Committee Scoring Rules

The paper proposes a general definition of positionalist voting rules. Unlike the commonly-employed scoring rules, our notion of positionalism allows for non-linear criteria to be included in the requisite class. We define a voting rule as positionalist if, for any profile of strict individual orderings, any two alternatives are compared collectively solely on the basis of their positional scores according to the individual rankings. In contrast to the class of scoring rules, however, we do not restrict attention to linear aggregation procedures. Two plausible unanimity properties are examined in the context of our new class of positionalist rules and, moreover, we characterize the lexicographic extensions that refine the plurality rule and its inverse counterpart.

Axiomatic characterization of committee scoring rules

The concept of distance rationalizability has several applications within social choice. In the context of voting, it allows one to define (rationalize) voting rules via a consensus class (roughly, a set of elections in which it is obvious who should win) and a distance function: namely, a candidate is said to be an election winner if it is ranked first in one of the nearest (with respect to the given distance) consensus elections. It is known that many classic voting rules can be represented in this manner. In this paper, we provide new results on distance rationalizability of several well-known voting rules such as all scoring rules, Approval, Young's rule and Maximin. We also show that a previously published proof of distance rationalizability of Young's rule is incorrect: the consensus notion and the distance function used in that proof give rise to a voting rule that is similar to---but distinct from---the Young's rule. Finally, we demonstrate that some voting rules cannot be rationalized via certain notions of consensus. To the best of our knowledge, these are the first non-distance-rationalizability results for voting rules.

This article examines strategic elements of voter behaviour in parliamentary elections where the voting method is a scoring rule other than plurality: the Borda Count, which is used for the election of ethnic minorities in Slovenia, and the Dowdall rule, which is used in the Pacific island state of Nauru in multi-seat districts. After first examining the general properties of scoring rules, and generating theoretical differences between the two rules, we look at empirical evidence from Nauru and Slovenia. This casts a doubt on predictions based simply on a voting rule's mathematical properties and on the accuracy of assumptions of sincere rank ordering.本文研究了议会选举投票者行为的策略因素。议会选举中的投票方法是一个有别于多数法的计分法则：斯洛文尼亚少数族群选举使用的波达计数法；太平洋岛屿国家瑙鲁多席位选区使用的斗多尔法则。作者首先分析了计分法则的一般属性，并对两种法则做了理论区分。然后研究了瑙鲁和斯洛文尼亚的实证资料。作者对仅仅基于投票规则数学属性的预测以及有关纯粹排行假设的精确性表示了质疑。

Election databases are the main elements of a recently introduced framework that aims to create bridges between the computational social choice and the data management communities. An election database consists of incomplete information about the preferences of voters, in the form of partial orders, alongside with standard database relations that provide contextual information. Earlier work in computational social choice focused on the computation of possible winners and necessary winners that are determined by the available incomplete information and the voting rule at hand. The presence of the relational context, however, permits the formulation of sophisticated queries about voting rules, candidates, potential winners, issues, and positions on issues. Such queries can be given possible answer semantics and necessary answer semantics on an election database, where the former means that the query is true on some completion of the given partial orders and the latter means that the query is true on every such completion. %In this paper, łooseness = -1 We carry out a systematic investigation of query evaluation on election databases by analyzing how the interaction between the partial preferences, the voting rules and the relational context impacts on the complexity of query evaluation. To this effect, we focus on positional scoring rules and unions of conjunctive queries. We establish a number of results that delineate the complexity of the possible answers and of the necessary answers for different positional scoring rules and for various classes of unions of conjunctive queries. Furthermore, we show that query evaluation is fixed-parameter tractable, where the parameter is the number of candidates in the election.

When predicting future events, it is common to issue forecasts that are probabilistic, in the form of probability distributions over the range of possible outcomes. Such forecasts can be evaluated using proper scoring rules. Proper scoring rules condense forecast performance into a single numerical value, allowing competing forecasters to be ranked and compared. To facilitate the use of scoring rules in practical applications, the scoringRules package in R provides popular scoring rules for a wide range of forecast distributions. This paper discusses an extension to the scoringRules package that additionally permits the implementation of popular weighted scoring rules. Weighted scoring rules allow particular outcomes to be targeted during forecast evaluation, recognizing that certain outcomes are often of more interest than others when assessing forecast quality. This introduces the potential for very flexible, user-oriented evaluation of probabilistic forecasts. We discuss the theory underlying weighted scoring rules, and describe how they can readily be implemented in practice using scoringRules. Functionality is available for weighted versions of several popular scoring rules, including the logarithmic score, the continuous ranked probability score, and the energy score. Two case studies are presented to demonstrate this, whereby weighted scoring rules are applied to univariate and multivariate probabilistic forecasts in the fields of meteorology and economics.

