Donald G. Saari | Academic Influence

Donald G. Saari's AcademicInfluence.com Rankings

Donald G. Saari

Mathematics

#2531

World Rank

#3888

Historical Rank

#998

USA Rank

Measure Theory

#898

World Rank

#1174

Historical Rank

#334

USA Rank

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Mathematics

Donald G. Saari's Degrees

PhD Mathematics Purdue University
Masters Mathematics Purdue University
Bachelors Mathematics California Institute of Technology

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Why Is Donald G. Saari Influential?

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According to Wikipedia, Donald Gene Saari is an American mathematician, a Distinguished Professor of Mathematics and Economics and former director of the Institute for Mathematical Behavioral Sciences at the University of California, Irvine. His research interests include the -body problem, the Borda count voting system, and application of mathematics to the social sciences.

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Donald G. Saari's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Stable and Random Motions in Dynamical Systems (1975) (1359)
Basic Geometry of Voting (1995) (369)
Decisions and elections : explaining the unexpected (2001) (294)
Social Norms and Global Environmental Challenges: The Complex Interaction of Behaviors, Values, and Policy (2013) (226)
Chaotic Elections! - A Mathematician Looks at Voting (2001) (179)
Geometry of voting (1994) (170)
Explaining All Three-Alternative Voting Outcomes (1999) (161)
Effective Price Mechanisms (1978) (148)
On the role and the properties ofn body central configurations (1980) (147)
A dictionary for voting paradoxes (1989) (140)
The generic existence of a core forq-rules (1997) (139)
Iterative Price Mechanisms (1985) (139)
Susceptibility to manipulation (1990) (133)
Collisions, Rings, and Other Newtonian -Body Problems (2005) (128)
The Borda dictionary (1990) (117)
Disposing dictators, demystifying voting paradoxes (2008) (106)
A geometric examination of Kemeny's rule (2000) (106)
Mathematical Structure of Voting Paradoxes: II. Positional Voting (1999) (94)
The Copeland method (1996) (88)
Hill regions for the general three-body problem (1975) (85)
Mathematical Structure of Voting Paradoxes: I. Pairwise Votes (1999) (85)
A chaotic Exploration of Aggregation Paradoxes (1995) (79)
Connecting and resolving Sen's and Arrow's theorems (1998) (78)
The problem of indeterminacy in approval, multiple, and truncated voting systems (1988) (75)
Improbability of collisions in Newtonian gravitational systems (1971) (74)
Which is better: the Condorcet or Borda winner? (2006) (69)
The Sum of the Parts Can Violate the Whole (2001) (68)
Mathematical Complexity of Simple Economics (1996) (66)
On the final evolution of the n-body problem (1976) (64)
Decisions and elections (2001) (63)
Off to infinity in finite time (1995) (62)
The Copeland method: I.: Relationships and the dictionary (1996) (59)
Capturing the “Will of the People” (2003) (57)
Singularities of the n-body problem. I (1968) (57)
Disposing Dictators, Demystifying Voting Paradoxes: Social Choice Analysis (2008) (57)
Expanding gravitational systems (1971) (57)
Are partwise comparisons reliable? (2004) (55)
Millions of election outcomes from a single profile (1992) (54)
Copeland Method II: Manipulation, Monotonicity, and Paradoxes☆ (1997) (53)
Some Surprising Properties of Power Indices (2001) (51)
Is approval voting an ‘unmitigated evil’?: A response to Brams, Fishburn, and Merrill (1987) (51)
Consistency of decision processes (1990) (51)
NEWTON'S METHOD, CIRCLE MAPS, AND CHAOTIC MOTION (1984) (50)
Singularities and collisions of Newtonian gravitational systems (1973) (47)
The manifold structure for collision and for hyperbolic-parabolic orbits in the n-body problem☆ (1984) (46)
The Source of Some Paradoxes from Social Choice and Probability (1987) (45)
