Arrow's Impossibility Theorem: Preference Diversity in a Single-Profile World

In this paper we provide two simple new versions of Arrow’s impossibility theorem, in a model with only one preference profile. Both versions are transparent, requiring minimal mathematical sophistication. The first version assumes there are only two people in society, whose preferences are being aggregated; the second version assumes two or more people. Both theorems rely on assumptions about diversity of preferences, and we explore alternative notions of diversity at some length. Our first theorem also uses a neutrality assumption, commonly used in the literature; our second theorem uses a neutrality/monotonicity assumption, which is stronger and less commonly used. We provide examples to illustrate our points.Arrow's Theorem; single-profile

Nine Theorems of Inconsistency in GRT with Resolutions via Isogravitation

This paper presents nine inconsistency theorems for general relativity theory (GRT), and shows that they ultimately originate from the use of Riemannian curvature and the abandonment of universal invariance (which is stronger than the customary covariance). These features cause GRT to be non-canonical at the classi-cal level and non-unitary at the operator level, resulting under time evolution in catastrophic structural prob-lems, such as lack of invariant basic measurement units, loss of stable numerical predictions, absence of reliable observables, etc. The nine inconsistency theorems are re-inspected via isotopic methods and the related new theory of gravitation known as isogravitation. This new theory offers swift and simple resolutions for all the in-consistencies identified in GRT.Comment: 10 pages pd

Characterizing and Adapting the Consistency-Latency Tradeoff in Distributed Key-value Stores

The CAP theorem is a fundamental result that applies to distributed storage systems. In this paper, we first present and prove two CAP-like impossibility theorems. To state these theorems, we present probabilistic models to characterize the three important elements of the CAP theorem: consistency (C), availability or latency (A), and partition tolerance (P). The theorems show the un-achievable envelope, i.e., which combinations of the parameters of the three models make them impossible to achieve together. Next, we present the design of a class of systems called PCAP that perform close to the envelope described by our theorems. In addition, these systems allow applications running on a single data-center to specify either a latency SLA or a consistency SLA. The PCAP systems automatically adapt, in real-time and under changing network conditions, to meet the SLA while optimizing the other C/A metric. We incorporate PCAP into two popular key-value stores -- Apache Cassandra and Riak. Our experiments with these two deployments, under realistic workloads, reveal that the PCAP system satisfactorily meets SLAs, and performs close to the achievable envelope. We also extend PCAP from a single data-center to multiple geo-distributed data-centers

Kochen-Specker theorem revisited

The Kochen-Specker theorem is a basic and fundamental 50 year old non-existence result affecting the foundations of quantum mechanix, strongly implying the lack of any meaningful notion of "quantum realism", and typically leading to discussions of "contextuality" in quantum physics. Original proofs of the Kochen-Specker theorem proceeded via brute force counter-examples; often quite complicated and subtle (albeit mathematically "elementary") counter-examples. Only more recently have somewhat more "geometrical" proofs been developed. We present herein yet another simplified geometrical proof of the Kochen-Specker theorem, one that is valid for any number of dimensions, that minimizes the technical machinery involved, and makes the seriousness of the issues raised manifest.Comment: V1:12 pages. V2: Now 17 pages, 8 figures. Massive revision of the technical heart of the article. We now use a simplified two-step descent argument; the measure-theoretic arguments used in V1 were deeply flawed and have been replaced. Physics conclusions are of course unaltere

Extensions of quantum gravity theories - Final theory and cosmology

The fields of application of general relativity (GR) and quantum field theory (QFT) are different, so most situations require the use of only one of the two theories. The overlaps occur in regions of extremely small size and high mass, such as the black hole or the early universe (immediately after the Big Bang). This conflict is supposed to be solved only by unifying gravity with the other three interactions, to integrate GR and QFT into one theory. At the cosmological level, the standard cosmological model contains Einstein's theory of gravity as part of the "hard core". Dark matter, dark energy, and inflation were added to the theory in response to observations. None of these ancillary hypotheses have yet been confirmed. DOI: 10.13140/RG.2.2.34318.7200

Introduction to social choice and welfare

Social choice theory is concerned with the evaluation of alternative methods of collective decision-making, as well as with the logical foundations of welfare economics. In turn, welfare economics is concerned with the critical scrutiny of the performance of actual and/or imaginary economic systems, as well as with the critique, design and implementation of alternative economic policies. The Handbook of Social Choice and Welfare, which is edited by Kenneth Arrow, Amartya Sen and Kotaro Suzumura, presents, in two volumes, essays on past and on-going work in social choice theory and welfare economics. This paper is written as an extensive introduction to the Handbook with the purpose of placing the broad issues examined in the two volumes in better perspective, discussing the historical background of social choice theory, the vistas opened by Arrow's Social Choice and Individual Values, the famous "socialist planning" controversy, and the theoretical and practical significance of social choice theory.social choice theory, welfare economics, socialist planning controversy, social welfare function, Arrovian impossibility theorems, voting schemes, implementation theory, equity and justice, welfare and rights, functioning and capability, procedural fairness

Why Physics Needs Quantum Foundations

We discuss the motivation for pursuing research on the foundations of quantum theory.Comment: 4 pages,to appear in a special issue of Physics in Canad