Every abstraction of a system/problem is a mathematical model. Specifically in social sciences we can create a graph, i.e. a mathematical model that represents members of a society as vertices and their interaction ( say friendship, co-workers, common mutual interest etc.) as edges. The vertices, the type of edges and the subsequent algorithms that are run depend on the problem in question. There are other models based on matrices etc.. You can try to answer questions like what are the common features of people who form friendship cliques etc.. For this, you can use a graph model in conjunction with statistics/regression-analysis/feature-enrichment etc..

Best regards.

Mathematical - and by extension statistical models - are located in a post-positivist paradigm that permit generalisation, and thereby forecasting as in econometrics. They are abstractions from reality, seeking to isolate key determining factors, the relationships between those factors, and directions of causality. By being abstractions they do not seek to capture the full complexities of reality - that is the nature of other research paradigms, but permit the researcher to establish probabilities of outcomes when given changes in determining variables occur. Mathematical models can be found in a range of social sciences. Anyway - that is a quick response that I hope is of help.

Cheers

Chris

I can't agree with BC above that "Every abstraction of a system/problem is a mathematical model." Most abstractions of systems/problems are clearly not mathematical models particularly in the social sciences. Rather it is true to say that every piece of research is an abstraction of a system or problem. What else could any research finding be other than an abstraction of a problem? Many of these abstractions are unquantified and in natural language e.g. Nerlich, B. and M. Döring (2005). "Poetic Justice? Rural policy clashes with rural poetry in the 2001 outbreak of foot and mouth disease in the UK." Journal of Rural Studies 21(2): 165-180. to take one of tens of thousands of abstractions in natural language. They may contain mathematical models or not. One could possibly represent such studies mathematically if one made the effort but they are not de facto mathematical models as they stand unless of course you believe that natural language is a mathematical model or are one of those people who believe everything is a mathematical model.

Dear Amir,

Do you have specific question in your mind? A philosophical discussion as to the precision in the definition of a math. model might not be pertinent to you.

Math models (by extension stat. models) is a vast area. I was referring to the models that can be represented in a computer. Any abstraction that uses entities and relations among them, can be worked on by a computer and it constitutes a math. model. Please look into Entity-Relationship diagrams. One can do requirements gathering on a given social system and represent it in an abstract way. The mere abstraction typically yields tuples in relational calculus (this is just an abstraction). The application of certain queries ( i.e. relational algebra) yields answers to a specific question. Here the first phase is about representing the system and the second phase is about making inferences.

Does the mere abstract representation on a computer of facts in day to day life constitutes a mathematical model? I say yes and invite the opinion of experts. According to Wiki: A mathematical model is a description of a system using mathematical concepts and language. A model may help to explain a system and to study the effects of different components, and to make predictions about behavior. A model may just explain the system. In AI knowledge representation deals with how to use a set of symbols effectively to denote a set of facts within a knowledge domain.

Is there any need of quantification in a model to qualify as a mathematical model? Here the answer is negative because several relations are binary (y/n) in nature and admit subsequent mathematical analysis (logic, automatic theorem proving ). A language that follows a grammar is abstracted by its grammar (i.e. the corr. production rules). This mere representation paves way for the processing (parsing) of the text in a given language. Here the first step is the production rules which is the model and the parsing is the corr. application.

I apologize for any lapses. I hope it helps.

Best regards.

Which aspects of social research do you consider ?

Social phenomena do fit to some extend into statistical descriptions. An yet, those are indeed rough abstractions, approximate ones. As new discoveries and understandings of social phenomena emerge new mathematics are to be developped. With an additional remark: we should always keep in mind that there are three kinds of social phenomena: natural or biological, artificial, and human. Hence, a right mathematical and conceptual explanation should take into consideration such a distinction, to say the least.

A combination of quantitative and qualitative models in social - especiallly in environmental research that copes with a large number of variables related each other in not causal (linear) way - is increasingly accepted. I do not see constraints in combining math models with social research if you keep in mind that the main objective of social research is describe, explain or give a picture os a social reality in context. However, math models never can be spurred as the main method, I mean, they are accessory, and need to respect the epistemology behind the social research design.

If you are interested in methodological criticisms of the use of mathematical models to explain social phenomena, then I recommend the following books:

Manicas, P. (2006) Realist Philosophy of Social Science. New York: Cambridge University Press (Especially Chapter 1 and Appendix A)

Sayer, A. (1992) Method in Social Science: A realist approach. London: Routledge (Especially Chapter 6)

To understand the concept in a better way kindly go through my research paper

" 0n The Job Training: A step towards job satisfaction- A Case Study of Public Sector Organization"(Link)Edit International Journal of Mathematical Modeling & Applied Computing, Academic & Scientific Publishing, ISSN: 2332-3744(Online)New York, USA, Vol.1, No.2, May 2013.

Mathematical models are not just equations composed of variables. They are composed of variables with coefficients and constants. These coefficients and constants are generated through past social researches or experiments. These models allow one to estimate, to make a forecast, or to compare. These models could make you believe that "you now know what would be the situation" or caution you that they are just a "picture of the past". Hence, mathematical models could give you insights or glimpses of the "incoming reality" with the "reality of the past" using mathematical functions..

Implications of mathematical models are that you have to define very clearly the concepts that you are using to model mathematically. In fuzzy areas of some social research or if you are just exploring undefined issues such a modelling approach might be less productive

I would like to point out to a very sensitive problem. The complexity of social phenomena does not necessarily coincide with the numebr of variables. Moreover -and more radically-, from the standpoint of complexity science, it is important to keep in mind that complex phenomena cannot be parametrized. In other words, parametrization simply kills -i.e. avoids- complexity. Analytical methods are appropriate in a number of fields, but they are highly limited when adequately considering complex phenomena.