Given a phenomenon, how should we conceptualise it?
Pinker notes: ‘we have several grounds for supposing that enhanced powers of reason – specifically, the ability to set aside immediate experience, detach oneself from a parochial vantage point, and frame one’s ideas in abstract, universal terms – would lead to better moral commitments, including an avoidance of violence’(p. 656).
The appropriate conceptualisation of phenomena is an important issue and mathematics can play an important role in this. However there can sometimes be debate about which conceptualisation is the most appropriate.
.(1) The arms race
‘The value of mathematical models in sociology is amply proven ... On the other hand ... some difficulties might be inherent in the whole approach.’ [p. 464]
Etzioni, A. (1962) Review of ‘Arms and insecurity; statistics of deadly quarrels.’
American Journal of Sociology, 67, 4, 464-466. http://amitaietzioni.org/D5.pdf.pdf
.(2) The critical positivity ratio
‘Scholars have found that disputants in ongoing relationships need somewhere between three and a half to five positive experiences for every negative one, to keep the negative encounters from becoming harmful.’ (Coleman, 2013, p. 106).
Losada and Heaphy (2004):
http://abs.sagepub.com/content/47/6/740.abstract; http://en.wikipedia.org/wiki/Marcial_Losada
Brown, N. J. L., Sokal, A. D. and Friedman, H. L. (2013) The complex dynamics of wishful thinking: the critical positivity ratio. American Psychologist, 68, xxx-xxx.
http://arxiv.org/pdf/1307.7006v1.pdf
.(3) Pairwise comparison ... pairwise competition
A set of individuals or teams play one another in pairwise competition. Unobserved abilities influences the observed play and the observed outcomes. Given the outcomes how can we infer the abilities?
Jan Lasek; Zoltán Szlávik; Sandjai Bhulai (2013) The predictive power of ranking systems in association football. International Journal of Applied Pattern Recognition, 1, 1, 27-46.
http://www.few.vu.nl/~z.szlavik/papers/IJAPR.pdf ; http://www.inderscience.com/info/inarticle.php?artid=52339 ;
http://en.wikipedia.org/wiki/Elo_rating_system ; http://en.wikipedia.org/wiki/Sports_rating_system
The Times (2013) Fink tank. Daniel Finkelstein. Football Sport. p. 13. Saturday October 5.
Keener, J. P. (1993) The Perron-Frobenius theorem and the ranking of football teams
SIAM review, 35, 1, 80-93
https://umdrive.memphis.edu/ccrousse/public/MATH%207375/PERRON.pdf
The Perron-Frobenius theorem: http://en.wikipedia.org/wiki/Perron%E2%80%93Frobenius_theorem
Decision technology: http://www.dectech.co.uk/index.html
.(4) The legislative median and partisan policy
Burt, G. (2010) Conflict, complexity and mathematical social science. Bingley: Emerald Press. [Chapter 4: Theory, evidence and reality, pp. 80-86.]
http://www.emeraldinsight.com/books.htm?issn=1572-8323&volume=15&chapterid=1876237&show=abstract
.(5) Party policy
Burt, G. (1997) Party policy: decision rule or chance? A note on Budge's new spatial theory of party competition. British Journal of Political Science, 27, 4, 647-658.
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=1295
.(6) The relationship between two questionnaires
http://onlinelibrary.wiley.com/doi/10.1111/j.1467-8535.2005.00494_1.x/abstract
Burt, G. (2005) Measuring the relationship between two questionnaires: appropriate definitions of intuitive understandings. Assessment & Evaluation in Higher Education, 30, 6, 621-631.http://www.tandfonline.com/doi/abs/10.1080/02602930500260746