Comment: 25 pages, 10 figuresWe introduce a new framework to study the group dynamics and game-theoretic considerations when voters in a committee are allowed to trade votes. This model represents a significant step forward by considering vote-for-vote trades in a low-information environment where voters do not know the preferences of their trading partners. All voters draw their preference intensities on two issues from a common probability distribution and then consider offering to trade with an anonymous partner. The result is a strategic game between two voters that can be studied analytically. We compute the Nash equilibria for this game and derive several interesting results involving symmetry, group heterogeneity, and more. This framework allows us to determine that trades are typically detrimental to the welfare of the group as a whole, but there are exceptions. We also expand our model to allow all voters to trade votes and derive approximate results for this more general scenario. Finally, we emulate vote trading in real groups by forming simulated committees using real voter preference intensity data and computing the resulting equilibria and associated welfare gains or losses.