Public choice theory is an approach that in the focus of its study has interest groups and their relationship with the state. The public choice theory uses microeconomic perspectives of market exchange and applies them to the political theory in order to determine how policy preferences of interest groups and their relative bargaining power affect government policies. One of the first works that relate to this approach is Anthony Downs’ An Economic Theory of Democracy (1957), which shows that governments select their policies in a way to appeal to a winning coalition of voters. Public choice theory presupposes that government directs its policies to the groups that are in the best position to lobby for their interests.

Although a market analogy is used to explain policy selection, the public choice theory also points to the differences between economic and political markets.  The economic market exchange is voluntary, benefits all, and functions at a Pareto's optimal. In political markets, on the other hand, groups, by their inherent logic and goals, are using their resources in the fight over limited resources, so the benefit of one group can go against the benefit of another group. That makes the political market distributional and inherently conflictual.

The theory argues that policy changes are the result of changes in the distribution of the power between opposed groups or they come when some group loses its relevance over the public policy issue. The public choice theory has two versions, one is the “Chicago School,” and the “Virginia School”. Some of the notable authors within this approach are: Kenneth Arrow, Mancur Olson, Gary Becker, Anthony Downs, James Buchanan, and Gordon Tullock.

References:

Arrow, Kenneth J.  Social Choice and Individual Values (1951);

Becker, Gary S. “A Theory of Competition Among Pressure Groups for Political Influence”, in Quarterly Journal of Economics (1983);

Buchanan, James M.,  and Gordon Tullock. The Calculus of Consent: Logical Foundations of Constitutional Democracy (1962);

Downs, Anthony.  An Economic Theory of Democracy (1957); 

Olson, Mancur.  The Logic of Collective Action  (1965); 

Mueller, Dennis C. Public Choice III. (2003);

Tullock, Gordon. The Economics of Special Privilege and Rent Seeking (1989).