Nash's bargaining problem and the scale-invariant Hirsch citation index

A number of citation indices have been proposed for measuring and ranking the research publication records of scholars. Some of the best known indices, such as those proposed by Hirsch and Woeginger, are designed to reward most highly those records that strike some balance between productivity (number of papers published), and impact (frequency with which those papers are cited). A large number of rarely cited publications will not score well, nor will a very small number of heavily cited papers. We discuss three new citation indices, one of which was independently proposed in \cite{FHLB}. Each rests on the notion of scale invariance, fundamental to John Nash's solution of the two-person bargaining problem. Our main focus is on one of these -- a scale invariant version of the Hirsch index. We argue that it has advantages over the original; it produces fairer rankings within subdisciplines, is more decisive (discriminates more finely, yielding fewer ties) and more dynamic (growing over time via more frequent, smaller increments), and exhibits enhanced centrality and tail balancedness. Simulations suggest that scale invariance improves robustness under Poisson noise, with increased decisiveness having no cost in terms of the number of ``accidental" reversals, wherein random irregularities cause researcher A to receive a lower index value than B, although A's productivity and impact are both slightly higher than B's. Moreover, we provide an axiomatic characterization of the scale invariant Hirsch index, via axioms that bear a close relationship, in discrete analogue, to those used by Nash in \cite{Nas50}. This argues for the mathematical naturality of the new index. An earlier version was presented at the 5th World Congress of the Game Theory Society, Maastricht, Netherlands in 2016.Comment: 44 pages, 8 figure

A Moving-Knife Solution to the Four-Person Envy-Free Cake-Division Problem

Envy-freeness

10101 Abstracts Collection -- Computational Foundations of Social Choice

From March 7 to March 12, 2010, the Dagstuhl Seminar 10101 ``Computational Foundations of Social Choice \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

10101 Executive Summary -- Computational Foundations of Social Choice

This seminar addressed some of the key issues in computational social choice, a novel interdisciplinary field of study at the interface of social choice theory and computer science. Computational social choice is concerned with the application of computational techniques to the study of social choice mechanisms, such as voting rules and fair division protocols, as well as with the integration of social choice paradigms into computing. The seminar brought together many of the most active researchers in the field and focussed the research community currently forming around these important and exciting topics

Almost Envy-Free Allocations with Connected Bundles

We study the existence of allocations of indivisible goods that are envy-free up to one good (EF1), under the additional constraint that each bundle needs to be connected in an underlying item graph G. When the items are arranged in a path, we show that EF1 allocations are guaranteed to exist for arbitrary monotonic utility functions over bundles, provided that either there are at most four agents, or there are any number of agents but they all have identical utility functions. Our existence proofs are based on classical arguments from the divisible cake-cutting setting, and involve discrete analogues of cut-and-choose, of Stromquist\u27s moving-knife protocol, and of the Su-Simmons argument based on Sperner\u27s lemma. Sperner\u27s lemma can also be used to show that on a path, an EF2 allocation exists for any number of agents. Except for the results using Sperner\u27s lemma, all of our procedures can be implemented by efficient algorithms. Our positive results for paths imply the existence of connected EF1 or EF2 allocations whenever G is traceable, i.e., contains a Hamiltonian path. For the case of two agents, we completely characterize the class of graphs G that guarantee the existence of EF1 allocations as the class of graphs whose biconnected components are arranged in a path. This class is strictly larger than the class of traceable graphs; one can check in linear time whether a graph belongs to this class, and if so return an EF1 allocation

The Paradox of Multiple Elections

Aggregation paradoxes, paradox of voting, electoral systems, legislatures, referenda, divided government

Old and NewMoving-Knife Schemes

resource allocation ; decision making ; economic theory

How Should Voting on Related Propositions be Conducted?

Voting

Supervised Domain Adaptation using Graph Embedding

Getting deep convolutional neural networks to perform well requires a large amount of training data. When the available labelled data is small, it is often beneficial to use transfer learning to leverage a related larger dataset (source) in order to improve the performance on the small dataset (target). Among the transfer learning approaches, domain adaptation methods assume that distributions between the two domains are shifted and attempt to realign them. In this paper, we consider the domain adaptation problem from the perspective of dimensionality reduction and propose a generic framework based on graph embedding. Instead of solving the generalised eigenvalue problem, we formulate the graph-preserving criterion as a loss in the neural network and learn a domain-invariant feature transformation in an end-to-end fashion. We show that the proposed approach leads to a powerful Domain Adaptation framework; a simple LDA-inspired instantiation of the framework leads to state-of-the-art performance on two of the most widely used Domain Adaptation benchmarks, Office31 and MNIST to USPS datasets.Comment: 7 pages, 3 figures, 3 table