Abstract and Keywords
This article examines the dynamics of conditional choice as a mechanism for explaining social action, with particular emphasis on identifying model frameworks for the analysis of the trajectory and outcome of conditional decision-making processes. It begins with an overview of conditional decision-making, including key words and concepts, followed by a discussion of conditional decision rules and initial states of activity and how they shape the basic trajectory and outcome of a conditional decision-making process. It then considers possible sources of resistance to influence, focusing on the ways unconditional actors pull all other group members towards their position and how individual variation in resistance to influence can stop a process from reaching complete conformity. It also explores patterns of social interaction and how they work in combination with resistance to influence to account for variation in activity among individuals or groups, paying attention to the contingent effect of local networks.
Keywords: conditional choice, social action, conditional decision-making, conditional decision rules, initial states of activity, resistance to influence, unconditional actors, influence, social interaction, local networks
What do buying a pair of jeans (Bearden and Rose 1990), expressing political attitudes or choosing a political candidate (Berelson, Lazarsfeld, and McPhee 1954; Niemi 1974; Zuckerman 2005), prescribing tetracycline (Coleman, Katz, and Menzel 1966), implementing a policy reform (Mintrom 1997; Simmons and Elkins 2006), clapping in a standing ovation (Miller and Page 2004), eating bagels or other foods (Latané 1996), wearing belts (Axelrod 1997), choosing a restaurant (Granovetter and Soong 1988), and liking the latest hit on the radio (Salgarik, Dodds, and Watts 2006) all have in common? The people involved—consumers, voters, doctors, policy makers, or radio listeners—are influenced by the people around them. Their actions, in other words, are conditionally dependent: what one person does depends in part on what others are doing.
Conditional decision-making research spans many disciplines and analytical approaches, yielding a rich but unruly proliferation of specialized literatures that have defied orderly synthesis. Previous reviews are limited to a particular decision model (e.g. diffusion) and are often organized around empirical variables used (p. 420) in research (Valente 1995; Strang and Soule 1998; Rogers 2003; Greenhalgh et al. 2005). This chapter takes a different approach, identifying theoretical explanations of variation in the trajectory and outcome of conditional decision-making processes from a review of the various formal literatures, both mathematical and simulation-based.
When individuals make conditional decisions, only a limited number of formal mechanisms can explain variation in the resulting social activity. Obvious explanations stem from variation in individual decision-making: what individuals do before observing others (initial activity); how individuals respond to the observed actions of those around them (conditional decision rules); and how resistance to influence is introduced into the process. Less intuitive explanations, meanwhile, invoke social networks: the size of a group; the structure of the relevant networks of influence; social cleavages; and the location of particularly influential individuals within a social network.
This chapter introduces and details each of these formal mechanisms. Section 18.1 provides a brief introduction to conditional decision-making, defining key words and concepts used throughout the chapter. Section 18.2 introduces conditional decision rules and initial states of activity, describing how together they shape the basic trajectory and outcome of a conditional decision-making process. Section 18.3 reviews possible sources of resistance to influence, describing how unconditional actors pull all other group members towards their position, and how individual variation in resistance to influence can stop a process from reaching complete conformity. Section 18.4 addresses patterns of social interaction, which work in combination with resistance to influence to explain variation in activity among individuals or groups.
18.1 What is Conditional Decision-Making?
Conditional decision-making refers to both the set of models that assume conditional decisions, and the process generated by that assumption. Just as game theory is not limited to prisoners’ dilemmas or coordination games, conditional decision-making is not limited to diffusion or threshold models. Numerous specific models described in the literature (see Table 18.1 at the end of this chapter for examples) meet the sole requirement for classification as a conditional decision model: actors make decisions using rules that are conditional on the actions of others.1
Conditional decision-making also refers to a dynamic decision-making process or sequence of states of activity. When individuals base their actions or opinions (p. 421) on what other people do or say, any small change (initial activity) sets off a chain reaction of conditional decision-making. If ten people decide to buy a new iPod, some of their friends will buy one as well, and then the friends’ friends will join in, and so on. This dynamic trajectory of changes in activity will eventually settle down to a stable outcome state. Stable states may be characterized by convergence to complete or partial conformity, where everyone does the same thing or holds the same opinion, or multipeaked outcomes, in which there is a greater diversity of social action.
Empirical research generally seeks to explain variation in outcomes or trajectories of change in activity. Explaining outcomes might involve understanding why some innovations that inspire initial activity spread successfully (e.g. iPods), while others fizzle out (e.g. Beta VCRs). We wonder why in some situations all actors eventually adopt the same approach (e.g. use of the Australian ballot in American elections (Walker 1969)) but in others they do not (e.g. not everyone wears the same brand of jeans, or votes for the same political candidates). Alternatively, why is the same outcome reached in processes that follow very different trajectories? For example, the tipping point leading to widespread adoption may come only after a long and steady buildup of activity (e.g. public support for recycling), or it may occur virtually overnight (e.g. cultural fads).
