arXiv subjects

Felix Brandt

Publications and source records attributed to Felix Brandt.

At least 55 records · Page 3Linked to original sources

arXiv2022

Relaxed Notions of Condorcet-Consistency and Efficiency for Strategyproof Social Decision Schemes

Social decision schemes (SDSs) map the preferences of a group of voters over some set of $m$ alternatives to a probability distribution over the alternatives. A seminal characterization of strategyproof SDSs by Gibbard implies that there are no strategyproof Condorcet extensions and that only random dictatorships satisfy ex post efficiency and strategyproofness. The latter is known as the random dictatorship theorem. We relax Condorcet-consistency and ex post efficiency by introducing a lower bound on the probability of Condorcet winners and an upper bound on the probability of Pareto-dominated alternatives, respectively. We then show that the SDS that assigns probabilities proportional to Copeland scores is the only anonymous, neutral, and strategyproof SDS that can guarantee the Condorcet winner a probability of at least 2/m. Moreover, no strategyproof SDS can exceed this bound, even when dropping anonymity and neutrality. Secondly, we prove a continuous strengthening of Gibbard's random dictatorship theorem: the less probability we put on Pareto-dominated alternatives, the closer to a random dictatorship is the resulting SDS. Finally, we show that the only anonymous, neutral, and strategyproof SDSs that maximize the probability of Condorcet winners while minimizing the probability of Pareto-dominated alternatives are mixtures of the uniform random dictatorship and the randomized Copeland rule.

econ.TH↗

arXiv2021

Funding Public Projects: A Case for the Nash Product Rule

We study a mechanism design problem where a community of agents wishes to fund public projects via voluntary monetary contributions by the community members. This serves as a model for public expenditure without an exogenously available budget, such as participatory budgeting or voluntary tax programs, as well as donor coordination when interpreting charities as public projects and donations as contributions. Our aim is to identify a mutually beneficial distribution of the individual contributions. In the preference aggregation problem that we study, agents report linear utility functions over projects together with the amount of their contributions, and the mechanism determines a socially optimal distribution of the money. We identify a specific mechanism -- the Nash product rule -- which picks the distribution that maximizes the product of the agents' utilities. This rule is Pareto efficient, and we prove that it satisfies attractive incentive properties: it spends each agent's contribution only on projects the agent finds acceptable, and agents are strongly incentivized to participate.

cs.GT↗

arXiv2021

TetraPackNet: Four-Corner-Based Object Detection in Logistics Use-Cases

While common image object detection tasks focus on bounding boxes or segmentation masks as object representations, we consider the problem of finding objects based on four arbitrary vertices. We propose a novel model, named TetraPackNet, to tackle this problem. TetraPackNet is based on CornerNet and uses similar algorithms and ideas. It is designated for applications requiring high-accuracy detection of regularly shaped objects, which is the case in the logistics use-case of packaging structure recognition. We evaluate our model on our specific real-world dataset for this use-case. Baselined against a previous solution, consisting of a Mask R-CNN model and suitable post-processing steps, TetraPackNet achieves superior results (9% higher in accuracy) in the sub-task of four-corner based transport unit side detection.

cs.CV↗

arXiv2021

Rigorous Analysis and Dynamics of Hibler's sea ice model

This article develops for the first time a rigorous analysis of Hibler's model of sea ice dynamics. Identifying Hibler's ice stress as a quasilinear second order operator and regarding Hibler's model as a quasilinear evolution equation, it is shown that Hibler's coupled sea ice model, i.e., the model coupling velocity, thickness and compactness of sea ice, is locally strongly well-posed within the $L_q$-setting and also globally strongly well-posed for initial data close to constant equilibria.

math.AP↗

arXiv2020

An Image Processing Pipeline for Automated Packaging Structure Recognition

Dispatching and receiving logistics goods, as well as transportation itself, involve a high amount of manual efforts. The transported goods, including their packaging and labeling, need to be double-checked, verified or recognized at many supply chain network points. These processes hold automation potentials, which we aim to exploit using computer vision techniques. More precisely, we propose a cognitive system for the fully automated recognition of packaging structures for standardized logistics shipments based on single RGB images. Our contribution contains descriptions of a suitable system design and its evaluation on relevant real-world data. Further, we discuss our algorithmic choices.

