Arrow's impossibility theorem: Two simple single-profile versions

In this short paper we provide two simple new versions of Arrow's impossibility theorem, in a world with only one preference profile. Both versions are extremely transparent. The first version assumes a two-agent society; the second version, which is similar to a theorem of Pollak, assumes two or more agents. Both of our theorems rely on diversity of preferences axioms, and we explore alternative notions of diversity at 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 show the logical independence of the axioms, and to illustrate our points.Arrow's theorem; single-profile

Comparative Vigilance: a Simple Guide

In this paper we discuss a new tort liability rule, which we call super-symmetric comparative negligence and vigilance. When both injurer and victim in an accident are negligent, it provides for liability shares that depend on the degrees of negligence of the two parties, similar to the standard comparative negligence rule. Unlike standard liability rules, however, when both parties are vigilant (i.e., taking more care than is efficient), the rule provides for liability shares that depend on the parties’ degrees of vigilance. Moreover, when one party is negligent and the other is non-negligent, our rule provides for variable liability shares, that respond to both carefulness and carelessness of the parties. Our liability rule is equitable; it has no discontinuity at the efficient point where both parties are just meeting their standards of care; and it provides incentives that guarantee the injurer and victim will choose the efficient care levels. This paper does not include theorems and proofs; rather it explains the results with the aid of a simple example, laid out in an easy 3 x 3 table.Comparative vigilance; equity; economic efficiency; tort liability rules; Nash equilibrium; social costs; pure comparative vigilance; super-symmetric rule

Comparative Vigilance

A growing body of literature suggests that courts and juries are inclined toward division of liability between two strictly non-negligent or “vigilant” parties. However, standard models of liability rules do not provide for vigilance-based sharing of liability. In this paper, we explore the economic efficiency of liability rules based on comparative vigilance. We devise liability rules that are efficient and that reward vigilance exhibited by the parties. It is commonly believed that discontinuous liability shares are necessary for efficiency, but we develop a liability rule that is both efficient and continuous, based on comparative negligence when both parties are negligent and on comparative vigilance when both parties are vigilant. Moreover, our rule divides accident losses into two parts: one part creates incentives for efficiency; the other part provides equity.Comparative vigilance; equity; economic efficiency; tort liability rules; Nash equilibrium; social costs; pure comparative vigilance; super-symmetric rule

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

COMPARATIVE VIGILANCE

A growing body of literature suggests that courts and juries are inclined toward division of liability between two strictly non-negligent or “vigilant” parties. However, standard models of liability rules do not provide for vigilance-based sharing of liability. In this paper, we explore the economic efficiency of liability rules based on comparative vigilance. We devise rules that are efficient and that reward vigilance. It is commonly believed that discontinuous liability shares are necessary for efficiency. However we develop a liability rule, which we call the “super-symmetric rule,” that is both efficient and continuous, that is based on comparative negligence when both parties are negligent and on comparative vigilance when both parties are vigilant, and that is always responsive to increased care. Moreover, our super-symmetric rule divides accident losses into two parts: one part creates incentives for efficiency; the other part provides equity.Comparative vigilance, equity, economic efficiency, tort liability rules, Nash equilibrium, social costs, pure comparative vigilance, super-symmetric rule

Research Report

The University of Massachusetts (UMass) STEM Education Institute and the UMass School of Education hosted a National Science Foundation funded conference entitled “Science, Technology, Engineering and Math—Alternative Certification for Teachers” (STEM ACT) in Arlington, Virginia on May 5-7, 2006. This white paper summarizes issues presented at the conference that are of importance for academic researchers of alternative certification (AC) for science teachers. It also outlines a research agenda for the initial preparation of science teachers, regardless of programs, which is intended to identify and examine how teacher learning occurs in their preparation, what is learned, and how teachers put that learning to use. Two similar papers have been prepared for program providers and policy maker