The complexity of using instruments for measuring the technological parameters of induction melting in a continuous mode, and sometimes the impossibility of this, requires the creation of reliable indirect methods for assessing the numerical values of these parameters. This is especially important for quality control of control systems that ensure a given melting temperature regime. The paper proposes a classification rule based on parametric classification methods, which makes it possible to determine the temperature regime of induction melting based on the SiO2 content in the slag and the distribution coefficient. Checking the classifying ability of the obtained rule showed that it is high, since for all the numerical data of the factor-signs, both the high-temperature and low-temperature modes were classified correctly. The restrictions on the application of the classification rule are shown, among them: the restrictions imposed by the range of variation of the values of the attribute factors, and the restrictions imposed by the small sample of the initial data, as well as the arbitrary area of their distribution in the space of the factor-attributes. The rule is presented in a normalized form, and also converted to natural form for ease of practical use. Application of the rule can be recommended to technologists of metallurgical production of foundries to check the compliance of the technological process operations with the specified melting regulations. It can also be used to diagnose processes or temperature control systems that determine the quality of the resulting cast iron. To do this, it is enough to substitute the actual values of SiO2, and Kd into the classification rule. The value of the distribution coefficient Кd is calculated according to the actual data on the content of FeO and MnO in the slag

Proper scoring rules provide a theoretically principled framework for the quantitative assessment of the predictive performance of probabilistic forecasts. While a wide selection of such scoring rules for univariate quantities exists, there are only few scoring rules for multivariate quantities, and many of them require that forecasts are given in the form of a probability density function. The energy score, a multivariate generalization of the continuous ranked probability score, is the only commonly used score that is applicable in the important case of ensemble forecasts, where the multivariate predictive distribution is represented by a finite sample. Unfortunately, its ability to detect incorrectly specified correlations between the components of the multivariate quantity is somewhat limited. In this paper the authors present an alternative class of proper scoring rules based on the geostatistical concept of variograms. The sensitivity of these variogram-based scoring rules to incorrectly predicted means, variances, and correlations is studied in a number of examples with simulated observations and forecasts; they are shown to be distinctly more discriminative with respect to the correlation structure. This conclusion is confirmed in a case study with postprocessed wind speed forecasts at five wind park locations in Colorado.

PurposeThis study aims to investigate the trending term: “Netiquette” as an important element in the effective digital citizenship. The research suggests a systematic framework of netiquette rules in the field of online education based on the classical core rules of netiquette and according to the digital citizenship scale (DCS). The research also studies the corresponding responsibilities of both educators and students to raise awareness towards using technology in a balanced, safe, smart and ethical way as the shift towards the digital activities increased significantly in the post-corona time.Design/methodology/approachThe research used the qualitative data that were based on the everyday observation and analysis of the online education experience at the university of Jordan in the academic year 2020/2021; the online group discussions of students and teachers; and investigating the guidelines of the online learning netiquette rules in various academic institutes. Comparative analysis was conducted to merge and eliminate redundant rules and to add sub rules, and then to cluster them into groups. The suggested clustered groups were distributed into the classical core rules outline of netiquette. In each core rule, the sub rules were reclassified and recategorized according to the DCS by studying the complexity levels and their corresponding factors. The suggested framework updates and adds DCS levels and factors considering the exceptional experience of online education through the pandemic.FindingsThe research finds that “Netiquette” had been neglected in cyber ethics literature, and so it has to be rediscovered through the lens of digital citizenship that becomes very noticeable issue in the post-COVID era. So, the research presents a systematic framework that outlines more than 150 netiquette sub rules in the field of online education, and that were clustered according to DCS and the classical core rules of netiquette. It also adds a new factor to the bottom level of DCS which is the primarily skills and traits, and also updates the internet and political activism fac-tor by adding the social perspective.Originality/valueA novel classification of the classical core rules of netiquette was proposed in the field of online education to serve as a spectrum of identifying the complexity of digital citizenship levels and factors. This research can be a starting point of more works on netiquette research in online education and on other fields such as online business meetings, social media networking and online gaming.

Proper scoring rules for general decision models

Positional scoring rules in voting compute the score of an alternative by summing the scores for the alternative induced by every vote. This summation principle ensures that all votes contribute equally to the score of an alternative. We relax this assumption and, instead, aggregate scores by taking into account the rank of a score in the ordered list of scores obtained from the votes. This defines a new family of voting rules, rank-dependent scoring rules (RDSRs), based on ordered weighted average (OWA) operators, which, include all scoring rules, and many others, most of which of new. We study some properties of these rules, and show, empirically, that certain RDSRs are less manipulable than Borda voting, across a variety of statistical cultures.

