  We 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.