To identify possible explanations, I develop a systematic framework to organize and synthesize results from a range of conditional decision models. Game theory again provides a helpful parallel, isolating four key aspects of a strategic situation: players, strategies, payoffs or utility functions, and information. Similar key components fully describe a conditional decision situation: actions, decision rules, information, and networks. Brief descriptions of the key components and related parameters of conditional decision models appear in the Glossary, while Table 18.1 characterizes well-known models using the same framework.
(a) Important terms
The likely trajectory and outcome of a conditional decision-making process, ignoring the impact of model factors related to resistance to influence and social networks. Depends on three factors: type of action, conditional decision rules, and initial activity (Sect. 18.2).
Conditional decision model factors or parameters
Formal elements of a conditional decision-making model that can take on different values. These parameters are classified (p. 422) as aspects of: (1) action, (2) decision rules, (3) information about others, and (4) networks of social interaction (see App. (b)).
Critical point or mass
Proportion of the population that must adopt an action before a particular conditional decision-making process tips from one likely outcome to another.
Actual state of activity prior to observation of the choices of other people. May be described as initial-opinion distribution, or situation where only initial actors are active. Examples of initial actors: first movers, unconditional actors, innovators, index case.
Stable state of activity, in which no one changes what they are doing; equilibrium.
An outcome state in which all actors do the same thing.
An outcome state in which most actors do the same thing (binary action) or the distribution of attitudes is unimodal (continuous action).
An outcome state in which the distribution of attitudes is multimodal (continuous action) or a substantial portion of actors are engaged on both sides of a binary action or in more than one categorical action.
Resistance to influence
Umbrella term for model factors which decrease conditional responsiveness. Includes unconditional actors, partial resistance, fixed decisions, deterministic threshold rules, and memory (Sect. 18.3).
State of activity
Complete description of what all actors are doing at a particular moment in time.
Dynamic set of all states of activity between initial state and outcome state.
(b) Conditional decision model parameters
The decision, behavior, or attitude statement to be modeled or explained. A better term to use is practice (Strang and Soule 1998; Wedeen 2002), but the term ‘action’ will be used in keeping with the rest of the volume. Examples: joining in a riot, adopting a new technology, contributing money to a campaign, expressing support for health-care spending.
Type of action
The metric in which the action is expressed. Includes binary, continuous, ordinal-categorical, nominal-categorical (Sect. 18.2.1).
An actor might have repeated opportunities to change her mind. If so, the length of time after which an action can be changed or revised is specified. If there is no chance to change her mind, the action is fixed. Fixed actions are found in threshold, diffusion, and herding models (Sect. 18.3.4).
Decision rules tell the actor to engage in an action with some probability.
Initial activity rules
Rules which assign actors to their initial state of activity. Rules may assign activity randomly, or according to some characteristic of the actor (e.g. conditional or unconditional decision rules, attributes, social location) (Sect. 18.2.3).
Conditional decision rule
A rule that assigns a probability of action as a function of what other people are doing. Includes threshold or stochastic focal point rules, linear mean (p. 423) matching rules, and less frequently uses rules incorporating unimodal or decreasing functions (Sect. 18.2.2).
Unconditional decision rule
A rule that assigns a constant probability of engaging in an activity. Actors rely either partially or completely on unconditional rules (Sects. 18.3.1 and 18.3.2).
Specifies which decision rules are used and by what proportion of the population, when all actors do not use the same rule (Sect. 18.2.2).
A decision rule that allows for random fluctuation or errors, as opposed to deterministic rules as often found in threshold models (Sect. 18.3.3).
Parameters specifying what an actor can observe about other people.
Actors may have particular attributes, which might or might not be observable by other actors (Sect. 18.4.3).
What is observed
What information about an individual is available to other actors. Includes attributes, actions, decision rules (Sect. 18.3.4).
In parallel or synchronous updating, actors revise their decisions simultaneously. In asynchronous updating, one or several actors at a time make a decision at each time point (and others can observe these changes immediately).
Do actors respond only to behavior observed during the present time step? If decision rules are conditional on observed behavior extending back over several time steps, a memory rule is required for updating across multiple observations (Sect. 18.3.4).
Umbrella term for factors which change the patterns of social interaction among actors.
The topology of potential interactions (e.g. all-see-all, grid/torus, specific-network-structure). Actors who choose interaction partners are limited by this space (Sect. 18.4.2).
Active choice of interactions
Do actors choose their friends? If yes, specify rules for selection (Sect. 18.4.3).
Can actors move in space? If yes, specify rules for movement (Sect. 18.4.3).
Particular actors (e.g. early movers, strong leaders) may be placed into particular social locations (e.g. near other early movers, on the end of a full or partial cleavage, in well-connected-network positions) (Sect. 18.4.4).
