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Formal Modeling in Social Science

Carol Mershon and Olga Shvetsova 2019

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A formal model in the social sciences builds explanations when it structures the reasoning underlying a theoretical argument, opens venues for controlled experimentation, and can lead to hypotheses. Yet more importantly, models evaluate theory, build theory, and enhance conjectures. Formal Modeling in Social Science addresses the varied helpful roles of formal models and goes further to take up more fundamental considerations of epistemology and methodology.

The authors integrate the exposition of the epistemology and the methodology of modeling and argue that these two reinforce each other. They illustrate the process of designing an original model suited to the puzzle at hand, using multiple methods in diverse substantive areas of inquiry. The authors also emphasize the crucial, though underappreciated, role of a narrative in the progression from theory to model.

Transparency of assumptions and steps in a model means that any analyst will reach equivalent predictions whenever she replicates the argument. Hence, models enable theoretical replication, essential in the accumulation of knowledge. Formal Modeling in Social Science speaks to scholars in different career stages and disciplines and with varying expertise in modeling.

ISBN(s)

978-0-472-05423-7 (paper)
978-0-472-07423-5 (hardcover)
978-0-472-12586-9 (ebook)

Subject

Citable Link

Figure 2.1 shows the place that formal models have in research design. It identifies linkages among theory, narrative, model, story, and evidence. Figure 2.1 presents how narratives and formal modeling enter into classical epistemology in political and social science.

Figure 2.1. The pace of formal models in research design: Multiple linkages among narrative, model, story, and evidence

From Chapter 2

Figure 2.1. The place of formal models in research design: Multiple linkages among theory, narrative, model, story, and evidence

Figure 2.2. The four quadrants of Figure 2.2 indicate how models enable the analyst to test theory and also build theory.

Figure 2.2. Models fulfilling their roles: Theory-testing and theory-building

From Chapter 2

Figure 2.2. Models fulfilling their roles: Theory-testing and theory-building

Figure 2.3. The four quadrants of Figure 2.3 convey strategies for reconciling theory and model.

Figure 2.3. Iterative reconciliation of model and theory

From Chapter 2

Figure 2.3. Iterative reconciliation of model and theory

Figure 5.0.1. Figure 5.0.1 presents baseline, extant knowledge about the behavior of members of the commons (here, fishers) with no regulation in place.

Figure 5.0.1. Extant knowledge: Members of the commons without regulation

From Chapter 5

Figure 5.0.1. Extant knowledge: Members of the commons without regulation

Figure 5.0.2. Figure 5.0.2 presents baseline, extant knowledge about members of the commons who create regulations. The regulations transform the game, and cooperative behavior becomes individually rational.

Figure 5.0.2. Extant knowledge: Members of the commons opt for regulation

From Chapter 5

Figure 5.0.2. Extant knowledge: Members of the commons opt for regulation

Figure 5.0.3. Figure 5.0.3 presents baseline, extant knowledge about members of the commons who operate under regulations and who are monitored. With fines, members of the commons have the incentive to cooperate and protect the future of the commons.

Figure 5.0.3. Extant knowledge: Members of the commons opt for regulation and establish the level of punishment F=6

From Chapter 5

Figure 5.0.3. Extant knowledge: Members of the commons opt for regulation and establish the level of punishment F = 6

Figure 5.1. In Figure 5.1, the commercial fisher is depicted as the key decision maker, choosing between Conservative and Aggressive technologies.

Figure 5.1. A commercial fisher's choice of technology

From Chapter 5

Figure 5.1. A commercial fisher’s choice of technology

Figure 5.2.1. Figure 5.2.1 portrays the commercial fisher's choice of technology under status quo regulation. It is equivalent to Figure 5.1: no change to regulation has occurred.

Figure 5.2.1. A commercial fisher's choice of technology under status quo regulation

From Chapter 5

Figure 5.2.1. A commercial fisher’s choice of technology under status quo regulation

Figure 5.2.2 portrays the commercial fisher's choice of technology under amended regulation.

Figure 5.2.2. A commercial fisher's choice of technology under amended regulation

From Chapter 5

Figure 5.2.2. A commercial fisher’s choice of technology under amended regulation

Figure 5.3. Figure 5.3 shifts to the regulator as the decision-maker, choosing whether to issue a recommendation to change existing regulation or leave the status quo in place.

Figure 5.3. Balancing conflicting preferences when making a decision

From Chapter 5

Figure 5.3. Balancing conflicting preferences when making a decision

Figure 6.1. Figure 6.1 illustrates a binary agenda that pairs all alternatives against each other as well against the status quo at the final decision-making stage, which requires unanimity.

Figure 6.1. Binary agenda based on Cameron's "packaged" alternatives

From Chapter 6

Figure 6.1. Binary agenda based on Cameron’s “packaged” alternatives

Figure 6.2. For two actors, the countries of the European Union and the Non-Annex I countries, Figure 6.2 displays the Pareto set in the two-dimensional economy-environment space.

Figure 6.2. Items under consideration in the speech, positioned in terms of gains from trade between countries of the EU and NAI countries

From Chapter 6

Figure 6.2. Items under consideration in the speech, positioned in terms of gains from trade between countries of the EU and NAI countries

Figure 6.3. Figure 6.3 illustrates the areas of mutually beneficial agreement (“gains from trade”) between the countries of the European Union and the Non-Annex I countries.

Figure 6.3. "Gains from trade" between the countries of the EU and NAI countries

From Chapter 6

Figure 6.3. “Gains from trade” between the countries of the EU and NAI countries

Figure 6.4. Figure 6.4 illustrates the areas of mutually beneficial agreement (“gains from trade”) between the countries of the United States and the Non-Annex I countries.

Figure 6.4. "Gains from trade" between the US and NAI

From Chapter 6

Figure 6.4. “Gains from trade” between the United States and NAI

Figure 6.5. Figure 6.5 illustrates the areas of mutually beneficial agreement (“gains from trade”) between the countries of the European Union and the United States.

Fgure 6.5. "Gains from trade" between the countries of the EU and the US

From Chapter 6

Figure 6.5. “Gains from trade” between the countries of the EU and the US

Figure 7.1.1. Figure 7.1.1 depicts a game between two players, prisoners, and guards.

Figure 7.1.1. A game between prisoners and guards

From Chapter 7

Figure 7.1.1. A game between prisoners and guards

Figure 7.1.2. Figure 7.1.2 depicts a compound game between prisoners and guards, representing the guards’ choice to institutionalize strong retaliation as an additional stage in the game.

Figure 7.1.2. A compound game between prisoners and guards

From Chapter 7

Figure 7.1.2. A compound game between prisoners and guards

Figure 7.2. Figure 7.2 depicts a game between the deputies and the federal agents.

Figure 7.2. A game between deputies and federal agents

From Chapter 7

Figure 7.2 A game between deputies and federal agents

Figure 7.3. Figure 7.3 depicts a game between the deputies and the judge.

Figure 7.3. A game between the deputies and the judge

From Chapter 7

Figure 7.3. A game between the deputies and the judge

Figure 7.4. Figure 7.4 retraces the path from one story to the three narratives we have extracted from that story, and then to the three models we have designed. More broadly, this figure illustrates the practical application in this chapter of the epistemological path introduced in chapter 2.

Figure 7.4. From one story to three narratives and then to three models

From Chapter 7

Figure 7.4. From one story to three narratives and then to three models