Donald G Saari
Biographic Data
| ID | 1081741 |
|---|---|
| NAME | Donald G Saari |
| GIVEN NAMES | Donald G |
| FAMILY NAME | Saari |
| SIGNATURE | SAARI D G |
| AFFILIATIONS | University of California, Irvine |
| VERIFIED | No |
| TOTAL WORKS | 18 |
| TOTAL CITATIONS | 59 |
| AUTHOR COUNT | 18 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 1982 |
| LATEST PUBLICATION YEAR | 2024 |
| H-INDEX | 5 |
Closed paths in graphs vs. voting theory
Features of graphs that hinder finding closed paths with particular properties, as represented by the Traveling Salesperson Problem—TSP, are identified for three classes of graphs. Removing these terms leads to a companion graph with identical closed path properties that is easier to analyze. A surprise is that these troubling graph factors are precisely what is needed to analyze certain voting methods, while the companion graph’s terms are what …
Selecting a voting method
Of importance when selecting a voting method is whether, on a regular basis, its outcomes accurately capture the intent of voters. A surprise is that very few procedures do this. Another desired feature is for a decision approach to assist groups in reaching a consensus (Sect. 5). As described, these goals are satisfied only with the Borda count. Addressing these objectives requires understanding what can go wrong, what causes voting difficulties…
Seeking consistency with paired comparisons
It is well known that decision methods based on pairwise rankings can suffer from a wide range of difficulties. These problems are addressed here by treating the methods as systems, where each pair is looked upon as a subsystem with an assigned task. In this manner, the source of several difficulties (including Arrow’s Theorem) is equated with the standard concern that the “whole need not be the sum of its parts.” These problems arise because the…
Norman James Schofield 1944–2019
Arrow, and unexpected consequences of his theorem
Mathematics Motivated by the Social and Behavioral Sciences
Mathematics Motivated by the Social and Behavioral Sciences
Likelihood of voting outcomes with generalized IAC probabilities
From Arrow’s Theorem to ‘Dark Matter
Arrow’s Impossibility Theorem and Sen’s Minimal Liberalism example impose ‘impossibility’ roadblocks on progress. A reinterpretation explained in this article exposes what causes these negative conclusions, which permits the development of positive resolutions that retain the spirit of Arrow’s and Sen’s assumptions. What precipitates difficulties is surprisingly common, and it affects most disciplines. This insight identifies how to analyze other…
Unifying voting theory from Nakamura’s to Greenberg’s theorems
Social Norms and Global Environmental Challenges
Government policies are needed when people's behaviors fail to deliver the public good. Those policies will be most effective if they can stimulate long-term changes in beliefs and norms, creating and reinforcing the behaviors needed to solidify and extend the public good.It is often the short-term acceptability of potential policies, rather than their longer-term efficacy, that determines their scope and deployment. The policy process should con…
Connecting pairwise and positional election outcomes
A Tool Kit for Voting Theory
This article lists down some results that can serve as useful tools to analyze actual elections. It first looks at representing profiles, which enumerate the number of voters who have each ranking of the candidates. Procedure line and hulls are used to provide a display of the different outcomes of computing tallies. The article moves on to the ‘axiomatic representations’ of voting rules, and then looks at how the ‘will of the voters’ is determin…
The Sum of the Parts Can Violate the Whole
We develop a geometric approach to identify all possible profiles that support specified votes for separate initiatives or for a bundled bill. This disaggregation allows us to compute the likelihood of different scenarios describing how voters split over the alternatives and to offer new interpretations for pairwise voting. The source of the problems-an unanticipated loss of available information-also explains a variety of other phenomena, such a…
Susceptibility to manipulation
Is approval voting an ‘unmitigated evil’
The problem of indeterminacy in approval, multiple, and truncated voting systems
Strategic equilibria and decisive set structures for social choice mechanisms
Susceptibility to manipulation
Is approval voting an ‘unmitigated evil’
The problem of indeterminacy in approval, multiple, and truncated voting systems
From Arrow’s Theorem to ‘Dark Matter
Arrow’s Impossibility Theorem and Sen’s Minimal Liberalism example impose ‘impossibility’ roadblocks on progress. A reinterpretation explained in this article exposes what causes these negative conclusions, which permits the development of positive resolutions that retain the spirit of Arrow’s and Sen’s assumptions. What precipitates difficulties is surprisingly common, and it affects most disciplines. This insight identifies how to analyze other…
The Sum of the Parts Can Violate the Whole