18.2 The Basic Dynamic
When conditional decision-making characterizes an action or opinion expression, everyone in the group will (theoretically) end up agreeing on an opinion or doing the same thing. Of course, political opinions, consumer choices, and other (p. 424) social practices are often characterized by the coexistence of social influence with lasting variation in opinion or behavior. Resistance to influence and breaks in network connectivity can keep a system of conditional decision-makers from reaching complete agreement (Abelson 1964). While these obstacles to agreement are considered later in the chapter, this section looks at the basic dynamic of conditional decision models absent these complications. Three factors shape the basic trajectory and likely outcome states produced by a conditional decision-making process: the type of action, the distribution of decision rules, and the initial state of activity.
18.2.1 Action types: binary, categorical, and continuous
As with any empirical variable, actions may be classified as binary, categorical, or continuous; examples of each appear in Table 18.1. Given the inherently binary nature of action (you either do something or you don’t), many social situations can be represented as offering a binary choice (or string of such choices) of whether or not to engage in some activity—such as protesting in the street, putting a campaign sign in the front yard, or voting in an election. A continuous action goes beyond a simple yes-or-no decision; examples include donations of money or time to volunteer organizations.
Categorical choice sets, either ordinal or nominal, are less common, but do have clear empirical analogues. Examples of ordinal actions include a voter choosing between multiple political parties aligned in a left–right issue space (Downs 1957) or a consumer choosing between products assessed along multiple dimensions (Bettman, Luce, and Payne 1998). Nominal categories are also intuitively appealing as a representation of cultural practices or social identities (Axelrod 1997; Lustick, Miodownik, and Eidelson 2004).
The key mathematical distinction between action types is between actions that produce linear or nonlinear dynamics.2 A system with nonlinear elements such as discrete actions (binary, nominal, or categorical) or nonlinear decision rules (fixed or stochastic focal point) does not change outcome states gradually, but may suddenly shift from one likely outcome to another (or one stable state to another) at a particular critical point, also known as the tipping point or critical mass.3 The sudden shifts, or phase transitions, are difficult to predict in real-life examples of nonlinear decision-making, but they are mathematically well understood (i.e. we know when they will occur in mathematical models and what sorts of changes in model parameters produce them). In any specific nonlinear decision model, the expected impact of changes in resistance to influence and social networks depends in part on the location of critical points.
Despite this significant difference between standard continuous-opinion models and other forms of conditional decision-making, the formal mechanisms driving (p. 425) these processes are similar. Both types of decision processes converge to a single point in the absence of resistance to influence or network cleavages; initial activity and the distribution of decision rules determine the likely trajectory and outcome; and only assumptions that introduce resistance to influence or changes in social interaction alter this basic dynamic. Differences are noted throughout the chapter: the initial trajectory of binary actions is more complex, a single unconditional actor has less influence over the outcome of binary models, and different assumptions produce partial and/or multipeaked convergence.
18.2.2 Distribution of conditional decision rules
Conditional decision rules are both the defining element of conditional choice models and the key factor affecting the likely outcome and trajectory of the decision-making process. This section introduces the three most common functional forms used to represent conditional decision rules and discusses empirical and motivational justifications for each. Next, I consider how decision-rule distributions affect the likely trajectory and outcomes of conditional action, and discuss how decision rules are used in empirical research.
A conditional decision rule expresses an actor’s decision as a function of what others around her are doing (e.g. definitely vote for Labour if the majority of her friends are voting Labour). Most research incorporates conditional decision-making using one of three rules: (1) fixed or threshold focal point matching, (2) stochastic focal point matching (often median matching), or (3) linear matching (often mean matching).4 Figure 18.1 provides an example of each of these rules, where the graphically represented rule gives the continuous opinion point or probability that a focal actor will engage in some action (y-axis) as a function of the average decision of her friends (x-axis).
Both fixed threshold (Fig. 18.1(a)) and stochastic (Fig. 18.1(b)) focal point matching rules are often described as a preference for conformity, but actors using focal point rules might be engaged in rational imitation (Hedström 1998) or contributing to a public good with an accelerating production function (Oliver 1993), rather than bandwagoning or bowing to social pressure. Members of a crowd who will only join in a riot once others have started rioting, people who change their minds if three of their neighbors agree, and decision makers who try to imitate the majority can be modeled using threshold focal point rules (see Table 18.1). Similar in spirit to threshold rules, stochastic or continuous focal point matching rules assume that even actors with a focal point of participation in mind (say 20 percent of their friends, or half of the crowd) may not change actions at that exact focal point every time. Subjects in public-goods experiments use focal point matching rules when making decisions about continuous actions, such as deciding how much money to contribute (Fischbacher, Gächter, and Fehr 2001). (p. 426)
The linear mean matching rule (see Fig. 18.1(c)) maps an individual’s decision to the average of her friends’ opinions, and is often used to describe changes in continuous opinions (see Table 18.1). Gould (1993) proposed that neighbors facing a social dilemma might respond fairly to the contributions of others using egocentric linear matching rule (with slope less than 1). Group members facing public goods with decelerating production functions, and who nonetheless wish to claim full credit for doing their fair share, may also rely on linear rules. Evidence confirms that up to half of all subjects rely on the ‘fair share’ mean matching rule in public-goods experiments (Ledyard 1995). Linear matching may also describe actors in a status competition who desire to ‘keep up with the Joneses’.5
Many of the models featured in Table 18.1 include homogeneous actors using the same decision rule; however, empirical evidence favors heterogeneous rule distributions. Individuals facing the same decision situations use different conditional rules (Ledyard 1995; Offerman, Sonnemans, and Schram 1996): some people might be wholly or largely immune to influence, while others quickly adopt new habits from friends. Different situations might also yield different rule distributions even among similar populations (Fehr and Gächter 2000; Casari and Plott 2003). A distribution of rules allows for multiple types of decision makers (e.g. innovators, crowd followers, elite adopters), and numerous potential motives (e.g. guilt, fairness, conformity) in the same situation. Cutting-edge formal work addresses how heterogeneity of conditional responses affects the likely trajectory and outcome of conditional decision processes (Delre, Jager, and Janssen 2007; Young 2007).
