Search

In this paper, we trace how mathematical models are made 'evidence enough' and 'useful for policy'. Working with the interview accounts of mathematical modellers and other scientists engaged in the UK Covid-19 response, we focus on two weeks in March 2020 prior to the announcement of an unprecedented national lockdown. A key thread in our analysis is how pandemics are made 'big'. We follow the work of one particular device, that of modelled 'doubling-time'. By following how modelled doubling-time entangles in its assemblage of evidence-making, we draw attention to multiple actors, including beyond models and metrics, which affect how evidence is performed in relation to the scale of epidemic and its policy response. We draw attention to: policy; Government scientific advice infrastructure; time; uncertainty; and leaps of faith. The 'bigness' of the pandemic, and its evidencing, is situated in social and affective practices, in which uncertainty and dis-ease are inseparable from calculus. This materialises modelling in policy as an 'uncomfortable science'. We argue that situational fit in-the-moment is at least as important as empirical fit when attending to what models perform in policy. • Pandemics are performed as crises of uncertain yet catastrophic potential. • Mathematical models are forms of scalar narrative affording epidemics their scale. • Models and projections are made useful as evidence in their situated policy events. • Calculations are given agency as affects in the evidencing of pandemics. • Modelling pandemics is a site of 'uncomfortable science' and 'dis-ease'. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study the restriction, to the class of bargaining problems with coalition structure, of several values which have been proposed on the class of non-transferable utility games with coalition structure. We prove that all of them coincide with the solution independently studied in Chae and Heidhues [Chae, S., Heidhues, P., 2004. A group bargaining solution. Mathematical Social Sciences 48, 37–53] and Vidal-Puga [Vidal-Puga, J.J., 2005a. A bargaining approach to the Owen value and the Nash solution with coalition structure. Economic Theory 25, 679–701]. Several axiomatic characterizations and two non-cooperative mechanisms are proposed. [Copyright &y& Elsevier]

Abstract: The correlational agreement coefficient CA(≤, D) [van Leeuwe, J.F.J., 1974. Item tree analysis. Nederlands Tijdschrift voor de Psychologie 29, 475–484.] is a descriptive measure for the fit of a quasi-order ≤ on an item set to a binary data set D. The coefficient is based on the comparison between the empirical correlations of the items to their assumed theoretical correlations. These theoretical correlations are derived from the assumption that the quasi-order is a correct representation of the data. In a recent paper Ünlü and Albert [Ünlü, A., Albert, D., 2004. The correlational agreement coefficient CA(≤, D) — A mathematical analysis of a descriptive goodness-of-fit measure. Mathematical Social Sciences 48, 281–314.] presented a detailed mathematical investigation of CA(≤, D). They describe a number of problems of this coefficient which show in their opinion that its use to compare quasi-orders is questionable. We do not agree with some of the statements in Ünlü and Albert [Ünlü, A., Albert, D., 2004. The correlational agreement coefficient CA(≤, D) — A mathematical analysis of a descriptive goodness-of-fit measure. Mathematical Social Sciences 48, 281–314.]. Especially we try to show that some of the problems of CA(≤, D) mentioned in Ünlü and Albert [Ünlü, A., Albert, D., 2004. The correlational agreement coefficient CA(≤, D) — A mathematical analysis of a descriptive goodness-of-fit measure. Mathematical Social Sciences 48, 281–314.] are in fact properties which a good measure of fit for a quasi-order should have. [Copyright &y& Elsevier]

Recent work by Borgatti and Everett (1989) has shown that the collection of regular equivalences described by White and Reitz (1983) forms a lattice. In this paper, we present a procedure called iterated roles for tracing systematic paths through the lattice. At the heart of iterated roles is the proof that the regular equivalence of a regular equivalence is itself regular. The procedure enables us to find several otherwise unknown regular equivalences, including an extension of automorphic equivalence (Everett 1985) that is not sensitive to degree. A key benefit of iterated roles is the generation of sequences of hierarchically nested equivalences. This capability suggests an approach to role structure analysis in which one examines not just one blocking of actors but a series of increasingly broad simplifications of the data. Consequently, we are able to (a) choose the level of simplification that proves most illuminating, and (b) view both to broad structural outlines of the data and the finer details simultaneously. [ABSTRACT FROM AUTHOR]

Stochastic relations frequently occur in the social sciences; however, their statistical properties are not well-known. A random relation can be used to model noise or observational error. This paper characterizes the structure of a random relation by deriving the distribution of the structural vector from Q-analysis and by simulating random relations. We propose a measure of structure and apply these concepts to the nominations of esteemed peers by mathematicians. [ABSTRACT FROM AUTHOR]

Although there has been much discussion in recent years of the applicability of mathematical methods in the social sciences, little attention has been paid to the interaction of the sociological analysis and the mathematics. In this paper, an example of an extremely fruitful interaction between anthropology and mathematics is described. The interaction has, on the one hand, greatly increased the subtlety and sophistication of the sociological analysis, while on the other hand it has posed interesting mathematical questions. [ABSTRACT FROM AUTHOR]

Abstract: This paper extends the formulation of complementarity in to the case of complete but -acyclic preferences. In such a case, quasi-supermodularity and the single-crossing property on their own do not guarantee monotone comparative statics or equilibrium existence: an additional condition, monotone closure, is required. [Copyright &y& Elsevier]