Mathematical Model

A mathematical model is an abstract model in mathematical language to describe the behaviour of a system. Eykhoff (1974) defines a mathematical model as 'a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form'.

Relationships and variables are the main elements included in mathematical models. Operators, such as algebraic operators, functions, etc, describe relationships. Variables play the role of abstracting systems parameter of interest that can be quantified. A mathematical model can even include operators without variables (King, 1999).

Mathematical models can be applied to construct dynamic systems, statistical models, differential equations, or game theoretic models. Davis (1996) provides a survey of mathematical models and formal approaches for decision and policy making. In his work, Davis shows how mathematics is indeed the foundation of modern decision and policy making, as it allows modeling complex systems, testing and evaluation, control and optimization (Davis, 1996).

Toshkov proposes a mathematical model for the timing and policy shift of implementation outcomes. Using a ‘decision making under institutional constraints’ framework, the model provides a number of hypotheses about the impact of  preferences, discretion, administrative capacity and policy-making constraints (Toshkov, 2007).

Related terms: Mathematical modelling

References:

Eykhoff,P. (1974) System Identification-Parameter and State Estimation. Wiley, New York.

Peter JB King (1999). Functions with no parameters

Aris, R. ( 1994 ). Mathematical Modelling Techniques, New York : Dover. ISBN 0-486-68131-9.

Davis, P. (1996). Mathematics and Decision Making. Mathematics Awareness Week 1996.

Toshkov, D. (2007).  A Formal Model of Policy Implementation in Multi-level Systems of Governance. PhD Thesis, 2007.


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