While all conditional decision-making processes follow a basic trajectory toward conformity, the shape of this trajectory depends on the conditional rules in use. In models of continuous opinions the decision rule determines whether a group is more likely to move towards an average or more extreme point on the continuum. Individuals responding linearly to the average opinion of those around them converge to the mean of the initial distribution of opinions (Abelson 1964; Hegselmann and Krause 2002), while focal point rules move opinion towards the (p. 427) extremes. Situationally specific use of linear versus nonlinear decision rules by actors expressing (continuous) opinions may be a potent explanation of varying outcomes of group decision-making processes. Juries and other deliberative groups often polarize when participants hold similar positions on one side of an issue, but moderate when initial opinions are evenly distributed (Isenberg 1986; Sunstein 2002). This pattern might reflect differential usage of decision rules in the two situations: nonlinear rules within a group with a shared identity, and linear rules when groups cross identity boundaries. The use of nonlinear rules may capture the effects of competition for status or power within a social group.
Meanwhile, binary choices produce one of three possible types of trajectories (Dodds and Watts 2004). In ‘critical mass’ models—where only a few people are spurred into action by the initial adopters of a new idea—the adoption curve is initially flat, and the behavior will fizzle out unless there is a sufficient critical mass of early adopters. In ‘vanishing critical mass’ models where people respond quickly to the actions of others, the curve shoots up faster, as a smaller critical mass is required for widespread diffusion. ‘Epidemic’ models are particularly responsive in the early stages (e.g. some or all people respond exponentially to exposure), thus resulting in an assured epidemic within the population even with low levels of initial activity. In general, widespread diffusion is more likely when people facing binary decisions rely on unconditional adoption, linear matching (at the mean or above) or low focal point rules. A larger proportion of high focal point or self-regarding linear rules make diffusion less likely, as these rules reduce early responsiveness.
Conditional rules are therefore a vital element of any explanation involving conditional decision-making. Research may start with an empirical assessment of decision rules in a particular situation. These assessments are used in conjunction with either simulations of conditional decision-making in the particular situation or the rules of thumb outlined in the preceding paragraphs to gain substantial insight into the dynamics of influence in that situation. Section 18.4 contains several examples of theory-testing using dynamics predicted from observed conditional responsiveness.
When conditional responses cannot be directly observed, creative approaches can incorporate the impact of decision rules on the likely trajectory and outcome of conditional decision processes. For example, Young (2007) compares the curve produced by two different individual-level models of conditional decision-making (social learning and simple imitation) to data on when farmers adopt a new hybrid corn. He finds that farmers are directly influenced by the decisions of other farmers, regardless of the payoffs of those decisions. Similarly, Axtell and Epstein (1999) compare real data on the age of retirement for people affected by a change in retirement law to the predicted retirement decisions made on the basis of rational choice and conditional decision-making. These data support the claim that most (p. 428) of the gradual shift to earlier retirement age was produced by social imitation, not rationality. In both cases the authors generate precise estimates of the decision-making dynamic and compare these estimates to observed behavior to assess theories of individual decision-making.
18.2.3 Initial state of activity affects the basic outcome
While the distribution of decision rules sets the basic trajectory of opinion change in a given situation, the initial state of activity determines the likely outcome of the conditional decision-making process. In a simple binary choice or diffusion model, initial activity that meets or exceeds the critical-mass level (as dictated by the degree of conditional responsiveness of decision-making) will ensure widespread diffusion, while lower levels of initial activity will eventually fizzle out. Initial activity can also be used to predict the outcome of continuous-opinion processes. For example, as noted above, when jury members update their opinions by averaging across the opinions of other jurors, all juror opinions will converge to the average of the group’s initial statements about the appropriate size of the award.
