Mathematics and democracy: designing better voting and fair-division procedures
Voters today often desert a preferred candidate for a more viable second choice to avoid wasting their vote. Likewise, parties to a dispute often find themselves unable to agree on a fair division of contested goods. InMathematics and Democracy, Steven Brams, a leading authority in the use of mathematics to design decision-making processes, shows how social-choice and game theory could make political and social institutions more democratic. Using mathematical analysis, he develops rigorous new procedures that enable voters to better express themselves and that allow disputants to divide goods more fairly. One of the procedures that Brams proposes is "approval voting," which allows voters to vote for as many candidates as they like or consider acceptable. There is no ranking, and the candidate with the most votes wins. The voter no longer has to consider whether a vote for a preferred but less popular candidate might be wasted. In the same vein, Brams puts forward new, more equitable procedures for resolving disputes over divisible and indivisible goods.
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Approval Voting in Practice
Approval Voting in Theory
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1st round additional-member aggregation apportionment method approval voting assume ballots bids Borda count Borda maximin allocations Borda score Brams and Fishburn cake chapter choice sequence choose committee Condorcet paradox Condorcet winner consider constraints controlled roundings critical strategy profile cumulative voting efficient election electorate ensure envy envy-ensuring envy-free equal equilibrium equitable Example fair division Gap Procedure give grand coalition Hamming distance illustrate induce integer program Israel issue Kilgour least majority coalition manipulable maximin and Borda maxsum assignment minimax outcomes minimizes ministry minisum outcomes Nash equilibrium number of voters Pareto-optimal parties PAV and FV payoff scheme percent player receives points poll possible PR systems preference profile preference ranking problem Proof Proposition proximity weights seats sequence sincere choices single transferable vote single-peaked social choice stable subset surplus TEFs tion total misrepresentation type of voter voting system weakly dominated whereas winning combination yields