The General Theory of Second Best Is More General Than You Think

Lipsey and Lancaster's "general theory of second best" is widely thought to have significant implications for applied theorizing about the institutions and policies that most effectively implement abstract normative principles. It is also widely thought to have little significance for theorizing about which abstract normative principles we ought to implement. Contrary to this conventional wisdom, I show how the second-best theorem can be extended to myriad domains beyond applied normative theorizing, and in particular to more abstract theorizing about the normative principles we should aim to implement. I start by separating the mathematical model used to prove the second-best theorem from its familiar economic interpretation. I then develop an alternative normative-theoretic interpretation of the model, which yields a novel second best theorem for idealistic normative theory. My method for developing this interpretation provides a template for developing additional interpretations that can extend the reach of the second-best theorem beyond normative theoretical domains. I also show how, within any domain, the implications of the second-best theorem are more specific than is typically thought. I conclude with some brief remarks on the value of mathematical models for conceptual exploration

MATCH - A Software Package for Robust Profile Matching Using S-Plus

This manual details the implementation of the profile matching techniques introduced in Robust Estimation of Air-Borne Particulate Matter (Wiens, Florence and Hiltz, Environmetrics, 2001 - included as an appendix). The program consists of a collection of functions written in S. It runs in S-Plus, including the student version. A graphical user interface is supplied for easy implementation by a user with only a passing familiarity with S-Plus. A description of the software is given, together with an extensive example of an analysis of a data set using the software. The software is available at http://www.stat.ualberta.ca/~wiens/publist.htm where it is linked to the listing for Wiens, Florence and Hiltz (2001).

The Tyranny of a Metaphor

Debates on the practical relevance of ideal theory revolve around Sen's metaphor of navigating a mountainous landscape. In *The Tyranny of the Ideal*, Gerald Gaus presents the most thorough articulation of this metaphor to date. His detailed exploration yields new insight on central issues in existing debates, as well as a fruitful medium for exploring important limitations on our ability to map the space of social possibilities. Yet Gaus's heavy reliance on the navigation metaphor obscures questions about the reasoning by which ideal theories are justified. As a result, Gaus fails to notice the ways in which his theory of the Open Society resembles the ideal theories he aims to dismiss. Ironically, Gaus winds up neglecting the ways in which the Open Society might tyrannize our efforts to realize greater justice. (This article is part of a symposium on Gaus's *The Tyranny of the Ideal*.

Morals From Rationality Alone? Some Doubts

Contractarians aim to derive moral principles from the dictates of instrumental rationality alone. But it is well-known that contractarian moral theories struggle to identify normative principles that are both uniquely rational and morally compelling. Michael Moehler's recent book, *Minimal Morality* seeks to avoid these difficulties by developing a novel "two-level" social contract theory, which restricts the scope of contractarian morality to cases of deep and persistent moral disagreement. Yet Moehler remains ambitious, arguing that a restricted version of Kant's categorical imperative is a uniquely rational principle of conflict resolution. We develop a formal model of Moehler's informal game-theoretic argument, which reconstructs a valid argument for Moehler's conclusion. This model, in turn, enables us to expose how a successful argument for Moehler's contractarian principle rests on assumptions that can only be justified by subtle yet significant departures from the standard conception of rationality. We thus extend our understanding of familiar contractarian difficulties by showing how they arise even if we restrict the scope of contractarian morality to a domain where its application seems both promising and necessary. We show that the problem lies not in contractarians' immodest ambitions but in the modest resources rationality can offer to satisfy them

Herbivory increases diversification across insect clades.

Insects contain more than half of all living species, but the causes of their remarkable diversity remain poorly understood. Many authors have suggested that herbivory has accelerated diversification in many insect clades. However, others have questioned the role of herbivory in insect diversification. Here, we test the relationships between herbivory and insect diversification across multiple scales. We find a strong, positive relationship between herbivory and diversification among insect orders. However, herbivory explains less variation in diversification within some orders (Diptera, Hemiptera) or shows no significant relationship with diversification in others (Coleoptera, Hymenoptera, Orthoptera). Thus, we support the overall importance of herbivory for insect diversification, but also show that its impacts can vary across scales and clades. In summary, our results illuminate the causes of species richness patterns in a group containing most living species, and show the importance of ecological impacts on diversification in explaining the diversity of life

Defining 'democracy': Are we staying on topic?

Political scientists' failure to pay careful attention to the content (as opposed to the operationalization) of their chosen definition of 'democracy' can make them liable to draw invalid inferences from their empirical research. With this problem in mind, we argue for the following proposition: if one wishes to conduct empirical research that contributes to an existing conversation about democracy, then one must choose a definition of 'democracy' that picks out the topic of that conversation as opposed to some other (perhaps nearby) topic of conversation. We show that, as a practical matter, one of the most effective methods for preserving "topic continuity" is to choose a definition of `democracy' that concurs with prevailing judgments about how to classify particular regimes, emphasizing the superiority (in this regard) of judgments about stylized hypothetical scenarios as opposed to judgments about the actual regimes we observe in our datasets

An efficient parallel immersed boundary algorithm using a pseudo-compressible fluid solver

We propose an efficient algorithm for the immersed boundary method on distributed-memory architectures, with the computational complexity of a completely explicit method and excellent parallel scaling. The algorithm utilizes the pseudo-compressibility method recently proposed by Guermond and Minev [Comptes Rendus Mathematique, 348:581-585, 2010] that uses a directional splitting strategy to discretize the incompressible Navier-Stokes equations, thereby reducing the linear systems to a series of one-dimensional tridiagonal systems. We perform numerical simulations of several fluid-structure interaction problems in two and three dimensions and study the accuracy and convergence rates of the proposed algorithm. For these problems, we compare the proposed algorithm against other second-order projection-based fluid solvers. Lastly, the strong and weak scaling properties of the proposed algorithm are investigated

Robust designs for series estimation

We discuss optimal design problems for a popular method of series estimation in regression problems. Commonly used design criteria are based on the generalized variance of the estimates of the coefficients in a truncated series expansion and do not take possible bias into account. We present a general perspective of constructing robust and e±cient designs for series estimators which is based on the integrated mean squared error criterion. A minimax approach is used to derive designs which are robust with respect to deviations caused by the bias and the possibility of heteroscedasticity. A special case results from the imposition of an unbiasedness constraint; the resulting unbiased designs are particularly simple, and easily implemented. Our results are illustrated by constructing robust designs for series estimation with spherical harmonic descriptors, Zernike polynomials and Chebyshev polynomials. --Chebyshev polynomials,direct estimation,minimax designs,robust designs,series estimation,spherical harmonic descriptors,unbiased design,Zernike polynomials