Condorcet method

Condorcet method
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Name	Condorcet method
Inventor	Marie Jean Antoine Nicolas de Caritat, Marquis de Condorcet
Year	1785
Type	Single-winner, pairwise comparison
Used in	Various organizations and academic studies

Condorcet method. The Condorcet method is an electoral procedure in which each pair of candidates is compared head-to-head so that the option winning every pairwise contest is elected; it is named after Marie Jean Antoine Nicolas de Caritat, Marquis de Condorcet and has influenced work by figures such as Jean-Charles de Borda, Victor Condorcet's contemporaries, John Stuart Mill, Kenneth Arrow, and Amartya Sen. The method connects to historical debates involving Thomas Jefferson, James Madison, Benjamin Franklin, Alexis de Tocqueville and later theorists including Kenneth Arrow and Arrow's theorem discussions in institutions like Princeton University, Harvard University, London School of Economics and research by ICPSR and RAND Corporation.

Overview

The Condorcet approach requires voters to rank candidates; each pair of candidates is evaluated in a head-to-head matchup, producing a Condorcet winner if one candidate defeats every other candidate in pairwise contests. Variants produce outcomes related to methods examined by Marie Jean Antoine Nicolas de Caritat, Marquis de Condorcet and referenced alongside Borda count, Instant-runoff voting, Plurality voting, Approval voting and systems studied at MIT, Stanford University, Yale University, Columbia University and University of Oxford. The method's analysis appears in literature associated with Encyclopædia Britannica, Cambridge University Press, Oxford University Press, Springer, and journals like The American Political Science Review and Journal of Economic Theory.

History and development

Origins trace to the writings of Marie Jean Antoine Nicolas de Caritat, Marquis de Condorcet in the late 18th century and contemporaries such as Jean-Charles de Borda; later formalization drew on mathematical work by Carl Friedrich Gauss, Pierre-Simon Laplace, Adrien-Marie Legendre, and statistical applications by Florence Nightingale. The 19th and 20th centuries saw engagement from John Stuart Mill, James Mill, Gustave Le Bon, William F. Riker, Kenneth Arrow and Amartya Sen in contexts linked to French Revolution, Congress of Vienna, University of Paris, École Polytechnique and publications like Philosophical Transactions of the Royal Society. Modern computational and social choice treatments involve groups at MIT, Princeton University, Harvard University, Oxford University, London School of Economics, Carnegie Mellon University, Stanford University, ETH Zurich, University of Cambridge, University of Chicago, and institutions including National Bureau of Economic Research and Institute for Advanced Study.

Condorcet winner and loser

A Condorcet winner is a candidate who defeats every other candidate in pairwise comparison; conversely, a Condorcet loser loses to every other candidate. Concepts are analyzed alongside examples from historical elections such as United States presidential elections, internal contests of Labour Party (UK), Conservative Party (UK), Democratic Party (United States), Republican Party (United States), leadership contests in Australian Labor Party, Canadian Liberal Party, and decision-making studies at United Nations, European Parliament, NATO, World Bank and International Monetary Fund. The notions are central to theorists like Kenneth Arrow, John Harsanyi, Amartya Sen, Duncan Black, Nicholas Rescher and institutions like Brookings Institution.

Voting procedures and variants

Multiple algorithms implement Condorcet principles: the Smith set based methods, the Schulze method, Minimax (electoral system), Ranked Pairs, Kemeny–Young method, Copeland's method, Tideman's method, Black's method (as a hybrid), and methods comparable to Borda count adjustments. These variants are studied in computational contexts at Google, Microsoft Research, IBM Research, Bell Labs, ETH Zurich, Max Planck Society and in open-source projects hosted by GitHub and analyzed in conferences such as NeurIPS, ICML, IJCAI and AAAI. Implementations appear in organizational elections at Green Party (UK), Pirate Party, Electoral Reform Society, Reform UK discussions, and in software by OpenSTV and groups including Equal Vote Coalition.

Condorcet paradox and cycles

The Condorcet paradox demonstrates that collective preferences can be cyclic even when individual preferences are transitive; this phenomenon relates to examples inspired by political contests involving figures such as Abraham Lincoln, Ulysses S. Grant, Theodore Roosevelt, Woodrow Wilson, Franklin D. Roosevelt and modeled in studies by Duncan Black, Kenneth Arrow, Amartya Sen, Condorcet and mathematicians like John von Neumann and Oskar Morgenstern. Cycles necessitate tie-breaking or further rules, leading to methods like Smith set selection, Schwartz set identification, and resolution techniques evaluated by scholars at Princeton University, Harvard University, Stanford University, University of Michigan and think tanks like Cato Institute and Heritage Foundation.

Properties and criteria

Condorcet methods are evaluated against criteria including Pareto efficiency (as framed by Vilfredo Pareto), Monotonicity analyses discussed by Kenneth Arrow and Amartya Sen, participation criteria investigated by Geoffrey Brennan and Lloyd Shapley, and strategic considerations in game-theoretic work by John Nash, John Harsanyi and Robert Aumann. Comparative studies reference alternatives like Instant-runoff voting, Plurality voting, Approval voting, Borda count, and theoretical constructs in texts from Cambridge University Press, Oxford University Press, Princeton University Press and articles in Econometrica, Journal of Political Economy.

Implementation and practical usecases

Condorcet methods are used in internal ballots of organizations such as Debian, GNU Project, Free Software Foundation, Green Party (US), Schulze method adopters including MediaWiki community and in academic surveys at MIT, Stanford University, Princeton University, University of Oxford, University of Cambridge, ETH Zurich, University of Toronto and non-governmental bodies like Transparency International, Amnesty International, Human Rights Watch for prioritization exercises. Practical deployment concerns—software by OpenSTV, auditing practices inspired by Election Assistance Commission, standards from National Institute of Standards and Technology and studies at RAND Corporation—address ballot design, voter education, and computational complexity analyzed by researchers at Carnegie Mellon University, Google Research and Microsoft Research.

Category:Voting systems