Abstract This paper studies the complexity of two microbribery problems under the model of group identification. In these problems, we are given a subset of distinguished individuals, and the questions are whether these individuals can be made socially qualified or whether they can be made exactly the socially qualified individuals, respectively, by modifying a limited number of entries in the qualifications-profile. For consent rules, the consensus-start-respecting rule, and the liberal-start-respecting rule, we obtain many NP-hardness results and polynomial-time solvability results. We also study the problems in r-profiles where each individual qualifies exactly r individuals.

Abstract We investigate the computational complexity of electoral control in elections. Electoral control describes the scenario where the election chair seeks to alter the outcome of the election by structural changes such as adding, deleting, or replacing either candidates or voters. Such control actions have been studied in the literature for a lot of prominent voting rules. We complement those results by solving several open cases for Copeland $$^{\alpha }$$ α , maximin,k-veto, plurality with runoff, veto with runoff, Condorcet, fallback, range voting, and normalized range voting.

Certainty around the regulatory environment is crucial to facilitate responsible AI innovation and its social acceptance. However, the existing legal liability system is inapt to assign responsibility where a potentially harmful conduct and/or the harm itself are unforeseeable, yet some instantiations of AI and/or the harms they may trigger are not foreseeable in the legal sense. The unpredictability of how courts would handle such cases makes the risks involved in the investment and use of AI incalculable, creating an environment that is not conducive to innovation and may deprive society of some benefits AI could provide. To tackle this problem, we propose to draw insights from financial regulatory best-practices and establish a system of AI guarantee schemes. We envisage the system to form part of the broader market-structuring regulatory framework, with the primary function to provide a readily available, clear, and transparent funding mechanism to compensate claims that are either extremely hard or impossible to realize via conventional litigation. We propose at least partial industry-funding, with funding arrangements depending on whether it would pursue other potential policy goals.

Manipulation, bribery, and control are well-studied ways of changing the outcome of an election. Many voting rules are, in the general case, computationally resistant to some of these manipulative actions. However when restricted to single-peaked electorates, these rules suddenly become easy to manipulate. Recently, Faliszewski, Hemaspaandra, and Hemaspaandra studied the computational complexity of strategic behavior in nearly single-peaked electorates. These are electorates that are not single-peaked but close to it according to some distance measure. In this paper we introduce several new distance measures regarding single-peakedness. We prove that determining whether a given profile is nearly single-peaked is NP-complete in many cases. For one case we present a polynomial-time algorithm. In case the single-peaked axis is given, we show that determining the distance is always possible in polynomial time. Furthermore, we explore the relations between the new notions introduced in this paper and existing notions from the literature.

Manipulation, bribery, and control are well-studied ways of changing the outcome of an election. Many voting systems are, in the general case, computationally resistant to some of these manipulative actions. However when restricted to single-peaked electorates, these systems suddenly become easy to manipulate. Recently, Faliszewski, Hemaspaandra, and Hemaspaandra studied the complexity of dishonest behavior in nearly single-peaked electorates. These are electorates that are not single-peaked but close to it according to some distance measure. In this paper we introduce several new distance measures regarding single-peakedness. We prove that determining whether a given profile is nearly single-peaked is NP-complete in many cases. For one case we present a polynomial-time algorithm. Furthermore, we explore the relations between several notions of nearly single-peakedness.