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An abstract model (or conceptual model) is a theoretical construct that represents physical, biological or social processes, with a set of variables and a set of logical and quantitative relationships between them. Models in this sense are constructed to enable reasoning within a idealized logical framework about these processes and are an important component of scientific theories. Idealized here means that the model may make explicit assumptions that are known to be false in some detail, but by their simplication of the model allow the production of acceptably accurate solutions, as is illustrated below.1 Examples
1.1 Mathematical models
Main article: Mathematical model
- Model of a particle in a potential field. In this model we consider a particle as being a point of mass m which describes a trajectory which is modeled by a function x: R → R3 given its coordinates in space as a function of time. The potential field is given by a function V:R3 → R and the trajetory is a solution of the differential equation
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- Note this model assumes the particle is a point mass, which is certainly known to be false in many cases we use this model, for example, as a model of planetary motion.
- Model of rational behavior for a consumer. In this model we assume a consumer faces a choice of n commodities labelled 1,2,...,n each with a market price p1, p2,..., pn. The consumer is assumed to have an cardinal utility function U (cardinal in the sense that it assign numerical values to utilities), depending on the amounts of coomodities x1, x2,..., xn consumed. The model further assumes that the consumer has a budget M which she uses to purchase a vector x1, x2,..., xn in such a way as to maximize U(x1, x2,..., xn). The problem of rational behavior in this model then becomes one of constrained maximization, that is maximize
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- subject to
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- This model has been used in models of general equilibrium theory, particularly to show existence and Pareto optimality of economic equilbria. However, the fact that this particular formulation assigns numerical values to levels of satisfaction is the source of criticism (and even ridicule). However, it is not an essential ingredient of the theory and again this is an idealization.
1.2 Other types of models
These two models are examples of mathematical models; following are example of model which are not mathematical (or at least not numerical).
- Myers-Briggs personality type. Myers-Briggs Type Indicator® is a technique which claims to produce a representation of a person's preferences, using four scales. These scales can be combined in various ways to produce 16 personality types. Types are typically denoted by four letters--for example, INTJ (Introverted intuition with extraverted thinking)--to represent a person's preferences. This model is claimed by CPP (formerly known as Consulting Psychologists Press, Inc.) to produce a good predictor of a person's career and marriage partner preference. It should be pointed out, see [1],that there is considerable disagreement among psychologists whether this assessment technique (and the implied idealized personality model) is of any value.
- Model of political contagion. Some versions of this model are sometimes referred to as the domino theory. In the broadest possible terms, according to this model, political movements that take hold in one country are likely to spread to geographically neighborhing ones. This model is surprisingly popular, although as it stands it is extremely impoverished conceptually saying nothing about the type of political movement, the degree of geographical proximity, the time scale at which these events take place etc.
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