In applied research, the initial state of activity can either be estimated on the basis of observed data or assumed for the purposes of theory-testing. In some cases initial activity is observed, for example the first American state or states adopting a new policy, or the first farmers adopting hybrid corn. In other cases researchers might model variation in initial activity to explore whether it can explain variation in the trajectory or outcome of a given conditional decision process. For example, Rolfe (2005a) examines whether variation in voter turnout in different populations might stem from different levels of initial, unconditional activity.
What empirical factors influence the level of initial activity? Initial activity may vary with properties of the action itself; some products or ideas may simply be more appealing than others. Buying an iPod is fun; volunteering to clean up litter is not. Thus, we expect more initial or early adopters for the iPod. It is tempting to extend this analogy and assume that popular products are always intrinsically better than their competitors, and thus initially chosen by more people. While this may well be true for the iPod, the popularity of an activity is not a simple function of its intrinsic qualities.
Initial adoption rates may also stem from characteristics of the people making choices, rather than the choice itself. As a possible example, in the USA those under the age of forty have led the way in pursuing ethical consumer goods and a ‘green lifestyle,’ while baby boomers have lagged behind. The younger population may contain more people willing to adopt new consumption patterns and lifestyles than the older demographic group with well-established habits and less time or motivation to seek out new consumption options. Thus, the same action might have a higher baseline probability of initial adoption in one population than another, generating greater diffusion in the younger population, even if members of both (p. 429) groups respond to initial activity at similar rates. Finally, if the initial activity level in a group is assumed to be random, some groups will randomly end up with more initial activity than others. Thus, different outcomes across different groups may be due to chance. The luck of the draw in initial states is linked to explanations based on group-size effects, as discussed below.
18.3 Resistance to Influence
In this section I review several ways of incorporating resistance to influence into mathematical models of conditional decision-making, highlighting situations in which these approaches are (or are not) empirically plausible. First, unconditional actors resist influence entirely, and can alter the likely outcome of a conditional decision-making process. Second, individuals who refuse to completely abandon their own initial opinion may slow down or completely halt the process of convergence, although partial resistance to influence is not a complete explanation of polarized opinions. Third, fixed decision rules produce multipeaked outcomes that are not robust to small changes in the model. Fourth, fixed actions capture resistance to influence of a different form, and thus threshold models are a reasonable approximation of decision-making in some situations.
18.3.1 Unconditional actors affect the direction of convergence
Even in conditional decision-making processes some people may make decisions independently of others’ actions. Unconditional action is characteristic of innovators of a new idea or product (Rogers 2003), first movers in collective action (Elster 1989), altruistic cooperators in social dilemmas (Ledyard 1995), and committed ideologues in political debates. Unconditional action may be motivated by personal preferences, but these preferences need not be innovative or prosocial; strategic actors following an equilibrium strategy may also be unconditional actors. As detailed below, individual differences in learning or information-processing might also produce differences in unconditional action. For example, unconditional actors might be slow to update opinions, or struggle to interpret social signals, or have strong prior reasons for believing they are correct, either habitually or in a particular situation.
Unconditional actors can alter the expected outcome of a conditional decision-making process in several ways. In conditional decision-making processes involving binary actions, unconditional actors may provide the critical mass required to ensure diffusion and thereby determine the outcome of the process. Unconditional (p. 430) opposition to a new idea or behavior, however, will increase the size of the necessary critical mass and thus reduce the likelihood of widespread adoption. In continuous-opinion dynamics, one person who refuses to change her mind drags everyone else in the population towards her position, as long as those other people are even partially open to influence (Friedkin and Johnsen 1997). Multiple unconditional actors produce multipeaked outcome states (Boccara 2000; Flache and Torenvlied 2001). Psychological studies of influence are consistent with this result. Both consistent minorities (Bond and Smith 1996) and self-confident individuals (Zarnoth and Sniezek 1997) can influence the positions of other subjects, even when the influentials hold an incorrect view.
18.3.2 Partial resistance to influence
In many cases individual resistance to influence is distributed in smaller doses throughout the population instead of being concentrated in a few unconditional actors. Partial resistance may be captured by an unconditional element in the decision rule, or by a gradual increase in weight put on one’s own former opinion. Partial resistance to influence produces partial convergence to the expected outcome in continuous choice models, but usually only slows down convergence in binary choice models. Individual differences in experiences and beliefs (Friedkin 1999; Hegselmann and Krause 2002) or preferences and payoffs (Bikhchandani, Hirshleifer, and Welch 1992) may result in independent, individual predispositions to particular attitudes or choices. In such cases conditional decision-making rules incorporate a weighted, unconditional element (see Table 18.1). This modeling approach can help recover the hidden dynamics of conditional decision-making that lie beneath stable patterns of observed opinions (Friedkin 1999, 2001). It is less satisfying as an explanation of cultural emergence, as it assumes the pre-existence of the diverse opinions it purports to explain.
