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We prove that the core for Borda count is empty in many cases in which the majority core is non-empty. We then compare Borda count and majority rule in a forward agenda using a two-dimensional spatial voting model with minimal-intelligence agents who vote sincerely and propose randomly. The analysis allows us to compare Borda count and majority rule in a dynamic setting and to show which voting rule is more capable of attaining Pareto-optimal policies and utilitarian ideals under those conditions. We find that Borda count moves policies in the rough vicinity of the Copeland winner and typically outperforms majority rule on both criteria in twenty rounds or less. Majority rule often outperforms Borda count in 1000 rounds. This provides a modest step in the application of new voting rules to committees. [ABSTRACT FROM AUTHOR]