Mean-Variance and Expected Utility: The Borch Paradox

The model of rational decision-making in most of economics and statistics is expected utility theory (EU) axiomatised by von Neumann and Morgenstern, Savage and others. This is less the case, however, in financial economics and mathematical finance, where investment decisions are commonly based on the methods of mean-variance (MV) introduced in the 1950s by Markowitz. Under the MV framework, each available investment opportunity ("asset") or portfolio is represented in just two dimensions by the ex ante mean and standard deviation $(\mu,\sigma)$ of the financial return anticipated from that investment. Utility adherents consider that in general MV methods are logically incoherent. Most famously, Norwegian insurance theorist Borch presented a proof suggesting that two-dimensional MV indifference curves cannot represent the preferences of a rational investor (he claimed that MV indifference curves "do not exist"). This is known as Borch's paradox and gave rise to an important but generally little-known philosophical literature relating MV to EU. We examine the main early contributions to this literature, focussing on Borch's logic and the arguments by which it has been set aside.Comment: Published in at http://dx.doi.org/10.1214/12-STS408 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

The search for modernity

Review of book: "From symbolic temple to dematerialization: a journey through library architecture from the 20th to the 21st century", by Daniel Gil-Solé

The search for modernity

Review of book: "From symbolic temple to dematerialization: a journey through library architecture from the 20th to the 21st century", by Daniel Gil-Solé

Elements of Social Learning Supporting Transformative Change

The body of literature on social learning is enormous, with differently framed ontologies and epistemologies aligned to multiple perspectives of learning in a social context. These have grown out of the many academic disciplines which have seen the value of social learning. This paper highlights the need to be aware of these multiple perspectives, and draws on the work of Lotz-Sisitka, Mukute and Belay (2012) to argue that there is a need to understand, and engage deeply with, the antecedent perspectives on social learning and to avoid ontological collapse in social-learning research in environmental education research and practice. It provides a broad-based understanding of transformative social learning by simply defining social learning with a socially critical orientation, and distilling key elements of social learning important to supporting social change. A recommendation is made for interventionist researchers and practitioners to use a theoretically sound, ontologically congruent methodology to support their social-learning research and implementation

El peso de la luz

The study explored whether the knowledge of Archimedes' law of the lever can be used to measure subjective intensities. Participants were presented with two achromatic rectangles on a horizontal line-drawn lever, one on the left and one on the right of the fulcrum. The left rectangle had a fixed low luminance. For different combinations of luminance and distance from the fulcrum of the right rectangle, participants were asked to position the left rectangle at a distance from the fulcrum such that the weight of the light emitted by the left rectangle kept the lever horizontal given the weight of the light emitted by the right rectangle. Most of the participants solved the task in accordance with their knowledge of Archimedes' law. This finding is interpreted to imply that the perceived distance of the left rectangle from the fulcrum was proportional to the perceived brightness of the right rectangle. It suggests that people's explicit or implicit knowledge of ratios and proportions in Archimedes' law of the lever, and perhaps in other physical laws, could potentially be used to measure any subjective intensity on a ratio scale

Interaction design and emotional wellbeing

The World Health Organisation has concluded that emotional wellbeing is fundamental to our quality of life. It enables us to experience life as meaningful and is an essential component of social cohesion, peace and stability in the living environment [21]. This workshop will bring together a diverse community to consolidate existing knowledge and identify new opportunities for research on technologies designed to support emotional wellbeing. The workshop will examine uses of technology in mental health settings, but will also consider the importance of emotional needs in physical healthcare and wellbeing more generally. The design of technology to provide social support and to extend traditional care networks will be key workshop themes

Beerbohm Tree's 1904 version of Shakespeare's Tempest

An edition of Beerbohm Tree's acting text of Shakespeare's Tempest as printed in the souvenir programme for the 50th presentation of the production in 1904. Illustrations by Buchel from the programme together with other newspaper cartoons of the actors are included