On the manifolds of total collapse orbits and of completely parabolic orbits for the n-body problem (1981) (43)
The likelihood of dubious election outcomes (1999) (41)
Analyzing a nail-biting election (2001) (38)
The ultimate of chaos resulting from weighted voting systems (1984) (38)
Complexity and the geometry of voting (2008) (35)
A qualitative model for the dynamics of cognitive processes (1977) (34)
The Lack of Consistency for Statistical Decision Procedures (1991) (34)
On Bounded Solutions of the n-Body Problem (1970) (33)
A visit to the newtonian N-body problem via elementary complex variables (1990) (33)
A global existence theorem for the four-body problem of Newtonian mechanics (1976) (33)
The Optimal Ranking Method is the Borda Count (1985) (31)
Dealing with femtorisks in international relations (2014) (30)
Consequences of reversing preferences (2003) (30)
From rotations and inclinations to zero configurational velocity surfaces I. A natural rotating coordinate system (1984) (29)
Dynamics of Macrosystems (1985) (29)
Erratic behavior in economic models (1991) (28)
From Arrow’s Theorem to ‘Dark Matter’ (2015) (28)
Negative externalities and Sen’s liberalism theorem (2006) (26)
Unsettling aspects of voting theory (2003) (26)
The aggregated excess demand function and other aggregation procedures (1992) (25)
The existence of oscillatory and superhyperbolic motion in Newtonian systems (1989) (25)
GEOMETRY, VOTING, AND PARADOXES (1998) (24)
Mathematical structure of voting paradoxes (2000) (23)
The geometry of Black's single peakedness and related conditions (1999) (22)
A method for constructing message systems for smooth performance functions (1984) (21)
Symmetry, voting, and social choice (1988) (21)
On the local convergence of economic mechanisms (1986) (20)
Restrictions on the Motion of the Three-Body Problem (1974) (20)
Calculus and extensions of Arrow's theorem (1991) (20)
Complexities of electing diverse committees (2014) (19)
From rotations and inclinations to zero configurational velocity surfaces, II. The best possible configurational velocity surfaces (1987) (18)
Unifying voting theory from Nakamura's to Greenberg's theorems (2014) (18)
The profile structure for Luce's choice axiom (2004) (17)
A New Way to Analyze Paired Comparison Rules (2014) (16)
Regularization and the artificial Earth satellite problem (1974) (15)
Inconsistencies of Weighted Summation Voting Systems (1982) (15)
Informational geometry of social choice (1997) (15)
Mathematics and the “Dark Matter” Puzzle (2015) (14)
Price Dynamics, Social Choice, Voting Methods, Probability and Chaos (1985) (14)
The ease of generating chaotic behavior in economics (1996) (13)
Geometry of Chaotic and Stable Discussions (2004) (13)
Symmetry of Nonparametric Statistical Tests on Three Samples (2007) (13)
Dynamics of macrosystems : proceedings of a Workshop on the Dynamics of Macrosystems held at the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria, September 3-7, 1984 (1985) (13)
Mathematics Motivated by the Social and Behavioral Sciences (2018) (12)
Aggregation and Multilevel Design for Systems: Finding Guidelines (2010) (12)
Relationship admitting families of candidates (1991) (12)
Chaos and the Theory of Elections (1987) (12)
Hamiltonian Dynamics and Celestial Mechanics (1996) (11)
TheN-body problem of celestial mechanics (1976) (11)
Symmetry extensions of “neutrality” I: Advantage to the condorcet loser (1992) (11)
Singularity theory of utility mappings - I. Degenerate Maxima and Pareto Optima (1977) (11)
On oscillatory motion in gravitational systems. (1973) (11)
N body spatial Parabolic orbits asymptotic to collinear central configurations (1983) (10)
Connecting pairwise and positional election outcomes (2013) (10)
Mathematics and Voting (2008) (10)
From the Luce Choice Axiom to the Quantal Response Equilibrium (2016) (10)
