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Edward W. Packel

Other affiliations: Columbia University
Bio: Edward W. Packel is an academic researcher from Lake Forest College. The author has contributed to research in topics: Social choice theory & Information-based complexity. The author has an hindex of 15, co-authored 37 publications receiving 1630 citations. Previous affiliations of Edward W. Packel include Columbia University.

Papers
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Journal ArticleDOI
01 Jul 1987-Nature
TL;DR: Information-based complexity seeks to develop general results about the intrinsic difficulty of solving problems where available information is partial or approximate and to apply these results to specific problems.
Abstract: Information-based complexity seeks to develop general results about the intrinsic difficulty of solving problems where available information is partial or approximate and to apply these results to specific problems. This allows one to determine what is meant by an optimal algorithm in many practical situations, and offers a variety of interesting and sometimes surprising theoretical results.

647 citations

Journal ArticleDOI
TL;DR: In this article, an alternative power index to the familiar Shapley/Shubik and Banzhaf indices is presented for the class of simplen-person games, which can be used for assessing the character of interpersonal interaction found in collective decision-making bodies.
Abstract: Measures of (a priori) power play a useful role in assessing the character of interpersonal interaction found in collective decision making bodies. We propose and axiomatically characterize an alternative power index to the familiarShapley/Shubik andBanzhaf indices which can be used for such purposes. The index presented is shown to be unique for the class of simplen-person games. By subsequent generalization of the index and its axioms to the class ofn-person games in characteristic function form we obtain an analog to theShapley value.

403 citations

Journal ArticleDOI
01 Mar 1983
TL;DR: In this article, the theoretical drawbacks of the traditional indices for measuring a priori voting power inasmuch as they are implied in considering the coalition value a private good were pointed out.
Abstract: We have pointed out the theoretical drawbacks of the traditional indices for measuring a priori voting power inasmuch as they are implied in considering the coalition value a private good. This criticism caused us to view the coalition outcome as a public good. From this aspect and additional considerations with respect to power, luck, and decisiveness, we obtained a “story” describing the characteristics of an adequate measure of a priori voting power. These characteristics were found to be fulfilled by an index presented by Holler (1978). Through the above analysis this index has received its theoretical justification. An independent view of this index was then provided by means of an axiomatic characterization. This characterization makes possible abstract comparison of the index with previously established “private good” indices. While we have restricted our attention to simple games, the index presented can be generalized to provide a “value” on games in characteristic function form. We leave this topic for future conideration.

208 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that for a wide class of voting rules, a limiting distribution always exists and bounds for the concentration of the limiting distribution around a centrally located set.
Abstract: This paper proves the existence of a stationary distribution for a class of Markov voting models. We assume that alternatives to replace the current status quo arise probabilistically, with the probability distribution at time t+1 having support set equal to the set of alternatives that defeat, according to some voting rule, the current status quo at time t. When preferences are based on Euclidean distance, it is shown that for a wide class of voting rules, a limiting distribution exists. For the special case of majority rule, not only does a limiting distribution always exist, but we obtain bounds for the concentration of the limiting distribution around a centrally located set. The implications are that under Markov voting models, small deviations from the conditions for a core point will still leave the limiting distribution quite concentrated around a generalized median point. Even though the majority relation is totally cyclic in such situations, our results show that such chaos is not probabilistically significant.

101 citations

Journal ArticleDOI
TL;DR: Packel as mentioned in this paper did his undergraduate work at Amherst College and received a Ph.D. in functional analysis from M.I.T. Since 1971 he has taught at Lake Forest College, where he served as department chair from 1986 to 1996.
Abstract: Ed Packel (packel@lakeforest.edu) did his undergraduate work at Amherst College and received a Ph.D. in functional analysis from M.I.T. in 1967. Since 1971 he has taught at Lake Forest College, where he served as department chair from 1986 to 1996. His research interests have oscillated among functional analysis, game theory, social choice theory, information-based complexity, and the use of technology (Mathematica) in teaching. His recreational enthusiasms have somehow gravitated towards sports where low numbers are good-namely, competitive distance running and golf.

46 citations


Cited by
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Journal ArticleDOI
TL;DR: The authors prove two results about this type of estimator that are unprecedented in several ways: with high probability f/spl circ/*/sub n/ is at least as smooth as f, in any of a wide variety of smoothness measures.
Abstract: Donoho and Johnstone (1994) proposed a method for reconstructing an unknown function f on [0,1] from noisy data d/sub i/=f(t/sub i/)+/spl sigma/z/sub i/, i=0, ..., n-1,t/sub i/=i/n, where the z/sub i/ are independent and identically distributed standard Gaussian random variables. The reconstruction f/spl circ/*/sub n/ is defined in the wavelet domain by translating all the empirical wavelet coefficients of d toward 0 by an amount /spl sigma//spl middot//spl radic/(2log (n)/n). The authors prove two results about this type of estimator. [Smooth]: with high probability f/spl circ/*/sub n/ is at least as smooth as f, in any of a wide variety of smoothness measures. [Adapt]: the estimator comes nearly as close in mean square to f as any measurable estimator can come, uniformly over balls in each of two broad scales of smoothness classes. These two properties are unprecedented in several ways. The present proof of these results develops new facts about abstract statistical inference and its connection with an optimal recovery model. >