cs.CV↗

arXiv2020

Fully-Automated Packaging Structure Recognition in Logistics Environments

Within a logistics supply chain, a large variety of transported goods need to be handled, recognized and checked at many different network points. Often, huge manual effort is involved in recognizing or verifying packet identity or packaging structure, for instance to check the delivery for completeness. We propose a method for complete automation of packaging structure recognition: Based on a single image, one or multiple transport units are localized and, for each of these transport units, the characteristics, the total number and the arrangement of its packaging units is recognized. Our algorithm is based on deep learning models, more precisely convolutional neural networks for instance segmentation in images, as well as computer vision methods and heuristic components. We use a custom data set of realistic logistics images for training and evaluation of our method. We show that the solution is capable of correctly recognizing the packaging structure in approximately 85% of our test cases, and even more (91%) when focusing on most common package types.

cs.CV↗

arXiv2020

On the Structure of Stable Tournament Solutions

A fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our understanding of stable choice functions. In particular, (i) we show that every stable choice function is generated by a unique simple choice function, which never excludes more than one alternative, (ii) we completely characterize which simple choice functions give rise to stable choice functions, and (iii) we prove a strong relationship between stability and a new property of tournament solutions called local reversal symmetry. Based on these findings, we provide the first concrete tournament---consisting of 24 alternatives---in which the tournament equilibrium set fails to be stable. Furthermore, we prove that there is no more discriminating stable tournament solution than the bipartisan set and that the bipartisan set is the unique most discriminating tournament solution which satisfies standard properties proposed in the literature.

econ.TH↗

arXiv2019

Arrovian Aggregation of Convex Preferences

We consider social welfare functions that satisfy Arrow's classic axioms of independence of irrelevant alternatives and Pareto optimality when the outcome space is the convex hull of some finite set of alternatives. Individual and collective preferences are assumed to be continuous and convex, which guarantees the existence of maximal elements and the consistency of choice functions that return these elements, even without insisting on transitivity. We provide characterizations of both the domains of preferences and the social welfare functions that allow for anonymous Arrovian aggregation. The domains admit arbitrary preferences over alternatives, which completely determine an agent's preferences over all mixed outcomes. On these domains, Arrow's impossibility turns into a complete characterization of a unique social welfare function, which can be readily applied in settings involving divisible resources such as probability, time, or money.

cs.GT↗

arXiv2017

Proving the Incompatibility of Efficiency and Strategyproofness via SMT Solving

Two important requirements when aggregating the preferences of multiple agents are that the outcome should be economically efficient and the aggregation mechanism should not be manipulable. In this paper, we provide a computer-aided proof of a sweeping impossibility using these two conditions for randomized aggregation mechanisms. More precisely, we show that every efficient aggregation mechanism can be manipulated for all expected utility representations of the agents' preferences. This settles an open problem and strengthens a number of existing theorems, including statements that were shown within the special domain of assignment. Our proof is obtained by formulating the claim as a satisfiability problem over predicates from real-valued arithmetic, which is then checked using an SMT (satisfiability modulo theories) solver. In order to verify the correctness of the result, a minimal unsatisfiable set of constraints returned by the SMT solver was translated back into a proof in higher-order logic, which was automatically verified by an interactive theorem prover. To the best of our knowledge, this is the first application of SMT solvers in computational social choice.

cs.GT↗

arXiv2017

Fractional Hedonic Games

The work we present in this paper initiated the formal study of fractional hedonic games, coalition formation games in which the utility of a player is the average value he ascribes to the members of his coalition. Among other settings, this covers situations in which players only distinguish between friends and non-friends and desire to be in a coalition in which the fraction of friends is maximal. Fractional hedonic games thus not only constitute a natural class of succinctly representable coalition formation games, but also provide an interesting framework for network clustering. We propose a number of conditions under which the core of fractional hedonic games is non-empty and provide algorithms for computing a core stable outcome. By contrast, we show that the core may be empty in other cases, and that it is computationally hard in general to decide non-emptiness of the core.

