scholarly journals Cycles and Intractability in a Large Class of Aggregation Rules

2018 ◽  
Vol 61 ◽  
pp. 407-431 ◽  
Author(s):  
William S. Zwicker
Keyword(s):  
Computational Complexity ◽  
Related Problem ◽  
Borda Count ◽  
Impossibility Theorem ◽  
Approval Voting ◽  
Winner Determination ◽  
Voting Rule ◽  
Special Cases ◽  
The Mean ◽  
Cyclic Part

We introduce the (j,k)-Kemeny rule -- a generalization of Kemeny's voting rule that aggregates j-chotomous weak orders into a k-chotomous weak order. Special cases of (j,k)-Kemeny include approval voting, the mean rule and Borda mean rule, as well as the Borda count and plurality voting. Why, then, is the winner problem computationally tractable for each of these other rules, but intractable for Kemeny? We show that intractability of winner determination for the (j,k)-Kemeny rule first appears at the j=3, k=3 level. The proof rests on a reduction of max cut to a related problem on weighted tournaments, and reveals that computational complexity arises from the cyclic part in the fundamental decomposition of a weighted tournament into cyclic and cocyclic components. Thus the existence of majority cycles -- the engine driving both Arrow's impossibility theorem and the Gibbard-Satterthwaite theorem -- also serves as a source of computational complexity in social choice.

scholarly journals Winner Determination and Strategic Control in Conditional Approval Voting

2021 ◽  
Author(s):  
Evangelos Markakis ◽  
Georgios Papasotiropoulos
Keyword(s):  
Computational Complexity ◽  
Polynomial Algorithms ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Strategic Control ◽  
Approval Voting ◽  
Winner Determination ◽  
Bounded Treewidth ◽  
Voting Rule ◽  
Necessary And Sufficient

Our work focuses on a generalization of the classic Minisum approval voting rule, introduced by Barrot and Lang (2016), and referred to as Conditional Minisum (CMS), for multi-issue elections. Although the CMS rule provides much higher levels of expressiveness, this comes at the expense of increased computational complexity. In this work, we study further the issue of efficient algorithms for CMS, and we identify the condition of bounded treewidth (of an appropriate graph that emerges from the provided ballots), as the necessary and sufficient condition for polynomial algorithms, under common complexity assumptions. Additionally we investigate the complexity of problems related to the strategic control of such elections by the possibility of adding or deleting either voters or alternatives. We exhibit that in most variants of these problems, CMS is resistant against control.

scholarly journals Computational Aspects of Conditional Minisum Approval Voting in Elections with Interdependent Issues

2020 ◽  
Author(s):  
Evangelos Markakis ◽  
Georgios Papasotiropoulos
Keyword(s):  
Approximation Algorithms ◽  
Structural Properties ◽  
Upper Bounds ◽  
Efficient Algorithms ◽  
Approval Voting ◽  
Voting Rule ◽  
Special Cases ◽  
Computational Aspects

Approval voting provides a simple, practical framework for multi-issue elections, and the most representative example among such election rules is the classic Minisum approval voting rule. We consider a generalization of Minisum, introduced by the work of Barrot and Lang [2016], referred to as Conditional Minisum, where voters are also allowed to express dependencies between issues. The price we have to pay when we move to this higher level of expressiveness is that we end up with a computationally hard rule. Motivated by this, we focus on the computational aspects of Conditional Minisum, where progress has been rather scarce so far. We identify restrictions to every voter's dependencies, under which we provide the first multiplicative approximation algorithms for the problem. The restrictions involve upper bounds on the number of dependencies an issue can have on the others. At the same time, by additionally requiring certain structural properties for the union of dependencies cast by the whole electorate, we obtain optimal efficient algorithms for well-motivated special cases. Overall, our work provides a better understanding on the complexity implications introduced by conditional voting.

