Voting Rules for
 Accurate
Democracy

Different uses for voting need different types of voting.

PoliticalSim software

Bibliography for
Better Democracies

Tools for developing democracy

Where to look next.
Key:
Common plurality rule's erratic flip flops
Better one-winner rules such as Instant Runoff Voting
Condorcet's rule for 1 central winner
PR by party lists or Single Transferable Vote for fairly distributed winners
Ensemble rules for a centrally- balanced council

Further Reading

  Behind the Ballot Box: A Citizen's Guide to Voting Systems, 2000.
Real Choices / New Voices: the case for Proportional Representation in the United States, 1993, 2002. and
Proportional Representation: The Case for a Better Election System, 1997 by Douglas Amy.  Professor Amy built the outstanding on-line PR library.

"Better Voting Methods through Technology: The Refinement-Manageability Trade-Off in the Single Transferable Vote" by T. Nicolaus Tideman and Daniel Richardson, Public Choice 103 (2000) pp. 13-34. They explain the development of STV, its various quota and transfer rules. Tideman's STV by Paired Comparisons (CPO-STV) might improve the selection of diverse winners, although at a cost in complexity.

  Choosing an Electoral System: Issues and Alternatives. edited by Arend Lijphart and Bernard Grofman, 1984. Authors advocating several election systems contribute to this even-handed collection of essays.

"The Choice of Voting Systems", by Richard G. Niemi and William H. Riker; in Scientific American, June 1976. This brief introduction to single-winner rules recommends 2 Condorcet-completion rules.

Collective Decisions and Voting: The Potential for Public Choice, " by T. Nicolaus Tideman $120. from Ashgate Publishing, 2006

Democracy, by Professor Stephen R. Graubard, in The Dictionary of the History of Ideas. Professor Emeritus of History at Brown University and former Editor of Daedalus.

"Dimensional Analysis of Ranking Data." by Henry E. Brady in American Journal of Political Science. 34 (11/90). Brady found that a spatial model with 2 or 3 issue dimensions depicted a real electorate fairly well. (Knowing a voter's position on 1 political issue helps predict his positions on the related issues in that dimension. Knowing a voter's 3D position helps predict his ranking of candidates.)

Efficient Public Goods Decisions Under an Established Tax System by Aanund Hylland and Richard Zeckhauser, 1984. This paper may be available from the authors at the University of Oslo and Harvard's John F. Kennedy School of Government. Explanation and analysis of the rule is published in Public Choice II, pages 134-139.

Elections as Instruments of Democracy, Majoritarian and Proportional Vissions; G. Bingham Powell Jr. New Haven and London: Yale University Press,

Electoral Systems in Comparative Perspective. edited by Joseph F. Zimmerman and Wilma Rule, 1994. The authors look closely at the effects of electoral systems on election of women and minorities.

How to Take Votes: New Ideas on Better Ways to Determine the Winners, (research draft) by Lowell Bruce Anderson, 1994. Appendix D section E describes the same rule which I called LERb.

Instant Runoff Voting and why you should support it by Peter A. Taylor covers PR and Condorcet rules with clear illustrations. He includes a very selective annotated bibliography similar to this page.

The International IDEA Handbook of Electoral System Design. Edited by Andrew Reynolds and Ben Reilly, 1997. Published by the International Institute for Democracy and Electoral Assistance, S-103 34 Stockholm, Sweden. This refreshingly pragmatic handbook covers: criteria and advise for designers; plurality, semi-PR and PR systems; representation of women and minorities; national and local elections; and cost and administration of elections. A pdf version can be downloaded. Administration and Cost of Elections Project

Is Democracy Fair: The Mathematics of Voting and Apportionment by Leslie Johnson Nielsen and Michael de Villiers, Key Curriculum Press, 1997, ISBN 1559532777. The authors use many examples, such as choosing pizza toppings or camping trips, to teach high school students why voting rules matter and how to evaluate them.

" A New Monotonic, Clone-Independent, Reversal Symmetric, and Condorcet-Consistent Single-Winner Election Method" Markus Schulze updates the highly-regarded Schulze Method (also known as Schwartz Sequential Dropping or Beatpath). It was published in Voting Matters, issue 17, September 2003 and is already used by thousands of voters in dozens of membership organizations. Both articles focus on the method's mathematical properties.

Making Multi-candidate Elections More Democratic. by Samuel Merrill III, 1988. Merrill's simulations of single-winner voting rules confirmed and expanded on Chamberlin's results. The main text is for lay readers while math proofs are confined to 6 appendices.

