scholarly journals An analytical and experimental comparison of maximal lottery schemes

2021 ◽  
Author(s):  
Florian Brandl ◽  
Felix Brandt ◽  
Christian Stricker
Keyword(s):  
Computer Simulations ◽  
Condorcet Winner ◽  
Average Degree ◽  
Experimental Comparison ◽  
Voting Rules ◽  
Weighted Majority ◽  
Interesting Class ◽  
Relative Notion

AbstractMaximal lottery ($$ ML $$ ML ) schemes constitute an interesting class of randomized voting rules that were proposed by Peter Fishburn in 1984 and have been repeatedly recommended for practical use. However, the subtle differences between different $$ ML $$ ML schemes are often overlooked. Two canonical subsets of $$ ML $$ ML schemes are "Image missing" schemes (which only depend on unweighted majority comparisons) and "Image missing" schemes (which only depend on weighted majority comparisons). We prove that "Image missing" schemes are the only homogeneous $$ ML $$ ML schemes that satisfy $$ SD $$ SD -efficiency and $$ SD $$ SD -participation, but are also among the most manipulable $$ ML $$ ML schemes. While all $$ ML $$ ML schemes are manipulable and even violate monotonicity, they are never manipulable when a Condorcet winner exists and satisfy a relative notion of monotonicity. We also evaluate the frequency of manipulable preference profiles and the degree of randomization of $$ ML $$ ML schemes via extensive computer simulations. In summary, $$ ML $$ ML schemes are rarely manipulable and often do not randomize at all, especially for few alternatives. The average degree of randomization of "Image missing" schemes is consistently lower than that of "Image missing" schemes.

scholarly journals An Analytical and Experimental Comparison of Maximal Lottery Schemes

2018 ◽  
Author(s):  
Florian Brandl ◽  
Felix Brandt ◽  
Christian Stricker
Keyword(s):  
Social Choice ◽  
Computer Simulations ◽  
Shannon Entropy ◽  
Experimental Comparison ◽  
Computational Social Choice ◽  
Voting Rules ◽  
Weighted Majority ◽  
Support Size ◽  
Interesting Class ◽  
Pareto Efficient

Randomized voting rules are gaining increasing attention in computational and non-computational social choice. A particularly interesting class of such rules are maximal lottery (ML) schemes, which were proposed by Peter Fishburn in 1984 and have been repeatedly recommended for practical use. However, the subtle differences between different ML schemes are often ignored. Two canonical subsets of ML schemes are C1-ML schemes (which only depend on unweighted majority comparisons) and C2-ML schemes (which only depend on weighted majority comparisons). We prove that C2-ML schemes are the only Pareto efficient---but also among the most manipulable---ML schemes. Furthermore, we evaluate the frequency of manipulable preference profiles and the degree of randomization of ML schemes via extensive computer simulations. In general, ML schemes are rarely manipulable and often do not randomize at all, especially when there are only few alternatives. For up to 21 alternatives, the average support size of ML schemes lies below 4 under reasonable assumptions. The average degree of randomization (in terms of Shannon entropy) of C2-ML schemes is significantly lower than that of C1-ML schemes.

Computer simulations of voting systems

2000 ◽  
Vol 03 (01n04) ◽  
pp. 181-194 ◽  
Author(s):  
Dominique Lepelley ◽  
Ahmed Louichi ◽  
Fabrice Valognes
Keyword(s):  
Monte Carlo ◽  
Computer Simulations ◽  
Monte Carlo Methods ◽  
Scoring Rules ◽  
Voting Systems ◽  
Voting Rules ◽  
Asymptotic Case ◽  
Majority Principle ◽  
Voting Procedures ◽  
Democratic Principles

All voting procedures are susceptible to give rise, if not to paradoxes, at least to violations of some democratic principles. In this paper, we evaluate and compare the propensity of various voting rules -belonging to the class of scoring rules- to satisfy two versions of the majority principle. We consider the asymptotic case where the numbers of voters tends to infinity and, for each rule, we study with the help of Monte Carlo methods how this propensity varies as a function of the number of candidates.

scholarly journals A Complete Description of the Dynamics of Legal Outer-totalistic Affine Continuous Cellular Automata

2021 ◽  
Author(s):  
Barbara Wolnik ◽  
Marcin Dembowski ◽  
Antoni Augustynowicz ◽  
Bernard De Baets
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Computer Simulations ◽  
Analytical Methods ◽  
Unique Combination ◽  
Binary Case ◽  
Interesting Class

Abstract We present an investigation into the evolution and dynamics of the simplest generalization of binary cellular automata: Affine Continuous Cellular Automata (ACCAs), with [0,1] as state set and local rules that are affine in each variable. We focus on legal outer-totalistic ACCAs, an interesting class of dynamical systems that show some properties that do not occur in the binary case. A unique combination of computer simulations (sometimes quite advanced) and a panoply of analytical methods allow to lay bare the dynamics of each and every one of these cellular automata.