Adopting a Plurality Vote Perspective (2002) (10)
Symmetry extensions of “neutrality” (1993) (9)
Escape from a gravitational system of positive energy (1970) (9)
On the types of information and mechanism design (1988) (9)
Apportionment Methods and the House of Representatives (1978) (9)
Systematic analysis of multiple voting rules (2010) (9)
On oscillatory motion in the problem of three bodies (1970) (9)
Collisions are of first category (1975) (9)
ARE PART WISE COMPARISONS RELIABLE ? (2003) (8)
Hamiltonian dynamical systems (1988) (8)
Periodic orbits for the planar Newtonian three-body problem coming from the elliptic restricted three-body problems (1995) (8)
Connections and Implications of the Ostrogorski Paradox for Spatial Voting Models (2010) (8)
An Elementary Tauberian Theorem for Absolutely Continuous Functions and for Series (1974) (7)
Finessing a point: augmenting the core (2006) (7)
Singularities of Newtonian Gravitational Systems (1973) (7)
Erratum to “Improbability of collisions in Newtonian gravitational systems” (1972) (7)
IMPLICATIONS OF THE INVERSE-SQUARE-LAW MODEL. (1971) (7)
Are Individual Rights Possible (1997) (7)
Changes that cause changes (2000) (7)
Fundamentals and Implications of Decision-Making (2006) (6)
Central Configurations — A Problem for the Twenty-first Century (2005) (6)
Condorcet Domains: A Geometric Perspective (2007) (6)
Strategic and Behavioral Decomposition of 2 × 2 × · · · × 2 Games (2013) (6)
Zero velocity hypersurfaces for the general three-dimensional three-body problem (1986) (5)
Security in the Age of Systemic Risk: Strategies, Tactics and Options for Dealing with Femtorisks and Beyond (2012) (5)
Toward a Theory of Systems Engineering (2020) (5)
How likely is it (2005) (5)
Singularities in the Newtonian n-body Problem (1996) (5)
On the design of complex organizations and distributive algorithms (1990) (5)
The angle of escape in the three body problem (1974) (5)
BAD DECISIONS ; EXPERIMENTAL ERROR OR FAULTY DECISION PROCEDURES ? (5)
Some informational requirements for convergence (1987) (5)
A globally convergent algorithm for determining approximate real zeros of a class of functions (1975) (5)
Superhyperbolic expansion, noncollision singularities and symmetry configurations (1994) (5)
On Newtonian cosmology with a varying gravitational constant (1977) (4)
Social science puzzles: a systems analysis challenge (2015) (4)
From Black's Advice and Arrow's Theorem to the Gibbard-Satterthewaite Result (2010) (4)
Hidden Mathematical Structures of Voting (2006) (4)
Seeking consistency with paired comparisons: a systems approach (2021) (4)
N-BODY SOLUTIONS AND COMPUTING GALACTIC MASSES (2015) (4)
Likelihood of voting outcomes with generalized IAC probabilities (2017) (4)
Interdependent Altruistic Preference Models (2020) (4)
Power series solutions (1970) (4)
Some Generic Properties of Paths Generated by Fixed Point Algorithms (1980) (3)
Arrow, and unexpected consequences of his theorem (2019) (3)
From Decision Problems to Dethroned Dictators (2008) (3)
Dynamical Systems and Mathematical Economics (1986) (3)
Toward a Mathematical Modeling of Creativity (1997) (3)
Sen's Theorem: Geometric Proof and New Interpretations (2005) (3)
Election Relations and a Partial Ordering for Positional Voting (1996) (3)
Mathematical snapshots motivated by “dark matter” (2010) (3)
With Potential Games, Which Outcome Is Better? (2020) (3)
Chaos, but in voting and apportionments? (1999) (3)
Source of complexity in the social and managerial sciences: an extended Sen’s theorem (2011) (3)
The symmetry and complexity of elections (1997) (3)
Sen’s theorem: geometric proof, new interpretations (2008) (3)
Explaining Positional Voting Paradoxes II: The General Case (1997) (2)
A Case Against Bullet, Approval and Plurality Voting (1985) (2)
Lectures on Celestial Mechanics (C. L. Siegel and J. K. Moser) (1973) (2)