cs.GT↗

arXiv2017

k-Majority Digraphs and the Hardness of Voting with a Constant Number of Voters

Many hardness results in computational social choice make use of the fact that every directed graph may be induced as the pairwise majority relation of some preference profile. However, this fact requires a number of voters that is almost linear in the number of alternatives. It is therefore unclear whether these results remain intact when the number of voters is bounded, as is, for example, typically the case in search engine aggregation settings. In this paper, we provide a systematic study of majority digraphs for a constant number of voters resulting in analytical, experimental, and complexity-theoretic insights. First, we characterize the set of digraphs that can be induced by two and three voters, respectively, and give sufficient conditions for larger numbers of voters. Second, we present a surprisingly efficient implementation via SAT solving for computing the minimal number of voters that is required to induce a given digraph and experimentally evaluate how many voters are required to induce the majority digraphs of real-world and generated preference profiles. Finally, we leverage our sufficient conditions to show that the winner determination problem of various well-known voting rules remains hard even when there is only a small constant number of voters. In particular, we show that Kemeny's rule is hard to evaluate for 7 voters, while previous methods could only establish such a result for constant even numbers of voters.

cs.GT↗

arXiv2016

Optimal Bounds for the No-Show Paradox via SAT Solving

Voting rules allow multiple agents to aggregate their preferences in order to reach joint decisions. Perhaps one of the most important desirable properties in this context is Condorcet-consistency, which requires that a voting rule should return an alternative that is preferred to any other alternative by some majority of voters. Another desirable property is participation, which requires that no voter should be worse off by joining an electorate. A seminal result in social choice theory by Moulin (1998) has shown that Condorcet-consistency and participation are incompatible whenever there are at least 4 alternatives and 25 voters. We leverage SAT solving to obtain an elegant human-readable proof of Moulin's result that requires only 12 voters. Moreover, the SAT solver is able to construct a Condorcet-consistent voting rule that satisfies participation as well as a number of other desirable properties for up to 11 voters, proving the optimality of the above bound. We also obtain tight results for set-valued and probabilistic voting rules, which complement and significantly improve existing theorems.

cs.GT↗

arXiv2016

An Ordinal Minimax Theorem

In the early 1950s Lloyd Shapley proposed an ordinal and set-valued solution concept for zero-sum games called \emph{weak saddle}. We show that all weak saddles of a given zero-sum game are interchangeable and equivalent. As a consequence, every such game possesses a unique set-based value.

cs.GT↗

arXiv2015

The Impossibility of Extending Random Dictatorship to Weak Preferences

Random dictatorship has been characterized as the only social decision scheme that satisfies efficiency and strategyproofness when individual preferences are strict. We show that no extension of random dictatorship to weak preferences satisfies these properties, even when significantly weakening the required degree of strategyproofness.

cs.MA↗

arXiv2015

Welfare Maximization Entices Participation

We consider randomized mechanisms with optional participation. Preferences over lotteries are modeled using skew-symmetric bilinear (SSB) utility functions, a generalization of classic von Neumann-Morgenstern utility functions. We show that every welfare-maximizing mechanism entices participation and that the converse holds under additional assumptions. Two important corollaries of our results are characterizations of an attractive randomized voting rule that satisfies Condorcet-consistency and entices participation. This stands in contrast to a well-known result by Moulin (1988), who proves that no deterministic voting rule can satisfy both properties simultaneously.

cs.GT↗

arXiv2015

Set-Monotonicity Implies Kelly-Strategyproofness

This paper studies the strategic manipulation of set-valued social choice functions according to Kelly's preference extension, which prescribes that one set of alternatives is preferred to another if and only if all elements of the former are preferred to all elements of the latter. It is shown that set-monotonicity---a new variant of Maskin-monotonicity---implies Kelly-strategyproofness in comprehensive subdomains of the linear domain. Interestingly, there are a handful of appealing Condorcet extensions---such as the top cycle, the minimal covering set, and the bipartisan set---that satisfy set-monotonicity even in the unrestricted linear domain, thereby answering questions raised independently by Barberà (1977) and Kelly (1977).

cs.MA↗

arXiv2013

A tournament of order 24 with two disjoint TEQ-retentive sets

Brandt et al. (2013) have recently disproved a conjecture by Schwartz (1990) by non-constructively showing the existence of a counterexample with about 10^136 alternatives. We provide a concrete counterexample for Schwartz's conjecture with only 24 alternatives.

cs.MA↗

arXiv2013

The Computational Complexity of Random Serial Dictatorship

In social choice settings with linear preferences, random dictatorship is known to be the only social decision scheme satisfying strategyproofness and ex post efficiency. When also allowing indifferences, random serial dictatorship (RSD) is a well-known generalization of random dictatorship that retains both properties. RSD has been particularly successful in the special domain of random assignment where indifferences are unavoidable. While executing RSD is obviously feasible, we show that computing the resulting probabilities is #P-complete and thus intractable, both in the context of voting and assignment.

cs.GT↗