Hypothetical Models in Social Science

Abstract

The chapter addresses the philosophical issues raised by the use of hypothetical modeling in the social sciences. Hypothetical modeling involves the construction and analysis of simple hypothetical systems to represent complex social phenomena for the purpose of understanding those social phenomena.

To highlight its main features hypothetical modeling is compared both to laboratory experimentation and to computer simulation. In analogy with laboratory experiments, hypothetical models can be conceived of as scientific representations that attempt to isolate, theoretically, the working of causal mechanisms or capacities from disturbing factors. However, unlike experiments, hypothetical models need to deal with the epistemic uncertainty due to the inevitable presence of unrealistic assumptions introduced for purposes of analytical tractability. Computer simulations have been claimed to be able to overcome some of the strictures of analytical tractability. Still they differ from hypothetical models in how they derive conclusions and in the kind of understanding they provide.

The inevitable presence of unrealistic assumptions makes the legitimacy of the use of hypothetical modeling to learn about the world a particularly pressing problem in the social sciences. A review of the contemporary philosophical debate shows that there is still little agreement on what social scientific models are and what they are for. This suggests that there might not be a single answer to the question of what is the epistemic value of hypothetical models in the social sciences.

Appendices

Appendix: J.H. von Thünen’s Model of Agricultural Land Use in the Isolated State

Von Thünen’s model of agricultural land use describes how the distance from a market affects the distribution of agricultural productions around a city [19.73]. This model is considered to be one of the first examples of modern economic modeling, and it is still a classic model in geography and urban economics from which an entire tradition of models of land use in urban spaces has originated. Von Thünen’s model has also received some attention in the philosophy of economics, and thanks to its analytical simplicity, it is particularly suitable for illustrating some of the ideas discussed in this chapter [19.23, 19.3, 19.74].

Von Thünen’s localization model is based on a set of assumptions that describes a homogeneous and isolated agricultural space in which a single town is located:

• 1. The area is a plain, i. e., there are no mountains or valleys

• 2. There are no streets or navigable rivers

• 3. The plain is completely cut off from the outside world

• 4. Climate and fertility are uniform across space

• 5. The town is located centrally and has no spatial dimension

• 6. All markets and industrial activities take place in the town

• 7. Production costs are constant across space

• 8. Transportation costs are directly proportional to the distance, the weight and the perishability of the goods

• 9. Selling prices are fixed and the demand is unlimited

• 10. Farmers have complete information and they act to maximize their revenue.

Under these assumptions, a pattern of concentric rings around the town emerges. Dairying and intensive farming (vegetables and fruit) occupy the ring closest to the town, because these products are perishable and incur the highest transportation costs. Timber and firewood are located in the second ring, because wood is heavy and hence difficult and costly to transport. The third ring consists of extensive farming of crops, such as grain for bread, that are more durable than fruit and less heavy than wood. On the outermost ring stock farming and cattle ranching take place, because animals can walk to the city to be sold at the market and thus have low transportation costs.

This result can also be described in analytical terms by determining which production is most profitable at different distances from the town.

The revenue r of each agricultural production consists in its selling price p minus its production and transportation costs. Since the selling price and the unitary production and transportation costs are fixed, the revenue depends only on the distance from the city

$$r^{i}(d)=(p-c)x-tdx\quad i=\{A,B,C\}\;,$$

where x is the quantity of the good, c the production cost per unit, t the transportation cost per unit and d the distance from the market. The apex i indicates the kind of agricultural production: Dairying and intensive farming A, timber and firewood B, and extensive farming C.

The slope of each revenue curve depends on transportation cost and distance −td.

The descending curves in Fig. 19.B4 represent the revenue of each production depending on its distance from the town; e. g., at distance a it becomes more profitable to produce product B.

Fig. 19.B4

The production revenue and the land use in von Thünen’s model (after [19.75, p. 76])

Appendix: T. Schelling’s Agent-Based Model of Segregation in Metropolitan Areas

Thomas Schelling’s work on racial segregation paved the way for the use of simulations in the study of social phenomena. In his seminal work, Schelling studied how macro-phenomena, such as segregation, can emerge as an unintended effect of the combination of many interrelated decisions [19.76]. Racial sorting is a case in point. Segregation has been proven to occur as a side effect of the preference of individuals for having a few neighbors of the same ethnic group, rather than as the consequence of a preference for segregation itself.

Schelling represented the segregation process by means of a checkerboard and dimes and pennies, standing respectively for a certain metropolitan area and for the individuals of two different groups (Fig. 19.C5). The model is based on a set of assumptions that describe an idealized metropolitan area and its inhabitants. Examples of such assumptions are:

• 1. There are only two kinds of agents, Blacks and Whites

• 2. Agents’ decisions only depend on preferences regarding their neighbors

• 3. The city is uniform, i. e., there are no architectural or topological boundaries that constrain individual choices

• 4. Agents move randomly in space

• 5. There are no costs of moving from one point to another.

On the checkerboard it is possible to track the movements of the agents and to observe how the configuration of the neighborhood changes over time.

Fig. 19.C5

Schelling’s checkerboard: Initial and final configuration (after [19.76, p. 155–157])

The resulting dynamics reflect the individual decisions to move to areas whose composition meets the agents’ preferences. Rather than obtaining analytical solutions, Schelling’s model explores the conditions under which segregation emerges by means of local rules. What it shows is that, regardless of the initial position of the agents and the spatial configuration, given a certain range of people’s preferences, clusters of neighbors of the same color eventually emerge.

Even though agent-based models do not need to be implemented on a computer, nowadays they are often used together. The premise is to build a model that captures the relevant variables of the agents’ decisions, such as personal preferences and responses to other agents’ behavior and to the context. Next, a way has to be found to implement the model and the other components that characterize the system – such as the network structure – in a computer code. Call the set of relevant factors that are external to the model its environment. Together, the model and the environment constitute the algorithm that runs on the computer.

Figure 19.C6 shows an extract of the algorithm of the segregation model implemented on NetLogo. Each run of the program corresponds to a step in the simulation, which in turn represents a change in the system. The evolution of the system can be represented graphically by means of software that transforms the numerical analysis into visual representations (Fig. 19.C7).

Fig. 19.C6

Netlogo code of Schelling segregation model (after [19.77])

Fig. 19.C7

Visual representation of Schelling’s segregation model (after [19.77])