The Conjunction Problem and the Logic of Jury Findings

For several decades, evidence theorists have puzzled over the following paradox, known as the “conjunction paradox” or “conjunction problem.” Probability theory appears to tell us that the probability of a conjunctive claim is the product resulting from multiplying the probabilities of its separate conjuncts. In a three element negligence case (breach of duty, causation, damages), a plaintiff who proves each element to a 0.6 probability will have proven her overall claim to a very low probability of 0.216. Either the plaintiff wins the verdict based on this low probability (if the jury focuses on elements), or the plaintiff loses despite having met the condition of proving each element to the stated threshold. To solve this “conjunction problem,” evidence theorists have advanced such proposals as changing the rules of probability, barring probability theory entirely from analysis of adjudicative fact-finding, abandoning the procedural principle that the defendant need not present a narrative of innocence or nonliability, or dispensing with the requirement that the overall claim meet an established burden of proof. This Article argues that the conjunction paradox in fact presents a theoretical problem of little if any consequence. Dropping the condition that proving each element is a sufficient, as opposed to merely a necessary, condition for proof of a claim makes the conjunction problem disappear. Nothing in logic or probability theory requires this “each element/sufficiency” condition, and the legal decision rules reflected in most jury instructions do not mandate it. Once this “each element/sufficiency” condition is removed, all that is left of the conjunction problem is a “probability gap,” an intuitive but ill-founded impression that the mathematical underpinnings of the conjunction problem are unfair to claimants. This probability gap is considerably narrowed by recognizing the probabilistic dependence of most facts internal to a given claim, and by applying the correct multiplication rule for probabilistically dependent events. Finally, this Article argues that solving the conjunction problem is an insufficient ground either to abandon probability theory as a useful analytical tool in the context of adjudicative fact-finding, or to reform decision rules for trial fact-finders

Appendix: Conjunction-Problem v. Non-Conjunction-Problem Jurisdictions

This appendix presents the relevant data from our survey of jury instructions in support of the article in the print edition of the William & Mary Law Review. The Conjunction Problem and the Logic of Jury Findings (59 Wm. & Mary L. Rev. 619, 673-87 (2017)

Joint evolution of multiple social traits: a kin selection analysis

General models of the evolution of cooperation, altruism and other social behaviours have focused almost entirely on single traits, whereas it is clear that social traits commonly interact. We develop a general kin-selection framework for the evolution of social behaviours in multiple dimensions. We show that whenever there are interactions among social traits new behaviours can emerge that are not predicted by one-dimensional analyses. For example, a prohibitively costly cooperative trait can ultimately be favoured owing to initial evolution in other (cheaper) social traits that in turn change the cost-benefit ratio of the original trait. To understand these behaviours, we use a two-dimensional stability criterion that can be viewed as an extension of Hamilton's rule. Our principal example is the social dilemma posed by, first, the construction and, second, the exploitation of a shared public good. We find that, contrary to the separate one-dimensional analyses, evolutionary feedback between the two traits can cause an increase in the equilibrium level of selfish exploitation with increasing relatedness, while both social (production plus exploitation) and asocial (neither) strategies can be locally stable. Our results demonstrate the importance of emergent stability properties of multidimensional social dilemmas, as one-dimensional stability in all component dimensions can conceal multidimensional instability

Plasticity facilitates sustainable growth in the commons

In the commons, communities whose growth depends on public goods, individuals often rely on surprisingly simple strategies, or heuristics, to decide whether to contribute to the common good (at risk of exploitation by free-riders). Although this appears a limitation, here we show how four heuristics lead to sustainable growth by exploiting specific environmental constraints. The two simplest ones --contribute permanently or switch stochastically between contributing or not-- are first shown to bring sustainability when the public good efficiently promotes growth. If efficiency declines and the commons is structured in small groups, the most effective strategy resides in contributing only when a majority of individuals are also contributors. In contrast, when group size becomes large, the most effective behavior follows a minimal-effort rule: contribute only when it is strictly necessary. Both plastic strategies are observed in natural systems what presents them as fundamental social motifs to successfully manage sustainability

Energy Calibration of the JLab Bremsstrahlung Tagging System

In this report, we present the energy calibration of the Hall B bremsstrahlung tagging system at the Thomas Jefferson National Accelerator Facility. The calibration was performed using a magnetic pair spectrometer. The tagged photon energy spectrum was measured in coincidence with $e^+e^-$ pairs as a function of the pair spectrometer magnetic field. Taking advantage of the internal linearity of the pair spectrometer, the energy of the tagging system was calibrated at the level of $\pm 0.1$. The absolute energy scale was determined using the $e^+e^-$ rate measurements close to the end-point of the photon spectrum. The energy variations across the full tagging range were found to be $<3$ MeV.Comment: 15 pages, 12 figure

The prisoners dilemma on a stochastic non-growth network evolution model

We investigate the evolution of cooperation on a non - growth network model with death/birth dynamics. Nodes reproduce under selection for higher payoffs in a prisoners dilemma game played between network neighbours. The mean field characteristics of the model are explored and an attempt is made to understand the size dependent behaviour of the model in terms of fluctuations in the strategy densities. We also briefly comment on the role of strategy mutation in regulating the strategy densties.Comment: 8 pages, 8 figure

The Gerasimov-Drell-Hearn Sum Rule and the Spin Structure of the Nucleon

The Gerasimov-Drell-Hearn sum rule is one of several dispersive sum rules that connect the Compton scattering amplitudes to the inclusive photoproduction cross sections of the target under investigation. Being based on such universal principles as causality, unitarity, and gauge invariance, these sum rules provide a unique testing ground to study the internal degrees of freedom that hold the system together. The present article reviews these sum rules for the spin-dependent cross sections of the nucleon by presenting an overview of recent experiments and theoretical approaches. The generalization from real to virtual photons provides a microscope of variable resolution: At small virtuality of the photon, the data sample information about the long range phenomena, which are described by effective degrees of freedom (Goldstone bosons and collective resonances), whereas the primary degrees of freedom (quarks and gluons) become visible at the larger virtualities. Through a rich body of new data and several theoretical developments, a unified picture of virtual Compton scattering emerges, which ranges from coherent to incoherent processes, and from the generalized spin polarizabilities on the low-energy side to higher twist effects in deep inelastic lepton scattering.Comment: 32 pages, 19 figures, review articl

Problems with Using Evolutionary Theory in Philosophy

Does science move toward truths? Are present scientific theories (approximately) true? Should we invoke truths to explain the success of science? Do our cognitive faculties track truths? Some philosophers say yes, while others say no, to these questions. Interestingly, both groups use the same scientific theory, viz., evolutionary theory, to defend their positions. I argue that it begs the question for the former group to do so because their positive answers imply that evolutionary theory is warranted, whereas it is self-defeating for the latter group to do so because their negative answers imply that evolutionary theory is unwarranted

Photofission of heavy nuclei at energies up to 4 GeV

Total photofission cross sections for 238U, 235U, 233U, 237Np, 232Th, and natPb have been measured simultaneously, using tagged photons in the energy range Egamma=0.17-3.84 GeV. This was the first experiment performed using the Photon Tagging Facility in Hall B at Jefferson Lab. Our results show that the photofission cross section for 238U relative to that for 237Np is about 80%, implying the presence of important processes that compete with fission. We also observe that the relative photofission cross sections do not depend strongly on the incident photon energy over this entire energy range. If we assume that for 237Np the photofission probability is equal to unity, we observe a significant shadowing effect starting below 1.5 GeV.Comment: 4 pages of RevTex, 6 postscript figures, Submitted to Phys. Rev. Let