Individuals may vary in the strength with which they hold onto their prior opinions. Some models allow opinions to ‘harden’, as actors who are initially open to influence place progressively larger weights on their own current opinion (Chatterjee and Seneta 1977).6 Latané and Nowak (1997) use a related technique to capture variation in personal conviction in a binary choice model, allowing actors to put a substantial weight on their own prior (but not necessarily initial) opinion. Either modeling approach could be justified on the basis of Bayesian learning, the tendency of opinions to become more fixed with age (Visser and Krosnick 1998), or differences in lay theories of personality (Dweck and Leggett 1988).7
Crucially, if a substantial portion of the population facing a continuous choice is even partially resistant to influence, the group will never converge completely (Friedkin 1999; Hegselmann and Krause 2002). Incomplete convergence in combination with linear decision rules produces opinions centered on a single opinion or (p. 431) action, but with some distribution around the mean opinion (partial convergence). In contrast, partial resistance to influence does not prevent nearly complete convergence to uniform positions in a binary choice model (Lewenstein, Nowak, and Latané 1992; Dodds and Watts 2004), although it slows down the process substantially and may produce a series of semi-stable steps along the way. Just as a single unconditional actor could change the direction of convergence in a continuous (but not binary) opinion model, partial resistance to influence changes the final outcome of continuous (but not binary) choice processes.
18.3.3 Fixed decision rules
Some simulated conditional decision models produce diverse outcome states (e.g. Latané and Nowak 1997; Huckfeldt, Johnson, and Sprague 2004; Lustick, Miodownik, and Eidelson 2004), although analytical results from the same models predict complete conformity (Lewenstein, Nowak, and Latané 1992; Klemm et al. 2003; Dodds and Watts 2004). Why do the simulation results differ from analytical expectations? It is tempting to attribute the difference to the impact of local community, but this is not the complete answer (Lewenstein, Nowak, and Latané 1992). Simulated binary (and probably categorical) choice models that combine threshold or fixed focal point rules and local network structure produce multipeaked outcomes, but such outcomes are generally not robust.8
When minority clusters result from a combination of fixed thresholds and local interactions, they will disappear if actors make stochastic decisions or interact in irregular formations or with randomly selected long-distance neighbors (San Miguel et al. 2005). Latanés social impact theory (see Table 18.1), however, allows for both of these possibilities and continues to produce minority clusters. In this case the social impact theory is the exception that points us to the more important principal driving the maintenance of local minority clusters: boundary protection. Local clusters are sustained by individuals who are strongly resistant to influence, and thus form a stable boundary between majority and minority groups (Latané 1996), often surrounded by other strong-minded or easily influenced actors who reinforce their commitment. These individuals effectively cut off communication between the majority and minority groups in the network, and function as a break in network connectivity (see Sect. 18.4).
Although boundary protection is unlikely to work in such a literal fashion, other forms of boundary policing do protect the distinctive character of social groups. Punishment of norm violation is typically seen as prosocial or altruistic (Boyd et al. 2003), but both political leaders and ordinary citizens punish group members who take moderate political positions.9 Parties use partisan whips to control legislators while in session, and may even use deliberate violence to bloody the hands of moderate party leaders (LeBas 2006). African American students actively (p. 432) resist and even censure black conservatives (Harris-Lacewell 2004), and partisan citizens censure candidates who move to the middle on core party issues (Morton, Postmes, and Jetten 2007). Pressure to adhere to the norms of a particular social identity can undermine the moderating influence of generalized social interaction. As mentioned earlier, people may even use different decision rules when responding to others with a shared social identity.
While it is easy to account for the difference between simulations and formal analysis of binary choice models, a considerable disjunction remains between the actions of real people facing binary decisions and those of simulated actors following conditional decision rules. If people make conditional decisions but remain partially resistant to influence, we would expect continuous opinions to partially converge to a single point while binary opinions largely converge to a uniform position. While it is true that responses to continuous measures such as political ideology appear partially convergent, vote choice and responses to binary questions that probe party identification are multipeaked and not uniform. Future research should distinguish conditional decision-making in controlled responses to questions about personal attitudes from conditional decision-making in the affective, implicit responses that govern binary evaluations and actions.
18.3.4 Thresholds: fixed actions and memory
The previous section showed that fixed threshold rules introduce a nonrobust form of resistance to influence, and may produce misleading results when used in simulations. Nonetheless, stochastic conditional decision-making produces threshold dynamics when: (1) actions are fixed for the course of the decision-making process, or (2) memory of past observations shapes actors’ choices. A multipeaked or partial-conformity outcome is likely when initial activity is at or below the critical point of the model.
Actions are clearly fixed when: a decision is difficult to revise (e.g. legislative adoption of an innovative policy reform); an individual expresses verbal or written commitment to an action (McAdam 1986; Ostrom, Walker, and Gardner 1992); or subsequent decisions are not interesting to the researcher (e.g. whether doctors stopped prescribing tetracycline). Repeated decisions may still exhibit threshold dynamics in any given ‘round’ of decision-making if a person is unable or unlikely to change her mind within a given period of time. Opinion statements made during the course of a single discussion might follow this type of path-dependent process (Wood 2000), as group members defend statements they made early in the discussion. Group members reflecting back on the discussion several days later, however, may undergo lasting opinion change better represented by simultaneous updating of mutable opinions.
