Tootfinder

Efficient reallocation of indivisible resources: Pair-efficiency versus Pareto-efficiency
Pinaki Mandal
https://arxiv.org/abs/2506.15169 https://

Efficient reallocation of indivisible resources: Pair-efficiency versus Pareto-efficiency
In the object reallocation problem, achieving Pareto-efficiency is desirable, but may be too demanding for implementation purposes. In contrast, pair-efficiency, which is the minimal efficiency requirement, is more suitable. Despite being a significant relaxation, however, pair-efficiency ensures Pareto-efficiency for any strategy-proof and individually rational rule when agents' preferences are unrestricted. What if agents' preferences have specific restricted structures, such as single-peak…

On a conjecture concerning the extensions of a reciprocal matrix
Ros\'ario Fernandes
https://arxiv.org/abs/2507.16593 https://arx…

On a conjecture concerning the extensions of a reciprocal matrix
Let $A$ be a reciprocal matrix of order $n$ and $w$ be its Perron eigenvector. To infer the efficiency of $w$ for $A$, based on the principle of Pareto optimal decisions, we study the strong connectivity of a certain digraph associated with $A$ and $w$. A reciprocal matrix $B$ of order $n+1$ is an extension of $A$ if the matrix $A$ is obtained from $B$ by removing its last row and column. We prove that there is no extension of a reciprocal matrix whose digraph associated with the extension and …

Robust and Smooth Estimation of the Extreme Tail Index via Weighted Minimum Density Power Divergence
Saida Mancer, Abdelhakim Necir, Djamel Meraghni
https://arxiv.org/abs/2507.15744

Robust and Smooth Estimation of the Extreme Tail Index via Weighted Minimum Density Power Divergence
By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These estimators can be viewed as a robust generalization of both weighted least squares and kernel-based tail index estimators. We establish the consistency and asymptotic normality of the proposed class. A simulation study is conducted to assess their finite-sample p…

Tight Efficiency Bounds for the Probabilistic Serial Mechanism under Cardinal Preferences
Jugal Garg, Yixin Tao, L\'aszl\'o A. V\'egh
https://arxiv.org/abs/2507.03359 …

Tight Efficiency Bounds for the Probabilistic Serial Mechanism under Cardinal Preferences
The Probabilistic Serial (PS) mechanism -- also known as the simultaneous eating algorithm -- is a canonical solution for the assignment problem under ordinal preferences. It guarantees envy-freeness and ordinal efficiency in the resulting random assignment. However, under cardinal preferences, its efficiency may degrade significantly: it is known that PS may yield allocations that are $Ω(\ln{n})$-worse than Pareto optimal, but whether this bound is tight remained an open question. Our first…

Optimising finite-time quantum information engines using Pareto bounds
Rasmus Hagman, Jonas Berx, Janine Splettstoesser, Henning Kirchberg
https://arxiv.org/abs/2507.00712

Optimising finite-time quantum information engines using Pareto bounds
Information engines harness measurement and feedback to convert energy into useful work. In this study, we investigate the fundamental trade-offs between ergotropic output power, thermodynamic efficiency and information-to-work conversion efficiency in such engines, explicitly accounting for the finite time required for measurement. As a model engine, we consider a two-level quantum system from which work is extracted via a temporarily coupled quantum harmonic oscillator that serves as the meas…

What Pareto-Efficiency Adjustments Cannot Fix
Josue Ortega, Gabriel Ziegler, R. Pablo Arribillaga, Geng Zhao
https://arxiv.org/abs/2506.11660 https://

What Pareto-Efficiency Adjustments Cannot Fix
The Deferred Acceptance (DA) algorithm is stable and strategy-proof, but can produce outcomes that are Pareto-inefficient for students, and thus several alternative mechanisms have been proposed to correct this inefficiency. However, we show that these mechanisms cannot correct DA's rank-inefficiency and inequality, because these shortcomings can arise even in cases where DA is Pareto-efficient. We also examine students' segregation in settings with advantaged and marginalized students. We pr…

Fair and Efficient Allocation of Indivisible Mixed Manna
Siddharth Barman, Vishwa Prakash HV, Aditi Sethia, Mashbat Suzuki
https://arxiv.org/abs/2507.03946

Fair and Efficient Allocation of Indivisible Mixed Manna
We study fair division of indivisible mixed manna (items whose values may be positive, negative, or zero) among agents with additive valuations. Here, we establish that fairness -- in terms of a relaxation of envy-freeness -- and Pareto efficiency can always be achieved together. Specifically, our fairness guarantees are in terms of envy-freeness up to $k$ reallocations (EFR-$k$): An allocation $A$ of the indivisible items is said to be EFR-$k$ if there exists a subset $R$ of at most $k$ items …