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One of the reasons for deadlock in global climate policy is countries' disagreement on how to share the mitigation burden. Normative theory suggests various fairness criteria for structuring burden sharing, most prominently, historical responsibility for emissions, economic capacity, and vulnerability to climate change. Governments have taken up these criteria in their rhetoric at UNFCCC negotiations. I examine whether normative criteria influence individual burden sharing preferences. This bottom-up perspective is important for two reasons. First, it is unknown if governments' fairness rhetoric matches citizens' actual preferences. Second, international climate agreements directly affect individuals through domestic policy measures (e.g. energy taxes), and therefore require domestic public support for successful implementation. I conducted two laboratory experiments where participants have to agree on how to share climate change mitigation costs in an ultimatum game. Treatment conditions include differences between proposer and responder in capacity, vulnerability (experiment 1), and historical emissions (experiment 2). Historical emissions are endogenously determined in a prior game. Capacity inequality strongly affects burden sharing, with richer players ending up paying more, and poorer players less. Vulnerability differences reduce the influence of fairness, leading to suggested cost distributions more unfavorable to vulnerable players. However, vulnerable responders still reject many "unfair" offers. Differences in historical responsibility result in cost distributions strongly correlated with players' relative contributions to climate change. The results suggest that more nuanced consideration of fairness criteria in burden sharing could make ambitious climate agreements more acceptable for reluctant countries and their citizens.