9,359 citations

Book
01 Jan 2002
TL;DR: In this paper, Veto players analysis of European Union Institutions is presented, focusing on the role of individual veto players and collective players in the analysis of the institutions of the European Union.
Abstract: List of Figures ix List of Tables xi Preface and Acknowledgments xiii Introduction 1 PART I: VETO PLAYERS THEORY 17 One: Individual Veto Players 19 Two: Collective Veto Players 38 PART II: VETO PLAYERS AND INSTITUTIONAL ANALYSIS 65 Three: Regimes: Nondemocratic, Presidential, and Parliamentary 67 Four: Governments and Parliaments 91 Five: Referendums 116 Six: Federalism, Bicameralism, and Qualified Majorities 136 PART III: POLICY EFFECTS OF VETO PLAYERS 161 Seven: Legislation 165 Eight: Macroeconomic Policies 187 PART IV: SYSTEMIC EFFECTS OF VETO PLAYERS 207 Nine: Government Stability 209 Ten: Judiciary and Bureaucracies 222 Eleven: Veto Players Analysis of European Union Institutions 248 Conclusion 283 Bibliography 291 Index 309

2,983 citations

Journal ArticleDOI
TL;DR: In this article, the authors compare different political systems with respect to one property: their capacity to produce policy change, and the potential for policy change decreases with the number of veto players, the lack of congruence (dissimilarity of policy positions among veto players) and the cohesion (similarity of policies among the constituent units of each veto player) of these players.
Abstract: The article compares different political systems with respect to one property: their capacity to produce policy change. I define the basic concept of the article, the ‘veto player’: veto players are individual or collective actors whose agreement (by majority rule for collective actors) is required for a change of the status quo. Two categories of veto players are identified in the article: institutional and partisan. Institutional veto players (president, chambers) exist in presidential systems while partisan veto players (parties) exist at least in parliamentary systems. Westminster systems, dominant party systems and single-party minority governments have only one veto player, while coalitions in parliamentary systems, presidential or federal systems have multiple veto players. The potential for policy change decreases with the number of veto players, the lack of congruence (dissimilarity of policy positions among veto players) and the cohesion (similarity of policy positions among the constituent units of each veto player) of these players. The veto player framework produces results different from existing theories in comparative politics, but congruent with existing empirical studies. In addition, it permits comparisons across different political and party systems. Finally, the veto player framework enables predictions about government instability (in parliamentary systems) or regime instability (in presidential systems); these predictions are supported by available evidence.

2,196 citations

Journal ArticleDOI
TL;DR: A method for curve estimation based on n noisy data: translate the empirical wavelet coefficients towards the origin by an amount √(2 log n) /√n and draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves.
Abstract: Much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects-curves, densities, spectral densities, images-from noisy data A now rich and complex body of work develops nearly or exactly minimax estimators for an array of interesting problems Unfortunately, the results have rarely moved into practice, for a variety of reasons-among them being similarity to known methods, computational intractability and lack of spatial adaptivity We discuss a method for curve estimation based on n noisy data: translate the empirical wavelet coefficients towards the origin by an amount √(2 log n) /√n The proposal differs from those in current use, is computationally practical and is spatially adaptive; it thus avoids several of the previous objections Further, the method is nearly minimax both for a wide variety of loss functions-pointwise error, global error measured in L p -norms, pointwise and global error in estimation of derivatives-and for a wide range of smoothness classes, including standard Holder and Sobolev classes, and bounded variation This is a much broader near optimality than anything previously proposed: we draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves Finally, the theory underlying the method is interesting, as it exploits a correspondence between statistical questions and questions of optimal recovery and information-based complexity

1,639 citations

Book
30 Oct 1997
TL;DR: This chapter discusses decision problems and Complexity over a Ring and the Fundamental Theorem of Algebra: Complexity Aspects.
Abstract: 1 Introduction.- 2 Definitions and First Properties of Computation.- 3 Computation over a Ring.- 4 Decision Problems and Complexity over a Ring.- 5 The Class NP and NP-Complete Problems.- 6 Integer Machines.- 7 Algebraic Settings for the Problem "P ? NP?".- 8 Newton's Method.- 9 Fundamental Theorem of Algebra: Complexity Aspects.- 10 Bezout's Theorem.- 11 Condition Numbers and the Loss of Precision of Linear Equations.- 12 The Condition Number for Nonlinear Problems.- 13 The Condition Number in ?(H(d).- 14 Complexity and the Condition Number.- 15 Linear Programming.- 16 Deterministic Lower Bounds.- 17 Probabilistic Machines.- 18 Parallel Computations.- 19 Some Separations of Complexity Classes.- 20 Weak Machines.- 21 Additive Machines.- 22 Nonuniform Complexity Classes.- 23 Descriptive Complexity.- References.

1,594 citations