scholarly journals The Incidence of Some Voting Paradoxes Under Domain Restrictions

2020 ◽  
Vol 29 (6) ◽  
pp. 1107-1120
Author(s):  
Hannu Nurmi
Keyword(s):  
Condorcet Winner ◽  
Additional Restriction ◽  
Voting Rules ◽  
Voting Rule ◽  
Starting Point ◽  
Voting Paradoxes ◽  
Domain Restrictions

Abstract Voting paradoxes have played an important role in the theory of voting. They typically say very little about the circumstances in which they are particularly likely or unlikely to occur. They are basically existence findings. In this article we study some well known voting paradoxes under the assumption that the underlying profiles are drawn from the Condorcet domain, i.e. a set of preference profiles where a Condorcet winner exists. The motivation for this restriction is the often stated assumption that profiles with a Condorcet winner are more likely than those without it. We further restrict the profiles by assuming that the starting point of our analysis is that the Condorcet winner coincides with the choice of the voting rule under scrutiny. The reason for making this additional restriction is that—intuitively—the outcomes that coincide with the Condorcet winner make those outcomes stable and, thus, presumably less vulnerable to various voting paradoxes. It will be seen that this is, indeed, the case for some voting rules and some voting paradoxes, but not for all of them.

A High Resolution Study of G.P. Zones in Aluminum - 4.2 at % Silver

1982 ◽  
Vol 40 ◽  
pp. 722-723 ◽  
Author(s):  
R. Gronsky
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
High Resolution ◽  
Computer Simulations ◽  
Structural Characteristics ◽  
X Ray Diffraction ◽  
X Ray ◽  
Transmission Electron ◽  
Resolution Study

The phenomenon of clustering in Al-Ag alloys has been extensively studied since the early work of Guinierl, wherein the pre-precipitation state was characterized as an assembly of spherical, ordered, silver-rich G.P. zones. Subsequent x-ray and TEM investigations yielded results in general agreement with this model. However, serious discrepancies were later revealed by the detailed x-ray diffraction - based computer simulations of Gragg and Cohen, i.e., the silver-rich clusters were instead octahedral in shape and fully disordered, atleast below 170°C. The object of the present investigation is to examine directly the structural characteristics of G.P. zones in Al-Ag by high resolution transmission electron microscopy.

Multislice calculations for quasi-periodic and non-periodic objects

1990 ◽  
Vol 48 (4) ◽  
pp. 138-139
Author(s):  
R. Herrera ◽  
A. Gómez
Keyword(s):  
Electron Diffraction ◽  
Computer Simulations ◽  
Periodic Table ◽  
Amorphous Materials ◽  
Space Group ◽  
Essential Step ◽  
Shape Effects ◽  
Atomic Scattering ◽  
Diffraction Patterns ◽  
Periodic Continuation

Computer simulations of electron diffraction patterns and images are an essential step in the process of structure and/or defect elucidation. So far most programs are designed to deal specifically with crystals, requiring frequently the space group as imput parameter. In such programs the deviations from perfect periodicity are dealt with by means of “periodic continuation”.However, for many applications involving amorphous materials, quasiperiodic materials or simply crystals with defects (including finite shape effects) it is convenient to have an algorithm capable of handling non-periodicity. Our program “HeGo” is an implementation of the well known multislice equations in which no periodicity assumption is made whatsoever. The salient features of our implementation are: 1) We made Gaussian fits to the atomic scattering factors for electrons covering the whole periodic table and the ranges [0-2]Å−1 and [2-6]Å−1.

Computer simulations for the TEM bend contour technique

1996 ◽  
Vol 54 ◽  
pp. 134-135
Author(s):  
Vladimir Yu. Kolosov ◽  
Anders R. Thölén
Keyword(s):  
Computer Simulations ◽  
Real Space ◽  
Advantages And Disadvantages ◽  
Short Overview ◽  
Diffraction Contrast ◽  
Beam Method ◽  
Convergent Beam ◽  
Contour Technique

In this paper we give a short overview of two TEM applications utilizing the extinction bend contour technique (BC) giving the advantages and disadvantages; especially we consider two areas in which the BC technique remains unique. Special attention is given to an approach including computer simulations of TEM micrographs.BC patterns are often observed in TEM studies but are rarely exploited in a serious way. However, this type of diffraction contrast was one of the first to be used for analysis of imperfections in crystalline foils, but since then only some groups have utilized the BC technique. The most extensive studies were performed by Steeds, Eades and colleagues. They were the first to demonstrate the unique possibilities of the BC method and named it real space crystallography, which developed later into the somewhat similar but more powerful convergent beam method. Maybe, due to the difficulties in analysis, BCs have seldom been used in TEM, and then mainly to visualize different imperfections and transformations.

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