Computational Aspects of Multi-Winner Approval Voting

We study computational aspects of three prominent voting rules that use approval ballots to elect multiple winners. These rules are satisfaction approval voting, proportional approval voting, and reweighted approval voting. We first show that computing the winner for proportional approval voting is NP-hard, closing a long standing open problem. As none of the rules are strategyproof, even for dichotomous preferences, we study various strategic aspects of the rules. In particular, we examine the computational complexity of computing a best response for both a single agent and a group of agents. In many settings, we show that it is NP-hard for an agent or agents to compute how best to vote given a fixed set of approval ballots from the other agents

On the manipulability of approval voting and related scoring rules

We characterize all preference profiles at which the approval (voting) rule is manipulable, under three extensions of preferences to sets of alternatives: by comparison of worstalternatives, best alternatives, or by comparison based on stochastic dominance. We perform a similar exercise for $k$-approval rules, where voters approve of a fixed number $k$ of alternatives. These results can be used to compare ($k$-)approval rules with respect to their manipulability. Analytical results are obtained for the case of two voters, specifically, the values of $k$ for which the $k$-approval rule is minimally manipulable -- has the smallest number of manipulable preference profiles -- under the various preference extensions are determined. For the number of voters going to infinity, an asymptotic result is that the $k$-approval rule with $k$ around half the number of alternatives is minimally manipulable among all scoring rules. Further results are obtained by simulation and indicate that $k$-approval rules may improve on the approval rule as far as manipulability is concerned.public economics ;

On the informational efficiency of simple scoring rules

efficient information aggregation, scoring rules, Poisson games, approval voting

Calculating the random guess scores of multiple-response and matching test items

For achievement tests, the guess score is often used as a baseline for the lowest possible grade for score to grade transformations and setting the cut scores. For test item types such as multiple-response, matching and drag-and-drop, determin-ing the guess score requires more elaborate calculations than the more straight-forward calculation of the guess score for True-False and multiple-choice test item formats. For various variants of multiple-response and matching types with respect to dichotomous and polytomous scoring, methods for determining the guess score are presented and illustrated with practical applications. The implica-tions for theory and practice are discussed

Approval Voting ion Dichotomous Preferences

The aim of this paper is to find normative foundations of Approval Voting. In order to show that Approval Voting is the only social choice function that satisfies anonymity, neutrality, strategy-proofness and strict monotonicity we rely on an intermediate result which relates strategy-proofness of a social choice function to the properties of Independence of Irrelevant Alternatives and monotonicity of the corresponding social welfare function. Afterwards we characterize Approval Voting by means of strict symmetry, neutrality and strict monotonicity and relate this result to May's Theorem. Finally, we show that it is possible to substitute the property of strict monotonicity by the one efficiency of in the second characterization.Approval Voting, Dichotomous Preferences, Social Choice Function, Social Welfare Function

Remarks on Young's theorem

In this paper we analyze the simple case of voting over two alternatives with variable electorate. Our findings are (a) the axiom of continuity is redundant in the axiomatization of scoring rules in Young (1975), SIAM J. Appl. Math. 28: 824-838, (b) the smaller set of axioms characterize this voting rule when indifferences are allowed in the voters' preferences, (c) a version of May's theorem can be derived from this last result, and finally, (d) in each of these results, axioms of neutrality and cancellation property can be used interchangeably.Scoring rules, Young's theorem, May's theorem

User's Privacy in Recommendation Systems Applying Online Social Network Data, A Survey and Taxonomy

Recommender systems have become an integral part of many social networks and extract knowledge from a user's personal and sensitive data both explicitly, with the user's knowledge, and implicitly. This trend has created major privacy concerns as users are mostly unaware of what data and how much data is being used and how securely it is used. In this context, several works have been done to address privacy concerns for usage in online social network data and by recommender systems. This paper surveys the main privacy concerns, measurements and privacy-preserving techniques used in large-scale online social networks and recommender systems. It is based on historical works on security, privacy-preserving, statistical modeling, and datasets to provide an overview of the technical difficulties and problems associated with privacy preserving in online social networks.Comment: 26 pages, IET book chapter on big data recommender system

Manipulation under k-approval scoring rules

Under a k-approval scoring rule each agent attaches a score of one to his k most preferred alternatives and zero to the other alternatives. The rule assigns the set of alternatives with maximal score. Agents may extend preferences to sets in several ways: they may compare the worst alternatives, or the best alternatives, or use a stochastic dominance criterion. In this paper we characterize the non-manipulable profiles for each of these set comparisons. For two-agent profiles we also determine the value(s) of k for which the number of non-manipulable profiles is maximal.microeconomics ;