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Justin Kruger

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5 papers

2 author rows

AIJ Journal 2023 Journal Article

Portioning using ordinal preferences: Fairness and efficiency

Stéphane Airiau
Haris Aziz
Ioannis Caragiannis
Justin Kruger
Jérôme Lang
Dominik Peters

A divisible public resource is to be divided among projects. We study rules that decide on a distribution of the budget when voters have ordinal preference rankings over projects. Examples of such portioning problems are participatory budgeting, time shares, and parliament elections. We introduce a family of rules for portioning, inspired by positional scoring rules. Rules in this family are given by a scoring vector (such as plurality or Borda) associating a positive value with each rank in a vote, and an aggregation function such as leximin or the Nash product. Our family contains well-studied rules, but most are new. We discuss computational and normative properties of our rules. We focus on fairness, and introduce the SD-core, a group fairness notion. Our Nash rules are in the SD-core, and the leximin rules satisfy individual fairness properties. Both are Pareto-efficient.

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AAMAS Conference 2019 Conference Paper

Fall if it Lifts your Teammate: A Novel Type of Candidate Manipulation

Justin Kruger
Sebastian Schneckenburger

We present a new interpretation of the traditional computational social choice framework, where what are traditionally the candidates are construed as the agents. The particular implementation in mind is the proposed system for determining the medal winners for sports climbing in the 2020 Olympic games. We consider the issues of ties and of potential manipulation with respect to this interpretation. Simulation results suggest that for the proposed system ties are unlikely to be a problem, but that there is at least potential for manipulation, of a novel type. We formalise this conception of manipulation axiomatically. The strongest axioms lead to an impossibility along the lines of Arrow’s impossibility, while a small weakening leads to a possibility. We also provide a hardness result concerning the determination of possible manipulation.

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IJCAI Conference 2019 Conference Paper

Portioning Using Ordinal Preferences: Fairness and Efficiency

Stéphane Airiau
Haris Aziz
Ioannis Caragiannis
Justin Kruger
Jérôme Lang
Dominik Peters

A public divisible resource is to be divided among projects. We study rules that decide on a distribution of the budget when voters have ordinal preference rankings over projects. Examples of such portioning problems are participatory budgeting, time shares, and parliament elections. We introduce a family of rules for portioning, inspired by positional scoring rules. Rules in this family are given by a scoring vector (such as plurality or Borda) associating a positive value with each rank in a vote, and an aggregation function such as leximin or the Nash product. Our family contains well-studied rules, but most are new. We discuss computational and normative properties of our rules. We focus on fairness, and introduce the SD-core, a group fairness notion. Our Nash rules are in the SD-core, and the leximin rules satisfy individual fairness properties. Both are Pareto-efficient.

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EUMAS Conference 2017 Conference Paper

Permutation-Based Randomised Tournament Solutions

Justin Kruger
Stéphane Airiau

Abstract Voting rules that are based on the majority graph typically output large sets of winners. In this full original paper our goal is to investigate a general method which leads to randomized version of such rules. We use the idea of parallel universes, where each universe is connected with a permutation over alternatives. The permutation allows us to construct resolute voting rules (i. e. rules that always choose unique winners). Such resolute rules can be constructed in a variety of ways: we consider using binary voting trees to select a single alternative. In turn this permits the construction of neutral rules that output the set the possible winners of every parallel universe. The question of which rules can be constructed in this way has already been partially studied under the heading of agenda implementability. We further propose a randomised version in which the probability of being the winner is the ratio of universes in which the alternative wins. We also briefly consider (typically novel) rules that elect the alternatives that have maximal winning probability. These rules typically output small sets of winners, thus provide refinements of known tournament solutions.

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AAMAS Conference 2017 Conference Paper

Refinements and Randomised Versions of Some Tournament Solutions

Justin Kruger
Sté phane Airiau

We consider voting rules that are based on the majority graph. Such rules typically output large sets of winners. Our goal is to investigate a general method which leads to refinements of such rules. In particular, we use the idea of parallel universes, where each universe is connected with a permutation over alternatives. The permutation allows us to construct resolute voting rules (i. e. rules that always choose unique winners). Such resolute rules can be constructed in a variety of ways: we consider using binary voting trees to select a single alternative. In turn this permits the construction of neutral rules that output the set the possible winners of every parallel universe. The question of which rules can be constructed in this way has already been partially studied under the heading of agenda implementability. We further propose a randomised version in which the probability of being the winner is the ratio of universes in which the alternative wins. We also investigate (typically novel) rules that elect the alternatives that have maximal winning probability. These rules typically output small sets of winners, thus provide refinements of known tournament solutions.

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