Threshold models may also capture stochastic decision-making when people respond conditionally to expectations of others based on memories of previous (p. 433) interactions.10 Most people decide whether or not to be helpful and fair multiple times a day. Should I wash the dishes or leave them for someone else; get paper for the copier or leave it for a coworker? While each decision is binary, memories of repeated decisions fall along a continuous scale. Thus, when people base conditional decisions on memories of past activity, two outcomes are likely. First, greater levels of cooperation are likely than might be expected on the basis of a single interaction (Chwe 1999). Second, behavioral diversity is more likely in groups where a large portion of the population relies on linear conditional decision rules.
Not all repeated decisions are characterized by threshold dynamics. Repeated decisions that can be revised on the basis of instant feedback may produce conformity, even when memory-based responses produce behavioral diversity. For example, subjects faced with a public-goods dilemma contribute around 50–60 percent of the maximum possible in a one-shot game or in the first round of a repeated game (Ledyard 1995). When the public-goods game is repeated several times with the same group of subjects, however, contributions partially converge towards zero. This behavior can be reproduced almost exactly by simulated actors who draw on the same distribution of conditional contribution rules used by real-life subjects (Ledyard 1995; Fischbacher, Gächter, and Fehr 2001). Threshold models produce an average contribution rate of 50–60 percent, while revisable, stochastic decision processes almost completely converge to the noncooperative equilibrium (Rolfe 2005a).
18.4 The Contingent Effect of Local Networks
Social influence requires social interaction. Not surprisingly, then, the structure of social interaction greatly affects social dynamics. Changes in patterns of social interaction can speed up or slow down the conditional decision-making process, but rarely alter the baseline outcome unless the connectivity of a network is fundamentally altered (Abelson 1964). Below, I consider the four factors, either alone or in conjunction with resistance to influence, most likely to impact conditional decision-making processes: group size, local-network structure, social cleavages and friendship selection, and social location of influential actors.
18.4.1 Group size
In some situations individuals in groups have information about large numbers of others, such as crowds at a protest or fans at a soccer game. In these situations larger (p. 434) groups will conform more closely to the expected trajectory and outcome of the basic dynamic than smaller groups. For example, when the baseline dynamic of a diffusion model supports widespread adoption, larger groups will be more likely to follow this trajectory. When the baseline dynamic works against widespread diffusion, however, innovations may be sustained in smaller groups purely through good luck. Any particular group is a sample from a population distribution, and larger samples are more likely to be representative than small ones.
A brief example clarifies the logic driving the group-size effect. Granovetter’s original threshold model of joining a riot (1978) assumes a uniform distribution of threshold-decision rules. The basic dynamic of this process is complete diffusion as long as there is some initial activity. Although Granovetter showed that rioting was still unlikely in most finite groups of a hundred people, larger groups are much more likely to riot given the same distribution of thresholds. For example, widespread rioting occurs in only 1 percent of simulated groups with a hundred people, while complete participation is the outcome in 10 percent of simulated groups of a thousand (Rolfe 2005b). When riot participation is averaged across all the simulated outcomes, only 12 percent of actors in groups of a hundred ultimately join in, while 34 percent of those in groups of a thousand participate. Larger crowds are thought to inspire more contagious phenomena because of psychological tendencies or emotional activation that is distinctly present in large crowds versus smaller groups or one-on-one interactions (LeBon  1995). However, in this example crowds of a hundred riot less often than crowds of a thousand not because individual behavior or psychology varies between the two groups, but simply because of the statistical properties of samples.
18.4.2 Local-network structure
The basic dynamic of conditional decision-making assumes that all decision makers are influenced by everyone else, as in ‘all see all’ networks (Granovetter 1978). People often respond most to the actions of those close to them, whether closeness is defined in terms of cohesiveness, physical location, similarity, or frequency of contact (Festinger, Schachter, and Back 1950; Festinger 1954; Homans 1958). A decision maker might respond to close relations because she has more information about their actions or opinion; because sanctioning and rewarding occurs more often in close relationships; or perhaps because of some other quality of face-to-face contact.11
The precise impact of local networks depends on both the network itself and the basic dynamic of the decision-making process. In general, local networks that are sufficiently large and that contain many random or long-distance ties (e.g. random, small-world, or large and loosely knit biased random networks) increase the likelihood that the model will conform to the basic dynamic, while small or (p. 435) highly structured personal networks (grids, scale-free networks, or small and dense biased random networks) work against the basic dynamic. Random networks often have little impact on expected trajectory aside from speeding up convergence to the expected outcome in some cases (San Miguel et al. 2005). Long-range ties typical of small-world networks counteract the dampening effects of dense local communities, and speed back up the convergence process (Guzmán-Vargas and Hernandez-Perez 2006). Scale-free networks, in which some actors have thousands of ties while most actors have only a handful, can slow down convergence (San Miguel et al. 2005). Networks with dense local communities, such as spatial grids or strongly biased random networks (Skvoretz 1985; Jin, Girvan, and Newman 2001), generally decrease the speed and extent of convergence. The impact of local networks may be nonlinear when initial activity is near the critical point of the model. Small personal networks slow down convergence in many circumstances (Klemm et al. 2003), but sometimes incubate nascent activity that might otherwise die out.
