On the stability of a scoring rules set under the IAC

A society facing a choice problem has also to choose the voting rule itself from a set of different possible voting rules. In such situations, the consequentialism property allows us to induce voters\u27 preferences on voting rules from preferences over alternatives. A voting rule employed to resolve the society\u27s choice problem is self-selective if it chooses itself when it is also used in choosing the voting rule. A voting rules set is said to be stable if it contains at least one self-selective voting rule at each profile of preferences on voting rules. We consider in this paper a society which will make a choice from a set constituted by three alternatives {a, b, c} and a set of the three well-known scoring voting rules {Borda, Plurality, Antiplurality}. Under the Impartial Anonymous Culture assumption (IAC), we will derive a probability for the stability of this triplet of voting rules. We use Ehrhart polynomials in order to solve our problems. This method counts the number of lattice points inside a convex bounded polyhedron (polytope). We discuss briefly recent algorithmic solutions to this method and use it to determine the probability of stabillity of {Borda, Plurality, Antiplurality} set

The effects of closeness on the election of a pairwise majority rule winner

Some studies have recently examined the effect of closeness on the probability of observing the monotonicity paradox in three-candidate elections under Scoring Elimination Rules. It has been shown that the frequency of such paradox significantly increases as elections become more closely contested. In this paper we consider the effect of closeness on one of the most studied notions in Social Choice Theory: The election of the Condorcet winner, i.e., the candidate who defeats any other opponent in pairwise majority comparisons, when she exists. To be more concrete, we use the well known concept of the Condorcet efficiency, that is, the conditional probability that a voting rule will elect the Condorcet winner, given that such a candidate exists. Our results, based on the Impartial Anonymous Culture (IAC) assumption, show that closeness has also a significant effect on the Condorcet efficiency of different voting rules in the class of Scoring and Scoring Elimination Rules

On Ehrhart Polynomials and Probability Calculations in Voting Theory

In voting theory, analyzing how frequent is an event (e.g. a voting paradox) is, under some specific but widely used assumptions, equivalent to computing the exact number of integer solutions in a system of linear constraints. Recently, some algorithms for computing this number have been proposed in social choice literature by Huang and Chua [17] and by Gehrlein ([12, 14]). The purpose of this paper is threefold. Firstly, we want to do justice to Eug`ene Ehrhart, who, more than forty years ago, discovered the theoretical foundations of the above mentioned algorithms. Secondly, we present some efficient algorithms that have been recently developed by computer scientists, independently from voting theorists. Thirdly, we illustrate the use of these algorithms by providing some original results in voting theory.voting rules, manipulability, polytopes, lattice points, algorithms.

Report on the 2016 Proficiency Test of the European Union Reference Laboratory for Mycotoxins for the network of National Reference Laboratories: Determination of aflatoxin B1 in defatted peanut powder

The Joint Research Centre (JRC), a Directorate-General of the European Commission, operates the European Union Reference Laboratory (EURL) for Mycotoxins. One of its core tasks is to organise proficiency tests (PTs) among appointed National Reference Laboratories (NRLs). This report presents the results of the PT on the determination of aflatoxins in defatted peanut powder. The test items for this PT were two contaminated defatted peanut powder samples. The materials were produced by the JRC and dispatched to the participants mid October 2016. Each participant received one bottle per test material containing approximately 55 g each. Fifty-six participants from thirty countries (among them 40 NRLs and 16 official food control laboratories) registered for the exercise and 54 sets (Sample A and B) of results were reported. The assigned values, established by an exact-matching double isotope dilution mass spectrometric technique, were 2.80 µg/kg (± 0.19 µg/kg) aflatoxin B1 in sample A and 3.20 µg/kg (± 0.20 µg/kg) in sample B. Participants' results were rated with z-scores and zeta-scores for aflatoxin B1 in accordance with ISO 13528:2015. The z-score compares the participant's deviation from the reference value with the target standard deviation accepted for the PT, whereas the zeta-score provides an indication of whether the participant's estimate of uncertainty is consistent with the observed deviation from the assigned value. Only z-scores were used for the evaluation whether an individual laboratory underperformed. In total, 96 % of the attributed z scores were below an absolute value of two for sample A and and 92 % for sample B. This indicates that most of the participants performed satisfactorily. The few participants that had z-scores above an absolute value of 2 will have to investigate the reasons for the deviation (root-cause analysis) and report the planned corrective actions to the EURL.JRC.F.5-Food and Feed Complianc