Instability and Diffusion in the Elliptic Restricted Three-body Problem (1998) (2)
Some large $O$ nonlinear Tauberian theorems (1969) (2)
Explaining Positional Voting Paradoxes: The Simple Case (1997) (2)
Explanations And Examples (2001) (2)
Guest editorial: special issue on electronic voting (2009) (2)
COOPERATION IN n-PLAYER REPEATED GAMES (2013) (2)
Sufficient Statistics, Utility Theory, and Mechanism Design (1995) (2)
Basis for binary comparisons and non-standard probabilities (2016) (2)
The Representation Problem and the Efficiency of the Price Mechanism (1985) (2)
An elementary Tauberian theorem of nonlinear type (1970) (2)
Virial Theorem, Dark Matter, and N‐Body Problems (2008) (2)
Stability of incompressible systems. (1971) (2)
The Core with Positional Spatial Voting (2009) (2)
Strategic equilibria and decisive set structures for social choice mechanisms (1982) (2)
What Else Can Go Wrong (2001) (1)
Modeling Decisions Involving Ambiguous, Vague, or Rare Events (2016) (1)
Reflections on my conjecture, and several new ones (2005) (1)
Random Behavior in Numerical Analysis, Decision Theory, and Macrosystems: Some Impossibility Theorems (1985) (1)
Game Theory and Strategy (Philip D. Straffin); Mathematics and Politics (Alan D. Taylor) (1996) (1)
Celestial mechanics: Orbits of all sorts (1998) (1)
“MATHEMATICAL SOCIAL SCIENCES;” AN OXYMORON? (2002) (1)
Some Consequences of ‘Recurrence and Expansion’: What Can We Learn about Logistic Networks from Chaos? (1993) (1)
On global existence and uniqueness theorems for gravitational systems (1973) (1)
Foliations Leaf Through Economics (1999) (1)
Inherent Symmetries of graphs, paths, and Traveling Salesperson Problems (2022) (1)
A Fourth Grade Experience (1997) (1)
Hamiltonian dynamical systems : proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held June 21-27, 1987 with support from the National Science Foundation (1988) (1)
A Tool Kit for Voting Theory (2008) (1)
Mathematics of Finance (2019) (1)
Peter Emerson (ed): Designing an all-inclusive democracy (2010) (1)
Strategic and behavioral decomposition of games (2015) (1)
Explaining All Possible Paired Comparison Problems (2013) (1)
Symmetry and Extensions of Arrow's Theorem (1987) (1)
Hamiltonian dynamics and celestial mechanics: a Joint Summer Research Conference n Hamiltonian Dynamics and Celestial Mechanics, June 25-29, 1995, Seattle, Washington (1996) (1)
How many mathematicians have won Nobels? (2006) (1)
The Black–Scholes Equation (2019) (1)
Paradoxes of Voting (2013) (0)
Decisions and Elections: Glossary, Notes, and Technical Talk (2001) (0)
In Memorian. Professor Harry Pollard. 1919-1985 (1985) (0)
Suppose You Want to Vote Strategically (2000) (0)
Reexamining the Complexities in Consensus Theory (2010) (0)
An Arrow’s Theorem Perspective on Networks (1998) (0)
Two-Person Multi-strategy Games (2019) (0)
Expertise and Complexity in the Social and Engineering Sciences : An Extended Sen ’ s Theorem (2007) (0)
Decisions and Elections: Preface (2001) (0)
Explaining Voting Paradoxes; Including Arrow's and Sen's Theorems - (Invited Tutorial) (2011) (0)
From Symmetry to the Borda Count and Other Procedures (1994) (0)
Multiplayer Games (2019) (0)
Extensive Form Games (2019) (0)
Complexities of electing diverse committees (2013) (0)
Geometry for Positional and Pairwise Voting (1994) (0)
The Problem with Condorcet (1995) (0)
Explaining All Voting Paradoxes (2008) (0)
Solutions of Black–Scholes (2019) (0)
Nonparametric Tests, Paradoxes in (2014) (0)
Evolution of the universe (2004) (0)
Modeling Complexity in Mathematics Education (2008) (0)
Clusters of galaxies and the N-body problem. (1972) (0)
The Copeland method * I . : Relat ionships and the dict ionary (0)
Finding central configurations (2005) (0)
Connecting Arrow's Theorem, voting theory, and the traveling salesperson problem (2022) (0)
QUALITATIVE FEATURES OF MEDICAL ETHICS (2017) (0)
Externalities, Public Goods and the Generic Stucture of Pareto Sets (1976) (0)
