Canadian philosopher Gerald A. Cohen developed an analytical Marxism approach in his book, Karl Marx's Theory of History: A Defence (1978).  In that book, Cohen uses an analytical approach to defend Marx's materialist conception of history. Cohen sees Marx's historical materialism as a purely technologically deterministic theory, and Cohen wanted to expand on it by introducing the rational actions of humans as a mediating factor between economic relations of production and historical change. 

American economist and sociologist John Roemer is one of the most important representatives of analytical Marxism. At the beginning of his career, he developed the theory of exploitation in the book General Theory of Exploitation and Class (1982). Roemer conceives the general theory of economic exploitation, which has its special forms, so there is feudal, socialist, status, neoclassical, and Marxist exploitation, which are special cases of the general theory of exploitation. According to Remer, for economic inequality to be a consequence of exploitation, there must be a special causal link between the incomes of different actors, that is, for the rich to exploit the poor, their wealth must be directly caused by the deprivation of the poor. Roemer thus comes to his definition of exploitation: "A group can be considered exploited if there are some hypothetically feasible alternatives in which its members would be better off than in its present situation" (Roemer: 1982). Roemer's theory of exploitation is broader than Marxist and can be applied to many situations, other than capitalism.

Roemer sees the distribution of the means of production as the basis of exploitation because ownership of these means is sufficient to explain the transfer of surplus labor, while different types of assets determine different systems of exploitation. Classes represent positions within social relations of production that are based on property relations that determine patterns of exploitation. In Remer, relations within the production process or within the work process do not enter into the definition of class relations. 

American sociologist Erik Olin Wright is one of the main representatives of analytical Marxism. He dedicated his career to returning the Marxist understanding of the phenomenon of classes to the center of scientific study. 

Wright’s first class scheme was greatly influenced by the class analysis of Poulantzas. Wright believes that Pulantzas' class scheme does not meet the criteria of Marxist class analysis because, according to such criteria, the proletariat would make up only 23 to 30 percent of the labor force in the United States in the early 1970s, so the proletariat would be a minority. Wright, in order to solve the problems of classifying social classes, introduces the notion of "contradictory locations within the class structure" as his own solution. There are locations within the class structure that are objectively contradictory in their properties, not only in relation to other classes, but in themselves, and they should be analyzed independently. The three contradictory class locations are: managers and supervisors; employees in semi-autonomous jobs and small employers.

Wright believes that three related processes took place during the development of modern capitalism: the reduction of control over the labor process by direct producers; the establishment of complex hierarchies within capitalist enterprises and bureaucracy; and the differentiation of functions previously performed by capitalists. The last process concerns the separation of three aspects of ownership: possession (control over the production process), economic ownership (control over investments and what is produced), and legal ownership. The consequence of this trend is an increase in the importance of management, but also an increase in the influence of large shareholders over small shareholders. From the analysis of all three processes, Wright derives three dimensions in the relations of production that affect one's class position: control over the means of production; control over other people's labor force, and control over investments and resource allocation. By combining the three dimensions of control in production with the three dimensions of legal status in production (legal ownership of production, legal status of employer, and legal status of employee), Wright constructs his class scheme with 10 classes. Wright believes that there are other contradictory locations in practice, but they are not of major importance for class analysis.

Wright determines the class position of individuals who do not participate directly in production relations by their class interests. Wright treats the position of housewife in the context of a family class situation. Students take a pre-class position, that is, their position depends, above all, on their future class position after gaining employment, rather than on their family background. Retirees take a post-class position and are bound by the trajectory of the class positions they have held during their careers. The position of the temporarily unemployed depends on their previous and potential future class positions, while the permanently unemployed belong to the marginal segment of the working class. Employees in the political and ideological apparatus are positioned according to their own attitude towards fundamental political and ideological interests, and not according to economic interests. Wright places members of the political and ideological apparatus in three classes: 1) bourgeois positions - those who create politics and ideology in the highest positions in the state, churches, universities, etc; 2) contradictory locations - those who implement political decisions and spread ideology (eg street police officers and high school teachers); 3) proletarian positions - individuals who are completely excluded from the creation and implementation of politics and ideology (e.g. a cleaner in a police station).

