This paper proposes a new negotiation game, based on the weighted voting paradigm in cooperative game theory, where agents need to form coalitions and agree on how to share the gains. Despite the prevalence of weighted voting in the real world, there has been little work studying people's behavior in such settings. We show that solution concepts from cooperative game theory (in particular, an extension of the Deegan-Packel Index) provide a good prediction of people's decisions to join coalitions in an online version of a weighted voting game. We design an agent that combines supervised learning with decision theory to make offers to people in this game. We show that the agent was able to obtain higher shares from coalitions than did people playing other people, without reducing the acceptance rate of its offers. We also find that people display certain biases in weighted voting settings, like creating unnecessarily large coalitions, and not rewarding strong players. These results demonstrate the benefit of incorporating concepts from cooperative game theory in the design of agents that interact with other people in weighted voting systems.