Olson focused on the logical basis of interest group membership and participation. The reigning political theories of his day granted groups an almost primordial status. Some appealed to a natural human instinct for herding, others ascribed the formation of groups that are rooted in kinship to the process of modernization. Olson offered a radically different account of the logical basis of organized collective action.

In his first book, The Logic of Collective Action: Public Goods and the Theory of Groups, he theorized that “only a separate and ‘selective’ incentive will stimulate a rational individual in a latent group to act in a group-oriented way”; that is, only a benefit reserved strictly for group members will motivate one to join and contribute to the group. This means that individuals will act collectively to provide private goods, but not to provide public goods.

In 1982, he expanded the scope of his earlier work in an attempt to explain The Rise and Decline of Nations. The idea is that small distributional coalitions tend to form over time in countries. Groups like cotton-farmers, steel-producers, and labor unions will have the incentives to form lobby groups and influence policies in their favor. These policies will tend to be protectionist and anti-technology, and will therefore hurt economic growth; but since the benefits of these policies are selective incentives concentrated amongst the few coalitions members, while the costs are diffused throughout the whole population, the "Logic" dictates that there will be little public resistance to them. Hence as time goes on, and these distributional coalitions accumulate in greater and greater numbers, the nation burdened by them will fall into economic decline. Olson's idea is cited as an influence behind the Calmfors-Driffill hypothesis of collective bargaining.

In his final book, Power and Prosperity, Olson distinguished between the economic effects of different types of government, in particular, tyranny, anarchy and democracy. Olson argued that a "roving bandit" (under anarchy) has an incentive only to steal and destroy, whilst a "stationary bandit" (a tyrant) has an incentive to encourage a degree of economic success, since he will expect to be in power long enough to take a share of it. The stationary bandit thereby takes on the primordial function of government - protection of his citizens and property against roving bandits. Olson saw in the move from roving bandits to stationary bandits the seeds of civilization, paving the way for democracy, which improves incentives for good government by more closely aligning it with the wishes of the population.

To honor Olson's many contributions to the fields of Economics and Political Science, the American Political Science Association introduced the Olson Award to the best PhD dissertation in Political Economy.