An Impossibility Result?

We propose multi-type probabilistic serial (MPS) and multi-type random priority (MRP) as extensions of the well-known PS and RP mechanisms to the multi-type resource allocation problems (MTRAs) with partial preferences. In our setting, there are multiple types of divisible items, and a group of agents who have partial order preferences over bundles consisting of one item of each type. We show that for the unrestricted domain of partial order preferences, no mechanism satisfies both sd-efficiency and sd-envy-freeness. Notwithstanding this impossibility result, our main message is positive: When agents' preferences are represented by acyclic CP-nets, MPS satisfies sd-efficiency, sd-envy-freeness, ordinal fairness, and upper invariance, while MRP satisfies ex-post-efficiency, sd-strategyproofness, and upper invariance, recovering the properties of PS and RP. Besides, we propose a hybrid mechanism, multi-type general dictatorship (MGD), combining the ideas of MPS and MRP, which satisfies sd-efficiency, equal treatment of equals and decomposability under the unrestricted domain of partial order preferences.

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Deterministic, Strategyproof, and Fair Cake Cutting

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/50 ◽

2017 ◽

Cited By ~ 3

Author(s):

Vijay Menon ◽

Kate Larson

Keyword(s):

Mechanism Design ◽

Impossibility Result ◽

Restricted Class ◽

Piecewise Constant ◽

Incentive Compatible ◽

Negative Results ◽

Cake Cutting ◽

Design Perspective ◽

A Minor ◽

Cutting Problem

We study the classic cake cutting problem from a mechanism design perspective, in particular focusing on deterministic mechanisms that are strategyproof and fair. We begin by looking at mechanisms that are non-wasteful and primarily show that for even the restricted class of piecewise constant valuations there exists no direct-revelation mechanism that is strategyproof and even approximately proportional. Subsequently, we remove the non-wasteful constraint and show another impossibility result stating that there is no strategyproof and approximately proportional direct-revelation mechanism that outputs contiguous allocations, again, for even the restricted class of piecewise constant valuations. In addition to the above results, we also present some negative results when considering an approximate notion of strategyproofness, show a connection between direct-revelation mechanisms and mechanisms in the Robertson-Webb model when agents have piecewise constant valuations, and finally also present a (minor) modification to the well-known Even-Paz algorithm that has better incentive-compatible properties for the cases when there are two or three agents.

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Cake Cutting: Envy and Truth

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/507 ◽

2017 ◽

Cited By ~ 4

Author(s):

Xiaohui Bei ◽

Ning Chen ◽

Guangda Huzhang ◽

Biaoshuai Tao ◽

Jiajun Wu

Keyword(s):

Nash Equilibrium ◽

Private Information ◽

General Setting ◽

Impossibility Result ◽

Market Model ◽

Truth Telling ◽

Piecewise Constant ◽

Cake Cutting ◽

Strategic Agents ◽

To Receive

We study envy-free cake cutting with strategic agents, where each agent may manipulate his private information in order to receive a better allocation. We focus on piecewise constant utility functions and consider two scenarios: the general setting without any restriction on the allocations and the restricted setting where each agent has to receive a connected piece. We show that no deterministic truthful envy-free mechanism exists in the connected piece scenario, and the same impossibility result for the general setting with some additional mild assumptions on the allocations. Finally, we study a large market model where the economy is replicated and demonstrate that truth-telling converges to a Nash equilibrium.

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Distributed Systems

Cryptographic Primitives in Blockchain Technology ◽

10.1093/oso/9780198862840.003.0005 ◽

2020 ◽

pp. 143-198

Author(s):

Andreas Bolfing

Keyword(s):

Distributed Systems ◽

Fault Tolerant ◽

Deterministic Algorithm ◽

Impossibility Result ◽

Software Systems ◽

Trade Off ◽

Byzantine Failures ◽

The Individual ◽

Special Case

Chapter 5 considers distributed systems by their properties. The first section studies the classification of software systems, which is usually distinguished in centralized, decentralized and distributed systems. It studies the differences between these three major approaches, showing there is a rather multidimensional classification instead of a linear one. The most important case are distributed systems that enable spreading of computational tasks across several autonomous, independently acting computational entities. A very important result of this case is the CAP theorem that considers the trade-off between consistency, availability and partition tolerance. The last section deals with the possibility to reach consensus in distributed systems, discussing how fault tolerant consensus mechanisms enable mutual agreement among the individual entities in presence of failures. One very special case are so-called Byzantine failures that are discussed in great detail. The main result is the so-called FLP Impossibility Result which states that there is no deterministic algorithm that guarantees solution to the consensus problem in the asynchronous case. The chapter concludes by considering practical solutions that circumvent the impossibility result in order to reach consensus.

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Unpredictability of AI: On the Impossibility of Accurately Predicting All Actions of a Smarter Agent

Journal of Artificial Intelligence and Consciousness ◽

10.1142/s2705078520500034 ◽

2020 ◽

Vol 07 (01) ◽

pp. 109-118

Author(s):

Roman V. Yampolskiy

Keyword(s):

Intelligent System ◽

Impossibility Result ◽

The Impact ◽

Ai Safety

The young field of AI Safety is still in the process of identifying its challenges and limitations. In this paper, we formally describe one such impossibility result, namely Unpredictability of AI. We prove that it is impossible to precisely and consistently predict what specific actions a smarter-than-human intelligent system will take to achieve its objectives, even if we know the terminal goals of the system. In conclusion, the impact of Unpredictability on AI Safety is discussed.

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