Gender gaps in influence are common in group decisions. When political decision-making is a collective endeavor, the presence of elected women thus does not guarantee that women have equal influence over outcomes. Can inclusive discussion rules reduce persistent gender gaps in influence within political groups with collective decision-making? To answer and identify the causal impact of such a change, we experimentally evaluate the effect of an arguably light touch intervention in Indian village councils: we request elected officials and bureaucrats in village councils to adopt explicit - and hence inclusive - discussion rules as part of a collective decision-making exercise about local development budgets. We test the impact of changing institutional rules in monthly meetings of elected political officials and bureaucrats tasked with local policy implementation across 605 villages in the state of Maharashtra. We hypothesize that explicit, inclusive discussion rules, which require that quota-elected women speak, will affect the subsequent influence of these officials in decision-making, leading to outcomes that better reflect the preferences of quota-elected officials. We measure whether such changes in formal rules of discussion increase the objective influence of women officials. Results show that limited changes in formal discussion rules can alter the responsiveness of peers to the substantive input of women elected leaders, shifting the outcomes of collective decision-making. We find evidence that explicit, inclusive discussion rules matter. In fact, although they disproportionately influence women elected via gender-quotas, they also influence all individuals elected in the absence and presence of gender quotas (men and women).