In social sciences, a cross-cutting cleavage exists when groups on one cleavage overlap among groups on another cleavage. "Cleavages" include such things as racial, political, religious divisions in society. Formally, members of a group j on a given cleavage x belong to groups on a second cleavage y with members of other groups k, l, m, etc. from the first cleavage x. For example, if a society contained two ethnic groups that had equal proportions of rich and poor it would be cross-cutting. The term's antonym is reinforcing cleavages", which would be the case of one of the ethnic groups being all rich and the other all poor. The term originates from Simmel (1908) in his work Soziologie.
Anthropologists used the term heavily in the first few decades of the 20th century as they brought back descriptions of non-Western societies throughout Asia and Africa.
The concept of cross-cutting cleavages is perhaps most heavily used in the field of Political Science. Cross-cutting cleavages were originally suggested as a mechanism for political stability, as no group can align all its members along a uniform cleavage-based platform, but rather has to appeal to members of the group that are spread throughout the groups created by other cleavages. The most in-depth discussion of this process is that by Seymour Martin Lipset in his 1960 book Political Man. Another classic essay is by Stein Rokkan on crosscutting cleavages in Norway. Cross-cutting theory was further applied to such topics as social order, political violence, voting behaviour, political organization and democratic stability. See Truman's The Governmental Process, Dahl's A Preface to Democratic Theory, among others. Around the same time, several scholars (including Lipset himself) suggested ways to measure the concept, the best-known being Rae and Taylor's in their 1970 book The Analysis of Political Cleavages. Due to data limitations, these theories were generally left untested for a couple of decades.
Diana Mutz revived the concept in the early 2000s looking at political participation and democratic theory using survey data in the US and other Western European democracies. She has been joined more recently by several scholars who have written on how cross-cutting cleavages relates to ethnic voting (Dunning and Harrison 2010), civil war (Selway 2011, Gubler and Selway 2012), ethnic censuses (Lieberman and Singh 2012) and economic growth (Selway 2011). Selway (2011) also suggested a new measure for crosscutting cleavages and published a crossnational dataset on crosscutting cleavages among several dimensions (ethnicity, class, geography and religion).
Sociologists have also used the term, especially in the sub-field of Macro Sociology. Peter Blau's work is the most well-known. See Peter Michael Blau and Joseph E. Schwartz, Crosscutting Social Circles: Testing a Macrostructural Theory of Intergroup Relations (Orlando, Fla.: Academic Press, 1984).