Groups make decisions on both the production and the distribution of resources. These decisions typically involve a tension between increasing the total level of group resources (i.e. social efficiency) and distributing these resources among group members (i.e. individuals' relative shares). This is the case because the redistribution process may destroy part of the resources, thus resulting in socially inefficient allocations. Here we apply a dual-process approach to understand the cognitive underpinnings of this fundamental tension. We conducted a set of experiments to examine the extent to which different allocation decisions respond to intuition or deliberation. In a newly developed approach, we assess intuition and deliberation at both the trait level (using the Cognitive Reflection Test, henceforth CRT) and the state level (through the experimental manipulation of response times). To test for robustness, experiments were conducted in two countries: the USA and India. Despite absolute-level differences across countries, in both locations we show that: (i) time pressure and low CRT scores are associated with individuals' concerns for their relative shares and (ii) time delay and high CRT scores are associated with individuals' concerns for social efficiency. These findings demonstrate that deliberation favours social efficiency by overriding individuals' intuitive tendency to focus on relative shares.