Neutral Aggregation in Finite Length Genotype space

The advent of modern genome sequencing techniques allows for a more stringent test of the neutrality hypothesis of Darwinian evolution, where all individuals have the same fitness. Using the individual based model of Wright and Fisher, we compute the amplitude of neutral aggregation in the genome space, i.e., the probability of finding two individuals at genetic (hamming) distance k as a function of genome size L, population size N and mutation probability per base \nu. In well mixed populations, we show that for N\nu\textless{}1/L, neutral aggregation is the dominant force and most individuals are found at short genetic distances from each other. For N\nu\textgreater{}1 on the contrary, individuals are randomly dispersed in genome space. The results are extended to geographically dispersed population, where the controlling parameter is shown to be a combination of mutation and migration probability. The theory we develop can be used to test the neutrality hypothesis in various ecological and evolutionary systems

Scoring rules for judgment aggregation

This paper studies a class of judgment aggregation rules, to be called 'scoring rules' after their famous counterpart in preference aggregation theory. A scoring rule delivers the collective judgments which reach the highest total 'score' across the individuals, subject to the judgments having to be rational. Depending on how we define 'scores', we obtain several (old and new) solutions to the judgment aggregation problem, such as distance-based aggregation, premise- and conclusion-based aggregation, truth-tracking rules, and a generalization of Borda rule to judgment aggregation. Scoring rules are shown to generalize the classical scoring rules of preference aggregation theory

Scoring rules for judgment aggregation

This paper studies a class of judgment aggregation rules, to be called `scoring rules' after their famous counterpart in preference aggregation theory. A scoring rule delivers the collective judgments which reach the highest total `score' across the individuals, subject to the judgments having to be rational. Depending on how we define `scores', we obtain several (old and new) solutions to the judgment aggregation problem,such as distance-based aggregation, premise- and conclusion-based aggregation, truth-tracking rules, and a Borda-type rule. Scoring rules are shown to generalize the classical scoring rules of preference aggregation theory

Scoring rules for judgment aggregation

This paper studies a class of judgment aggregation rules, to be called `scoring rules' after their famous counterpart in preference aggregation theory. A scoring rule delivers the collective judgments which reach the highest total `score' across the individuals, subject to the judgments having to be rational. Depending on how we define `scores', we obtain several (old and new) solutions to the judgment aggregation problem,such as distance-based aggregation, premise- and conclusion-based aggregation, truth-tracking rules, and a Borda-type rule. Scoring rules are shown to generalize the classical scoring rules of preference aggregation theory

Scoring rules for judgment aggregation

This paper studies a class of judgment aggregation rules, to be called `scoring rules' after their famous counterpart in preference aggregation theory. A scoring rule delivers the collective judgments which reach the highest total `score' across the individuals, subject to the judgments having to be rational. Depending on how we define `scores', we obtain several (old and new) solutions to the judgment aggregation problem,such as distance-based aggregation, premise- and conclusion-based aggregation, truth-tracking rules, and a Borda-type rule. Scoring rules are shown to generalize the classical scoring rules of preference aggregation theory

Ranking Median Regression: Learning to Order through Local Consensus

This article is devoted to the problem of predicting the value taken by a random permutation $\Sigma$, describing the preferences of an individual over a set of numbered items $\{1,\; \ldots,\; n\}$ say, based on the observation of an input/explanatory r.v. $X$ e.g. characteristics of the individual), when error is measured by the Kendall $\tau$ distance. In the probabilistic formulation of the 'Learning to Order' problem we propose, which extends the framework for statistical Kemeny ranking aggregation developped in \citet{CKS17}, this boils down to recovering conditional Kemeny medians of $\Sigma$ given $X$ from i.i.d. training examples $(X_1, \Sigma_1),\; \ldots,\; (X_N, \Sigma_N)$. For this reason, this statistical learning problem is referred to as \textit{ranking median regression} here. Our contribution is twofold. We first propose a probabilistic theory of ranking median regression: the set of optimal elements is characterized, the performance of empirical risk minimizers is investigated in this context and situations where fast learning rates can be achieved are also exhibited. Next we introduce the concept of local consensus/median, in order to derive efficient methods for ranking median regression. The major advantage of this local learning approach lies in its close connection with the widely studied Kemeny aggregation problem. From an algorithmic perspective, this permits to build predictive rules for ranking median regression by implementing efficient techniques for (approximate) Kemeny median computations at a local level in a tractable manner. In particular, versions of $k$-nearest neighbor and tree-based methods, tailored to ranking median regression, are investigated. Accuracy of piecewise constant ranking median regression rules is studied under a specific smoothness assumption for $\Sigma$'s conditional distribution given $X$

Measuring Eco-efficiency of Production: A Frontier Approach

Eco-efficiency of production is an important concept both from the viewpoint of society and business community; but as yet, there is no unambiguous way to its measurement. The purpose of this paper is to present a general measurement framework based on production theory and the activity analysis approach. Although we exploit the existing methods and techniques, our approach diverges essentially from the usual treatments of the environmental performance of firms in the productive efficiency analysis. The main difference between our approach and the earlier studies is that we build on the definition of eco-efficiency as the ratio of economic value added to the environmental damage index. Related to this orientation, we also approach eco-efficiency from a more aggregate perspective. Our general framework is illustrated by an empirical application to the evaluation of eco-efficiency of road transportation in Finland.Eco-efficiency, Environmental Pressures, Aggregation, Benefit of the Doubt Weighting, Distance Function, Activity Analysis, Data Envelopment Analysis, Road transportation