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 Barber\`a (1977) and Kelly (1977).Comment: 14 page

On Iterated Dominance, Matrix Elimination, and Matched Paths

We study computational problems arising from the iterated removal of weakly dominated actions in anonymous games. Our main result shows that it is NP-complete to decide whether an anonymous game with three actions can be solved via iterated weak dominance. The two-action case can be reformulated as a natural elimination problem on a matrix, the complexity of which turns out to be surprisingly difficult to characterize and ultimately remains open. We however establish connections to a matching problem along paths in a directed graph, which is computationally hard in general but can also be used to identify tractable cases of matrix elimination. We finally identify different classes of anonymous games where iterated dominance is in P and NP-complete, respectively.Comment: 12 pages, 3 figures, 27th International Symposium on Theoretical Aspects of Computer Science (STACS

A polyhedral model of partitions with bounded differences and a bijective proof of a theorem of Andrews, Beck, and Robbins

The main result of this paper is a bijective proof showing that the generating function for partitions with bounded differences between largest and smallest part is a rational function. This result is similar to the closely related case of partitions with fixed differences between largest and smallest parts which has recently been studied through analytic methods by Andrews, Beck, and Robbins. Our approach is geometric: We model partitions with bounded differences as lattice points in an infinite union of polyhedral cones. Surprisingly, this infinite union tiles a single simplicial cone. This construction then leads to a bijection that can be interpreted on a purely combinatorial level.Comment: 12 pages, 5 figure

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

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

Consistent Probabilistic Social Choice

Two fundamental axioms in social choice theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non-probabilistic social choice, these axioms are incompatible with each other. We show that in the context of probabilistic social choice, these axioms uniquely characterize a function proposed by Fishburn (Rev. Econ. Stud., 51(4), 683--692, 1984). Fishburn's function returns so-called maximal lotteries, i.e., lotteries that correspond to optimal mixed strategies of the underlying plurality game. Maximal lotteries are guaranteed to exist due to von Neumann's Minimax Theorem, are almost always unique, and can be efficiently computed using linear programming

The Air Cargo Load Planning Problem

A major operational planning problem in the air cargo industry is how to arrange cargo in an aircraft to fly safely and profitably. Therefore, a challenging planning puzzle has to be solved for each flight. Besides its complexity, the planning is mostly done manually today, which is a time consuming process with uncertain solution quality. The literature on loading problems in an air cargo context is scarce and the term is used ambiguously for different subproblems like selecting containers, packing items into containers, or loading containers into aircraft. All of the presented models only focus on certain aspects of what is in practice a larger planning problem. Additionally, some practical aspects have not been covered in the literature. In this work, we provide a comprehensive overview of the air cargo load planning problem as seen in the operational practice of our industrial partner. We formalize its requirements and the objectives of the respective stakeholders. Furthermore, we develop and evaluate suitable solution approaches. Therefore, we decompose the problem into four steps: aircraft configuration, build-up scheduling, air cargo palletization, and weight and balance. We solve these steps by employing mainly mixed-integer linear programming. Two subproblems are further decomposed by adding a rolling horizon planning approach and a Logic-based Benders Decomposition (LBBD). The actual three-dimensional packing problem is solved as a constraint program in the subproblem of the LBBD. We evaluated our approaches on instances containing 513 real and synthetic flights. The numerical results show that the developed approaches are suitable to automatically generate load plans for cargo flights. Compared to load plans from practice, we could achieve a 20 percent higher packing density and significantly reduce the handling effort in the air cargo terminal. The achieved costs of additional fuel burn due to aircraft imbalances and reloading operations at stop-over airports are almost negligible. The required runtimes range between 13 and 38 minutes per flight on standard hardware, which is acceptable for non-interactive planning. Cargo airlines can significantly profit from employing the developed approaches in their operational practice. More and especially the profitable last-minute cargo can be transported. Furthermore, the costs of load planning, handling effort, and aircraft operations can be significantly reduced