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In this talk, Holliday will report on joint work with Eric Pacuit aimed at solving the problems for democratic voting posed by Arrow’s Impossibility Theorem, the Paradox of Voting, and related results. They diagnose what went wrong with Arrow’s assumptions (https://arxiv.org/abs/2008.08451), explain how to resolve cycles in the majority relation of an election in a rational way (https:// arxiv.org/abs/2004.02350), and how to fairly break ties should they arise (https://arxiv.org/ abs/2108.00542). Logical methods, including SAT solving and interactive theorem proving (https://escholarship.org/uc/item/2g73d7qv), have been employed in this research, as well as computer simulations (https://arxiv.org/abs/2106.11502). Finally, Holliday will demo a website that makes new voting methods available to all for practical use.