Mathematics and Democracy. by Arkadii Slinko, 8pp in postscript format. Slinko's geometric proofs, in words and pictures, explore the existence and enactment of  ideal  policies. The proofs are shown on a 2-dimensional "Plane of Political Views" like that used in PoliticalSim. In The mathematics of group choice. he uses sets to look at axioms for voting rules. Auckland University, 1997, 27pp.

Patterns of Democracy - Government Forms and Performance in Thirty-Six Countries; Arend Lijphart. New Haven and London: Yale University Press, 1999.

PoliticalSim TM by Robert Loring. Election-simulation software is the best way to learn many voting concepts. Click to see a screen.

PR Proportional Representation, the Key to Democracy. by George H. Hallet Jr. 1940.

Public Choice III by Dennis C. Mueller, 2003. This is a comprehensive text for graduate-level economics courses on voting systems and the distribution of public goods.

Representation. edited by Hanna F. Pitkin, Atherton Press, 1969. The surprising history and subtle philosophies of representation are reviewed with precision in the editor's 20 page introduction.

Seats and Votes, the Effects and Determinants of Electoral Systems. by Rein Taagepera, and Mathew Soberg Shugart; 1989. These authors combine research from many others to build a mathematical model of political systems.

“Social Choice Observed: Five Presidential Elections of the American Psychological Association” by John R. Chamberlin, Jerry. L. Cohen, and Clyde H. Coombs in Journal of Politics. 46 (1984): 479-502. The authors used computer simulations to find the Condorcet efficiencies, violations of subset rationality, and frequencies of manipulable elections for 8 voting rules. A page here has some of their results. See also, “An Investigation into the Relative Manipulability of Four Voting Systems”, Behavioral Science; 30:4, 195-203; 1985.

“Some Aspects of Elections -- to Fill One Seat or Many” by I. D. Hill, in The Journal of the Royal Statistical Society, Series A (General), 151 part 2, (1988) 243-275. Hill briefly examines the most important voting rules; favors Condorcet and STV for 1-seat and many-seat elections respectively. He proposes a Condorcet-STV combination intended to prevent eliminating a broadly popular candidate who has few current firsts on the ballots. The current Condorcet winner, calculated using the current weights of ballots, is exempt from elimination. “It is evident that, for one seat, the method always selects the Condorcet winner if there is one. A Condorcet winner is not certain of a seat, however, where there is more than one seat.” Thus Hill's rule does not always elect an ensemble of the central Condorcet winner(s) and diverse STV winners.

Strategic Voting and Nomination” and “Four Condorcet-Hare Hybrid Methods for single-winner elections” in Voting Matters, upcoming; both by James Green-Armytage. The first updates and expands the simulation research of Chamberlin et al, and of Merrill. The second examines rules such as LOR1.

 The Structure of the Election-Generating Universe, by T. Nicolaus Tideman and Florenz Plassmann; 2010. Using ballots from hundreds of elections, the authors compared 12 models of electorates and concluded, “Our results suggest that a spatial model describes the structure of the election-generating universe much better than any other model that has been proposed so far, and so well that it may be difficult to find a model whose accuracy is significantly higher.”
PoliticalSim offers a similar spatial model.

Ten Recommendations for Building a Multiparty System in the U.S. by Matt Grossmann

Ten Steps to Repair American Democracy, PoliPoint Press, May 2006; by Steven Hill.
  1. Secure the vote
  2. Expand voter participation
  3. Introduce instant runoff voting
  4. Introduce proportional voting
  5. Direct election of the President
  1. Overhaul the U.S. Senate
  2. Reclaim the airwaves
  3. Minimize money’s role
  4. Reform the Supreme Court
  5. Restore faith in government

 Topics in the Theory of Voting. by Phillip D. Straffin, Boston: UMAP, 1980. Straffin's short book is the clearest introduction to the math in voting rules. He analyzes the faults possible under each rule. He does not write about the frequencies of failure as Chamberlin et al and Merrill did.

The Tyranny of the Majority, by Lani Guinier, 1994.

Voting and Democracy Research Reports. edited and published by the Center for Voting and Democracy. Authors from Lani Guinier to Clarence Thomas argue for using PR in the USA.  The CVD site also has very good sections introducing PR, and IRV

Democracy Evolves 1998:    Site Introduction    Site outline

Voting with Dollars: A New Paradigm for Campaign Finance; Ackerman, Bruce, and Ian Ayres (2002): (New Haven, CT: Yale University Press).

Web Sites

The next page links to the web's top sites about voting systems.Web sites about voting rules

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