We develop a geometric approach to identify all possible profiles that support specified votes for separate initiatives or for a bundled bill. This disaggregation allows us to compute the likelihood of different scenarios describing how voters split over the alternatives and to offer new interpretations for pairwise voting. The source of the problems-an unanticipated loss of available information-also explains a variety of other phenomena, such a…
Unifying voting theory from Nakamura’s to Greenberg’s theorems
Connecting pairwise and positional election outcomes
Selecting a voting method
Of importance when selecting a voting method is whether, on a regular basis, its outcomes accurately capture the intent of voters. A surprise is that very few procedures do this. Another desired feature is for a decision approach to assist groups in reaching a consensus (Sect. 5). As described, these goals are satisfied only with the Borda count. Addressing these objectives requires understanding what can go wrong, what causes voting difficulties…
Arrow, and unexpected consequences of his theorem
Likelihood of voting outcomes with generalized IAC probabilities
Strategic equilibria and decisive set structures for social choice mechanisms
Strategic equilibria and decisive set structures for social choice mechanisms
Is approval voting an ‘unmitigated evil’
The problem of indeterminacy in approval, multiple, and truncated voting systems
Susceptibility to manipulation
The Sum of the Parts Can Violate the Whole
We develop a geometric approach to identify all possible profiles that support specified votes for separate initiatives or for a bundled bill. This disaggregation allows us to compute the likelihood of different scenarios describing how voters split over the alternatives and to offer new interpretations for pairwise voting. The source of the problems-an unanticipated loss of available information-also explains a variety of other phenomena, such a…
A Tool Kit for Voting Theory
This article lists down some results that can serve as useful tools to analyze actual elections. It first looks at representing profiles, which enumerate the number of voters who have each ranking of the candidates. Procedure line and hulls are used to provide a display of the different outcomes of computing tallies. The article moves on to the ‘axiomatic representations’ of voting rules, and then looks at how the ‘will of the voters’ is determin…
Social Norms and Global Environmental Challenges
Government policies are needed when people's behaviors fail to deliver the public good. Those policies will be most effective if they can stimulate long-term changes in beliefs and norms, creating and reinforcing the behaviors needed to solidify and extend the public good.It is often the short-term acceptability of potential policies, rather than their longer-term efficacy, that determines their scope and deployment. The policy process should con…
Connecting pairwise and positional election outcomes
Unifying voting theory from Nakamura’s to Greenberg’s theorems
From Arrow’s Theorem to ‘Dark Matter
Arrow’s Impossibility Theorem and Sen’s Minimal Liberalism example impose ‘impossibility’ roadblocks on progress. A reinterpretation explained in this article exposes what causes these negative conclusions, which permits the development of positive resolutions that retain the spirit of Arrow’s and Sen’s assumptions. What precipitates difficulties is surprisingly common, and it affects most disciplines. This insight identifies how to analyze other…
Likelihood of voting outcomes with generalized IAC probabilities
Mathematics Motivated by the Social and Behavioral Sciences
Mathematics Motivated by the Social and Behavioral Sciences
Arrow, and unexpected consequences of his theorem
Norman James Schofield 1944–2019
Seeking consistency with paired comparisons
It is well known that decision methods based on pairwise rankings can suffer from a wide range of difficulties. These problems are addressed here by treating the methods as systems, where each pair is looked upon as a subsystem with an assigned task. In this manner, the source of several difficulties (including Arrow’s Theorem) is equated with the standard concern that the “whole need not be the sum of its parts.” These problems arise because the…
Selecting a voting method
Of importance when selecting a voting method is whether, on a regular basis, its outcomes accurately capture the intent of voters. A surprise is that very few procedures do this. Another desired feature is for a decision approach to assist groups in reaching a consensus (Sect. 5). As described, these goals are satisfied only with the Borda count. Addressing these objectives requires understanding what can go wrong, what causes voting difficulties…
Closed paths in graphs vs. voting theory
Features of graphs that hinder finding closed paths with particular properties, as represented by the Traveling Salesperson Problem—TSP, are identified for three classes of graphs. Removing these terms leads to a companion graph with identical closed path properties that is easier to analyze. A surprise is that these troubling graph factors are precisely what is needed to analyze certain voting methods, while the companion graph’s terms are what …
Mathematical economics (14 works) · Political science (14 works) · Game Theory and Voting Systems (12 works) · Law (12 works) · Voting (12 works) · Computer Science (11 works) · Economics (11 works) · Law (10 works) · Mathematics (9 works) · Arrow (7 works)