Decoration technique and surface physics

1978 ◽  
Vol 36 (1) ◽  
pp. 436-437 ◽  
Author(s):  
H. Bethge
Keyword(s):  
Diffusion Path ◽  
Special Importance ◽  
Surface Physics ◽  
Step Structure ◽  
Initial Stage ◽  
Special Cases ◽  
Atomic Surface ◽  
The Mean ◽  
Bulk Structure ◽  
Decoration Technique

Besides the atomic surface structure, diverging in special cases with respect to the bulk structure, the real structure of a surface Is determined by the step structure. Using the decoration technique /1/ it is possible to image step structures having step heights down to a single lattice plane distance electron-microscopically. For a number of problems the knowledge of the monatomic step structures is important, because numerous problems of surface physics are directly connected with processes taking place at these steps, e.g. crystal growth or evaporation, sorption and nucleatlon as initial stage of overgrowth of thin films.To demonstrate the decoration technique by means of evaporation of heavy metals Fig. 1 from our former investigations shows the monatomic step structure of an evaporated NaCI crystal. of special Importance Is the detection of the movement of steps during the growth or evaporation of a crystal. From the velocity of a step fundamental quantities for the molecular processes can be determined, e.g. the mean free diffusion path of molecules.

scholarly journals Thermodynamic and Elastic Properties of Interstitial Alloy FeC with BCC Structure at Zero Pressure

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Bui Duc Tinh ◽  
Nguyen Quang Hoc ◽  
Dinh Quang Vinh ◽  
Tran Dinh Cuong ◽  
Nguyen Duc Hien
Keyword(s):  
Nearest Neighbor ◽  
Young Modulus ◽  
Thermodynamic Quantities ◽  
Atom Concentration ◽  
Main Metal ◽  
Special Cases ◽  
Analytic Expressions ◽  
Rigidity Modulus ◽  
Bcc Structure ◽  
The Mean

The analytic expressions for the thermodynamic and elastic quantities such as the mean nearest neighbor distance, the free energy, the isothermal compressibility, the thermal expansion coefficient, the heat capacities at constant volume and at constant pressure, the Young modulus, the bulk modulus, the rigidity modulus, and the elastic constants of binary interstitial alloy with body-centered cubic (BCC) structure, and the small concentration of interstitial atoms (below 5%) are derived by the statistical moment method. The theoretical results are applied to interstitial alloy FeC in the interval of temperature from 100 to 1000 K and in the interval of interstitial atom concentration from 0 to 5%. In special cases, we obtain the thermodynamic quantities of main metal Fe with BCC structure. Our calculated results for some thermodynamic and elastic quantities of main metal Fe and alloy FeC are compared with experiments.

scholarly journals A New Approach for Analyzing the Reliability of the Repair Facility in a Series System with Vacations

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Renbin Liu ◽  
Yong Wu
Keyword(s):  
Renewal Process ◽  
Decomposition Method ◽  
Process Theory ◽  
Series System ◽  
New Approach ◽  
Numerical Examples ◽  
Special Cases ◽  
The Mean ◽  
Repair Facility

Based on the renewal process theory we develop a decomposition method to analyze the reliability of the repair facility in ann-unit series system with vacations. Using this approach, we study the unavailability and the mean replacement number during(0,t]of the repair facility. The method proposed in this work is novel and concise, which can make us see clearly the structures of the facility indices of a series system with an unreliable repair facility, two convolution relations. Special cases and numerical examples are given to show the validity of our method.

EXPLICIT FUNCTIONS OF FUZZY CONTROL SYSTEMS

1996 ◽  
Vol 04 (06) ◽  
pp. 515-535 ◽  
Author(s):  
LÁSZLÓ T. KÓCZY ◽  
MICHIO SUGENO
Keyword(s):  
Computational Complexity ◽  
Fuzzy Control ◽  
Control Systems ◽  
Mathematical Description ◽  
Membership Functions ◽  
Mathematical Functions ◽  
Low Computational Complexity ◽  
Special Cases ◽  
Single Input ◽  
Explicit Formulae

Fuzzy control systems have proved their applicability in many areas. Their user-friend-liness and transparency certainly belong to their main advantages, and these two enable developing and tuning such controllers easily, without knowing their exact mathematical description. Nevertheless, it is of interest to know, what mathematical functions hide behind a set of fuzzy rules and an inference machine. For practical purposes it is necessary to consider real, implementable fuzzy control systems with reasonably low computational complexity. This paper discusses the problem of what types of functions are generated by realistic fuzzy control systems. In the paper the explicit formulae of the transference functions for practically important special cases are determined, controllers having rules with triangular and trapezoidal membership functions, and crisp consequents. Here we restrict our investigations to rules with a single input.