In this paper, we study the metric distortion of deterministic social choice rules that choose a winning candidate from a set of candidates based on voter preferences. Voters and candidates are located in an underlying metric space. A voter has cost equal to her distance to the winning candidate. Ordinal social choice rules only have access to the ordinal preferences of the voters that are assumed to be consistent with the metric distances. Our goal is to design an ordinal social choice rule with minimum distortion, which is the worst-case ratio, over all consistent metrics, between the social cost of the rule and that of the optimal omniscient rule with knowledge of the underlying metric space. The distortion of the best deterministic social choice rule was known to be between $3$ and $5$. It had been conjectured that any rule that only looks at the weighted tournament graph on the candidates cannot have distortion better than $5$. In our paper, we disprove it by presenting a weighted tournament rule with distortion of $4.236$. We design this rule by generalizing the classic notion of uncovered sets, and further show that this class of rules cannot have distortion better than $4.236$. We then propose a new voting rule, via an alternative generalization of uncovered sets. We show that if a candidate satisfying the criterion of this voting rule exists, then choosing such a candidate yields a distortion bound of $3$, matching the lower bound. We present a combinatorial conjecture that implies distortion of $3$, and verify it for small numbers of candidates and voters by computer experiments. Using our framework, we also show that selecting any candidate guarantees distortion of at most $3$ when the weighted tournament graph is cyclically symmetric.

Proportional representation (PR) is often discussed in voting settings as a major desideratum. For the past century or so, it is common both in practice and in the academic literature to look towards the single transferable vote (STV) rule as the solution for achieving PR. Some of the most prominent electoral reform movements around the globe are pushing for the adoption of STV. It has been termed a major open problem to design a voting rule that satisfies the same PR properties as STV and better monotonicity properties. In this paper, we first present a taxonomy of proportional representation axioms for general weak order preferences, some of which generalise and strengthen previously introduced concepts. We then present a rule called the expanding approvals rule (EAR) that satisfies properties stronger than the central PR axiom satisfied by STV, can handle indifferences in a convenient and computationally efficient manner, and also satisfies better candidate monotonicity properties. In view of this, our proposed rule seems to be a compelling solution for achieving proportional representation in voting settings.

In this paper, the general monotonicity results concerning selection problems derived by Berger and Proschan (1984) are reviewed.They are then applied to several different formulations of the selection problem.These include comparison with a control and restricted subset selection problems.Several classes of selection rules previously proposed in the literature are shown to possess the monotonicity properties.In addition, a new class of rules for the restricted subset selection formulation is proposed and shown to possess the monotonicity properties.1. Introduction.In this paper we study some monotonicity properties of ranking and selection rules.Recall that in a selection problem the general goal is to determine which of several populations possesses the largest value of some parameter.Based on random observations from the populations, a selection rule selects a subset of the populations and leads to an assertion such as, "The population with the largest parameter is in the selected subset."(Different formulations of the selection problem entail different assertions resulting from the selection rule.)A reasonable selection rule should be more likely to choose populations with larger parameters rather than populations with smaller parameters.This property of selection rules is called monotonicity.In this paper we study some general monotonicity properties of a broad class of selection rules in a unified manner.We also discuss applications of these general results to several different formulations of the selection problem.In symbols, let X = (X u ... , X n ) be a random observation with distribution F(x; λ), where the unknown parameter vector λ = (λi, ... , λ n ) e Λ C #\ The general goal of a selection problem is to decide which of the coordinates of λ are the largest or which are larger than a value λ 0 (possibly unknown).A (nonrandomized) selection rule 5(x) is any measurable mapping from the sample space X of X into the set of subsets of {1, ... , n}.Having observed X = x, the selection rule 5 asserts that the largest parameters are in {λ,: /eS(x)}.The subset 5(X) may be of fixed or random size depending on the formulation of the selection problem under consideration.See, for example, Bechhofer (1954) (fixed size), Gupta and Sobel (1958) (random size), and Gupta (1965) (random size).Gupta (1965) calls a selection rule montone if (1.1) \i^ λj implies P x (ieS(X)) ^ P X (J€LS(X)).Monotonicity is a desirable property of a selection rule since the selected subset is supposed to consist of the large values of k r On a case by case basis, various authors have shown that their proposed selection rules are monotone.

In this paper, we study a maximum likelihood estimation (MLE) approach to voting when the set of alternatives has a multi-issue structure, and the voters' preferences are represented by CP-nets.We first consider general multi-issue domains, and study whether and how issue-by-issue voting rules and sequential voting rules can be represented by MLEs. We first show that issue-by-issue voting rules in which each local rule is itself an MLE (resp. a candidate scoring rule) can be represented by MLEs with a weak (resp. strong) decomposability property. Then, we prove two theorems that state that if the noise model satisfies a very weak decomposability property, then no sequential voting rule that satisfies unanimity can be represented by an MLE, unless the number of voters is bounded.We then consider multi-issue domains in which each issue is binary; for these, we propose a general family of distance-based noise models, of which give an axiomatic characterization. We then propose a more specific family of natural distance-based noise models that are parameterized by a threshold. We identify the complexity of winner determination for the corresponding MLE voting rule in the two most important subcases of this framework.