Wright continues with a theoretical analysis of the relationship between class structure and class struggle and introduces the notion of "class capacity" - the capacity of a class to pursue its own interests. He distinguishes between the structural capacities of the class, which depend on the structural development of capitalist societies, and the organizational capacities of the class, which represent the conscious organization of individuals to achieve their class interests, through, more or less, formal forms of organization (unions, labor collectives, strike committees).

In his second scheme, which he presented for the first time in his book Classes (1985), Wright divided the contradictory class situation into two types: 1) contradictory class locations within one form of production and 2) contradictory class locations between several forms of production. He believes that the main criterion for social relations of production, which are the basis for determining classes, is the unity of appropriation relations and domination relations. Based on this, Wright concludes that contradictory locations exist within the same form of production, but not between different forms of production; there are only heterogeneous or dual locations between them.

In his second class scheme, Wright shifts the focus from studying the relationship of domination to studying the relationship of exploitation. He argues that class concepts based on domination tend to slip into an approach of "diverse subordination" in the study of social relations. In such approaches, it is considered that every subordination is based on a different form of domination - sexual, racial, national, or economic - none of which has primacy. Class subordination thus becomes only one of many subordinations and its centrality in social and historical analysis is lost. Dominance, in itself, does not mean that the actors will have conflicting interests, while the concept of exploitation fully encompasses the conflicting material interests of the actors.

In operationalizing the concept of exploitation, Wright introduces a distinction between economic exploitation and economic oppression. In the case of exploitation, the wealth of the exploiting class directly depends on the work of the exploited class, while in the case of economic oppression, certain groups of people are excluded from the production relationship. In addition, Wright introduces "organization" as the fourth type of productive asset. The organization, as a coordinated cooperation between producers in a complex division of labor, represents a production resource in itself. In current capitalism, this resource is controlled by managers and capitalists. According to Wright, for bureaucracy (including political and economic leaders), authority is not a resource in itself, but the organization is a resource controlled by a hierarchy of authority. Organizational resources are the basis for exploitation because ordinary workers would be in a better position if the management of companies would be democratized. The peculiarity of this type of resource is that the organization cannot be the subject of legal ownership or ownership relations.

The newly formed class scheme has 12 class positions, employers are divided into three classes, while employees are divided into nine classes formed by crossing two axes of ownership of assets: the axis of ownership of skills/qualifications and the axis of ownership of organizational assets. In the new scheme, managers are ranked only by qualifications, not by the amount of organizational resources they control. The supervisors in the new scheme are divided into three classes, while in the previous one they formed a single class. The class of technocrats and semi-self-employed is now omitted and partially replaced by the class of non-manager experts. The proletariat, which used to be one class, is divided into two classes according to qualifications.

Wright used his new theory of exploitation to reformulate the Marxist theory of history. Wright's basic argument is that increasing the probability of a successful transition from one form of production to the next grows steadily with increasing social productivity. He believes that socialism is no longer the only possible future of capitalism, that is, capitalism can be transformed into either statism or socialism. The relative openness of the future of capitalism presumes that workers are no longer the bearers of revolutionary change. Socialism, in the new theory of history, is also a form of exploitation, which was not the case in classical theory.

Other influential members of Analytical Marxism are Adam Przeworski, Michael Burawoy, and Jon Elster. Norwegian philosopher Jon Elster's approach combines analytical Marxism with the rational choice theory. He also advocated methodological individualism.

Books: 

Burawoy, Michael. Manufacturing Consent: Changes in the Labor Process Under Monopoly Capitalism (1979);

Cohen, A. Gerald. Karl Marx's Theory of History: A Defence (1978).

Elster, Jon. Explaining Technical Change (1983);

     -     Making Sense of Marx (1985);

Roemer, John. A General Theory of Exploitation and Class (1982);

     -     Analytic Marxism (1986);

     -     Analytical Foundations of Marxian Economic Theory (1988);

Wright, Erik Olin. Class, Crisis, and the State (1978);

     -     Class Structure and Income Determination (1979);

     -     Classes (1985).