals; how could it be otherwise? What other constitutive or causal factors might influence social facts, beyond the actions and ideas of individuals?) If the facts about social life supervene upon facts about the psychological states of individuals, then it follows that the totality of facts about individual psychology fixes in principle the totality of facts about social life. (Otherwise there would be the situation that there are two total social worlds corresponding to one total "individual psychology" world; so there would be a difference at the social level without a difference at the level of individual psychology.)
So this provides the beginnings of an answer to our question: if we believe that social facts supervene upon facts about individuals, then we are forced to accept that the totality of facts about individuals "fix" the facts about society.
However, supervenience does not imply "reducibility in principle", let alone "reducibility in practice" between levels. In order to have reducibility, it is necessary to have a system of statements describing features of the lower level which are sufficient to permit deductive derivation (or perhaps probabilistic inference) of all of the true statements contained in the higher-level domain. If it is a social fact that "collective action tends to fail when groups are large", then there would need to be set of statements at the level of individual psychology that logically entail this statement. Two additional logical features would appear to be required for reduction: a satisfactory set of bridge statements (linking the social term to some construction of individual-level terms; "collective action" to some set of features of individual agents, so there is a mapping of concepts and ontologies between the two domains), and at least some statements at the lower level that have the form of general laws or law-like probabilistic statements. (If there are no general statements at the lower level, then deductive inference will be limited to truth-functional deduction.)
Now it is time for a speculative leap: a judgment call on the question of whether we ought to look for reductive links between social facts and individual-level facts. My intuition is that it is not scientifically useful to do so, for several reasons. First is the point about computational limits: even if the outcome of a riot is "fixed" by the full psychological states of participants ex ante and their strategic interactions during the event--it is obviously impossible to gather that knowledge and aggregate it into a full and detailed model of the event. So deriving a description of the outcome from a huge set of facts about the participants is unpromising. Second, it is telling that we need to refer to the strategic interactions of participants in order to model the social event; this means that the social event has a dynamic internal structure that is sensitive to sub-events that occur along the way. (Jones negotiates with Smith more effectively than Brown negotiates with Black. The successful and failed negotiations make a difference in the outcome but are unpredictable and contingent.) Third, the facts at the social level rarely aggregate to simple laws or regularities that might have been derived from lower-level laws and regularities; instead, social outcomes are contingent and varied.
So for a variety of reasons, it is reasonable to take the view that social facts supervene upon facts about individuals, but that social explanations are autonomous from laws of psychology. (This final point might be paraphrased as "the laws of psychology underdetermine social outcomes.")