IMPROBABILITY OF COLLISIONS IN NEWTONIAN (2010) (0)
Voting changed my teaching approach (2012) (0)
Arrow, and unexpected consequences of his theorem (2018) (0)
Book Review (2000) (0)
Nonlinear Dynamics Applied to Numerical Analysis and Economics (1988) (0)
Decisions and Elections: More Perversities (2001) (0)
Chaos, but in voting and apportionn (2016) (0)
COLLISIONS ARE OF FIRST CATEGORY 1 (2010) (0)
Expertise & Complexity in the Soc. & Engr. Sci. : An Extended Sen's Theorem (2008) (0)
UNIFYING VOTING THEORY RESULTS FROM NAKAMURA ’ S TO GREENBERG ’ S THEOREMS (2012) (0)
Sketching and the American Options (2019) (0)
From an Election Fable to Election Procedures (1994) (0)
Collisions–Both real and imaginary (2005) (0)
Explaining Paradoxes in Nonparametric Statistics (2011) (0)
Positional Voting and the BC (1995) (0)
Deliver Us from the Plurality Vote (2008) (0)
Norman James Schofield 1944–2019 (2020) (0)
Foreword (2020) (0)
Disposing Dictators, Demystifying Voting Paradoxes: Subtle Complexity of Social Choice (2008) (0)
Dynamics of Macrosystems; Proceedings of a Workshop, September 3-7, 1984 (1985) (0)
A NEW WAY TO ANALYZE PAIRED COMPARISONS (2010) (0)
Modeling (2019) (0)
MBS 00-19 Suppose You Want to Vote Strategically ? (0)
Other Voting Issues (1995) (0)
INSTITUTE FOR MATHEMATICAL AND BEHAVIORAL SCIENCES "VALIDATION. WHAT IS IT?" SSPA 2112, DUNCAN LUCE CONFERENCE ROOM February 13, 1:00 - 5:00 p.m. & February 14, 9:15 a.m. - 5:00 p.m. (2015) (0)
Reviews (2008) (0)
Introduction (2019) (0)
From Arrow's Theorem to Incentives and Price Dynamics (1999) (0)
Geometry of Voting 1 (2010) (0)
Selecting a voting method: the case for the Borda count (2022) (0)
Disposing Dictators, Demystifying Voting Paradoxes: References (2008) (0)
Options (2019) (0)
About books (1982) (0)
Fair Allocation (H. Peyton Young) (1988) (0)
Reflections on the "Saari Conjecture" and several new ones (2008) (0)
Corrigendum The likelihood of dubious election outcomes (1999) (0)
Dynamics and Clusters of Galaxies (1974) (0)
Appendix: Extending the Upset Child Example (2008) (0)
UC Irvine Other Recent Work Title Geometry of Chaotic and Stable Discussions Permalink (2003) (0)
Voting mysteries: a picture is worth a thousand words (2015) (0)
Decisions and Elections: A Search For Resolutions (2001) (0)
Hippocratic Paradox: Coevolution of Medical Ethics, Health Law, and Social Practice (2020) (0)
Decisions and Elections: Do We Get What We Expect? (2001) (0)
The Three Body Problem by Mauri Valtonen; Hannu Karrunen (2008) (0)
Decisions and Elections: From Sen To Prisoners and Prostitution (2001) (0)
The Underlying Mathematics (2019) (0)
On the design of coaplex organizations and distributive algorithas (1989) (0)
CALL FOR PAPERS IEEE Transactions on Information Forensics and Security: Special Issue on Electronic Voting (2009) (0)
Preliminaries via Gambles (2019) (0)
Aggregation and Multilevel Design for Systems: Finding (2012) (0)
Separation of clusters in theN-body problem (1970) (0)
Decisions and Elections: Arrow's Theorem (2001) (0)
Disposing Dictators, Demystifying Voting Paradoxes: Dethroning Dictators (2008) (0)
Social Stability and Equilibrium (1989) (0)
Partial Information: The Greeks (2019) (0)
L: Relationships and the dictionary (1996) (0)
Many Profiles; Many New Paradoxes (1994) (0)
Re: a New Approach to Social Dynamics (02-18-2004) Presentation for the Social Dynamics and Evolution Group of Mbs How Can We Understand Historical Process? Response Commentary and Questions (2004) (0)
Consequences (2019) (0)
Sharpest Possible Zero Configurational Velocity Surfaces (1986) (0)
The way it was : mathematics from the early years of the Bulletin (2003) (0)
Two-Player, Two-Strategy Games (2019) (0)
Celestial mechanics. (1982) (0)
From Paired Comparisons and Cycles to Arrow’s Theorem (2019) (0)

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