ON THE CONSISTENCY AND ROBUSTNESS PROPERTIES OF LINEAR DISCRIMINANT ANALYSIS

Strong consistency of linear discriminant analysis is established under wide assumptions on the class conditional densities. Robustness to the presence of a mild degree of class dispersion heterogeneity is also analyzed. Results obtained may help to explain analytically the frequent good behavior in applications of linear discrimination techniques.

How Likely A Coalition of Voters Can Influence A Large Election?

For centuries, it has been widely believed that the influence of a small coalition of voters is negligible in a large election. Consequently, there is a large body of literature on characterizing the asymptotic likelihood for an election to be influenced, especially by the manipulation of a single voter, establishing an $O(\frac{1}{\sqrt n})$ upper bound and an $\Omega(\frac{1}{n^{67}})$ lower bound for many commonly studied voting rules under the i.i.d.~uniform distribution, known as Impartial Culture (IC) in social choice, where $n$ is the number is voters. In this paper, we extend previous studies in three aspects: (1) we consider a more general and realistic semi-random model, where a distribution adversary chooses a worst-case distribution and then a data adversary modifies up to $\psi$ portion of the data, (2) we consider many coalitional influence problems, including coalitional manipulation, margin of victory, and various vote controls and bribery, and (3) we consider arbitrary and variable coalition size $B$. Our main theorem provides asymptotically tight bounds on the semi-random likelihood of the existence of a size-$B$ coalition that can successfully influence the election under a wide range of voting rules. Applications of the main theorem and its proof techniques resolve long-standing open questions about the likelihood of coalitional manipulability under IC, by showing that the likelihood is $\Theta\left(\min\left\{\frac{B}{\sqrt n}, 1\right\}\right)$ for many commonly studied voting rules. The main technical contribution is a characterization of the semi-random likelihood for a Poisson multinomial variable (PMV) to be unstable, which we believe to be a general and useful technique with independent interest

10101 Abstracts Collection -- Computational Foundations of Social Choice

From March 7 to March 12, 2010, the Dagstuhl Seminar 10101 ``Computational Foundations of Social Choice \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

A new procedure to analyze RNA non-branching structures

RNA structure prediction and structural motifs analysis are challenging tasks in the investigation of RNA function. We propose a novel procedure to detect structural motifs shared between two RNAs (a reference and a target). In particular, we developed two core modules: (i) nbRSSP_extractor, to assign a unique structure to the reference RNA encoded by a set of non-branching structures; (ii) SSD_finder, to detect structural motifs that the target RNA shares with the reference, by means of a new score function that rewards the relative distance of the target non-branching structures compared to the reference ones. We integrated these algorithms with already existing software to reach a coherent pipeline able to perform the following two main tasks: prediction of RNA structures (integration of RNALfold and nbRSSP_extractor) and search for chains of matches (integration of Structator and SSD_finder)

Using the area between two item response functions to index differential item functioning : a generalized approach

The area between two item response functions was used to construct two indicators of differential item functioning. The first indicator was designed from the integral of the difference of the two response functions across six standard deviations of ability. The second index was designed from the integral of the square of the difference of the two response functions across the same range of ability. Both indices were developed using the three-parameter item response theory model such that they subsume the two-and one-parameter models as special cases; and both were designed to be sensitive to uniform and non-uniform differential item functioning. The standard errors of the item response theory parameters were used to estimate the standard error of each integral. The ratio of the integral to the estimate of its standard error was shown to be normally distributed using Monte-Carlo data. Hence, both indices provide a multivariate assessment, a z test, of differences in the sets of item response theory parameters