Iterative Goal-Based Approval Voting

In iterative voting, a group of agents who has to take a collective decision has the possibility to individually and sequentially alter their vote, to improve the outcome for themselves. In this paper, we extend with an iterative component the recent framework of goal-based voting, where agents submit compactly expressed individual goals. For the aggregation, we focus on an adaptation of the classical Approval rule to this setting, and we model agents having optimistic or pessimistic satisfaction functions based on the Hamming distance. The results of our analysis are twofold: first, we provide conditions under which the application of the Approval rule is guaranteed to converge to a stable outcome; second, we study the quality of the social welfare yielded by the iteration process.