Three Social Choice Rules

2017 ◽  
pp. 54-71
Author(s):  
Andrei Marius Vlăducu
Keyword(s):  
Social Choice ◽  
Status Quo ◽  
Choice Rule ◽  
Borda Count ◽  
Social Choice Rule ◽  
Status Quo Bias ◽  
Approval Voting ◽  
The People ◽  
Viable Solution ◽  
Social Choice Rules

The authors analyze three social choice rules (plurality voting, approval voting and Borda count) from a behavioral economics perspective aiming three objectives: 1) if it is a viable solution to use these procedures during mass elections; 2) why individuals prefer a specific social choice rule and not another; 3) how status quo bias and framing effect influence the preference of individuals for a certain social choice rule. The research is conducted with 87 participants to a lab experiment and data suggest that for using approval voting and Borda count during mass elections is necessary to increase the people level of information about their benefits. When making a decision in a political or economic context seem that people tend to prefer simple plurality rule do to its availability and maybe because of its strong reliance with status quo bias.

On the theory of resonance integrals in the statistical region

1964 ◽  
Vol 1 (02) ◽  
pp. 335-346 ◽  
Author(s):  
A. Reichel ◽  
C. A. Wilkins
Keyword(s):  
Closed Form ◽  
Mean Value ◽  
Resonance Integral ◽  
Theoretical Terms ◽  
Special Cases ◽  
The Mean

The problem of determining infinitely dilute resonance integrals is formulated in renewal theoretical terms. The mean value of the integral for a single resonance is determined in simple closed form. On the assumption that Wigner's hypothesis holds, the resonance density is determined, and a usable approximation to it is derived. An expression for the infinitely dilute resonance integral in the statistical region is then given and its value calculated in special cases and compared with the results of a previous computation.

scholarly journals Credibility Approximations for Bayesian Prediction of Second Moments

1985 ◽  
Vol 15 (2) ◽  
pp. 103-121 ◽  
Author(s):  
William S. Jewell ◽  
Rene Schnieper
Keyword(s):  
Least Squares ◽  
Linear Functions ◽  
Quadratic Functions ◽  
Sample Variance ◽  
Credibility Theory ◽  
Sample Mean ◽  
Second Moment ◽  
Second Moments ◽  
Special Cases ◽  
The Mean

AbstractCredibility theory refers to the use of linear least-squares theory to approximate the Bayesian forecast of the mean of a future observation; families are known where the credibility formula is exact Bayesian. Second-moment forecasts are also of interest, for example, in assessing the precision of the mean estimate. For some of these same families, the second-moment forecast is exact in linear and quadratic functions of the sample mean. On the other hand, for the normal distribution with normal-gamma prior on the mean and variance, the exact forecast of the variance is a linear function of the sample variance and the squared deviation of the sample mean from the prior mean. Bühlmann has given a credibility approximation to the variance in terms of the sample mean and sample variance.In this paper, we present a unified approach to estimating both first and second moments of future observations using linear functions of the sample mean and two sample second moments; the resulting least-squares analysis requires the solution of a 3 × 3 linear system, using 11 prior moments from the collective and giving joint predictions of all moments of interest. Previously developed special cases follow immediately. For many analytic models of interest, 3-dimensional joint prediction is significantly better than independent forecasts using the “natural” statistics for each moment when the number of samples is small. However, the expected squared-errors of the forecasts become comparable as the sample size increases.

An analysis of the variation between dairy-sire progeny-groups for milk yield and fat content

1958 ◽  
Vol 1958 ◽  
pp. 19-29 ◽  
Author(s):  
Alan Robertson ◽  
S. S. Khishin
Keyword(s):  
Milk Yield ◽  
Comparison Method ◽  
Fat Content ◽  
Fat Percentage ◽  
Simple Method ◽  
Factors Affecting ◽  
Special Cases ◽  
The Mean ◽  
Milk Marketing ◽  
The Relationship

The past few years have seen the development in Great Britain of the ‘contemporary comparison’ method for evaluating progeny tests of dairy sires (Macarthur, 1954; Robertson, Stewart and Ashton 1956). The final overall figure attached to a sire is the mean difference between the yield of his daughters and that of other heifers milking in the same herd in the same year, with due regard for the numbers of animals in the two groups. Although it has some imperfections in special cases, this is probably the most informative simple method of evaluating a sire for yield and, fortunately, one which could be easily integrated with the existing recording system. The method has been turned into a simple routine in the Bureau of Records of the Milk Marketing Board and several thousand bulls have now been evaluated. In this paper, we shall be mostly concerned to use this material to investigate the heritabilities of milk yield and fat content and the relationship between the two in the different breeds. The information that we shall use consists, for each bull, of the mean contemporary comparison, with its effective ‘weight’, and the average fat percentage of the daughters. Before we deal with the observed results, we should go into rather more detail into the nature of these two figures and into the factors affecting them.

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