Local networks figure prominently in empirical explanation of variation in both the trajectory and outcome of conditional decision-making processes. In Coleman, Katz, and Menzel’s classic diffusion study (1966) the authors argue that doctors adopted tetracycline as a conditional response to the decisions of those close to them in medical-advice networks. Burt (1987) challenged these findings, arguing that doctors responded conditionally to other doctors occupying structurally equivalent network positions. Hedström (1994) shows that unionization in Sweden diffused through networks of geographic proximity, and that conditional decision-making did not reflect countrywide unionization activity (all-see-all networks). Andrews and Biggs (2006) argue that geographic networks of media coverage were more essential than networks of personal communication and social interaction in bringing the novel technique of lunch-counter sit-ins to the attention of potential protestors (primarily black male college students) in the southeastern United States during the civil-rights movement. Gould (1991) and Hedström, Sandell, and Stern (2000) provide evidence that long-range ties, whether formal or informal, can reinforce the spread of political activity through and between local communities. Rolfe (2005a) argues that larger social networks, not increased propensity to vote conditionally or unconditionally, account for the higher rate of voter turnout among the college educated. Bearman, Moody, and Stovel (2004) find that negative conditional preferences in the selection of sexual partners affect sexual-network structure, and in turn impact the likelihood that sexually transmitted diseases will spread.
18.4.3 Social cleavages and friendship selection
When there is no path through personal relationships that links each individual in the network to all other members, the network is not fully connected, and (p. 436) conditional decision-making will produce multipeaked outcomes. Each subgroup may converge to a single point, but rarely converge to the same point (Abelson 1964; Friedkin and Johnsen 1990). However, even one tie between the two subgroups ensures a shared point of convergence. It remains an open question which networks of personal relationships exhibit the six degrees of separation thought to characterize the small world of acquaintanceship (Sola Pool and Kochen 1978), but complete social cleavages are unlikely to explain much variation in contemporary social activity.12
In contrast, incomplete social cleavages in combination with resistance to influence may play a major role in explaining social phenomena. Incomplete social cleavages reduce the chances of observing unimodal distributions of activity in the outcome state when actors are partially resistant to influence. Friedkin (2001) describes a small group of wire connectors who are working in the same wiring room. The workers socialize in two distinct cliques with little contact between them. Members of both groups partially converge on a shared norm of work rate within the group, but one group converges on a substantially higher rate than the other.
Conditional decision-making models often produce complete social cleavages when actors select interaction partners with similar traits or opinions. While homophily may characterize many friendships (McPherson, Smith-Lovin, and Cook 2001), self-selection of friends theoretically produces complete social cleavages. The basic dynamic is familiar from Schelling’s work (1973), which shows that even weak preferences for homophily lead to completely segregated communities.13 Friendship selection is an integral feature of many models of emergent culture (see Table 18.1), but diversity is not robust when based on a complete social cleavage (Klemm et al. 2003; Flache and Macy 2006).
Active selection of potential sources of influence may still break up the flow of information without a complete social cleavage, and thus contribute to variation in observed opinions. Baldassari and Bearman (2007) allow actors to select discussion topics as well as friends, and diversity is preserved when friends avoid contentious discussion topics. Bounded-confidence models (Hegselmann and Krause 2002) posit that actors are only influenced by people whose (continuous) opinions are not dramatically different from their own. Opinions are multipeaked when network connectivity is broken via the bounded-confidence mechanism. Either approach fits with the increase in strongly partisan opinions among those with enough political knowledge to screen incoming information that is inconsistent with their political beliefs (Zaller 1992).
18.4.4 Social location of influentials
The ‘two-step flow’ theory of opinion formation (Lazarsfeld, Berelson, and Gaudet 1944) popularized the concept of influentials: individuals who have a (p. 437) disproportionate impact on those around them. While other scholars have identified influentials by the number of people they might be able to influence (e.g. Watts and Dodds 2007) or their structural location (Burt 1999), in this section I look at people who can change the outcome of social-influence processes. Earlier we saw that influentials arise endogenously when people who resist influence (unconditional decision makers) pull everyone else towards their position.14 Influentials may also alter the dynamic of conditional decision-making through either (1) their location relative to both other influentials and decision makers who are easily influenced (clustering), or (2) their location relative to social cleavages.
When initial activity is close to or below the critical mass needed for diffusion, clustering of influentials (unconditional actors) and early adopters (e.g. those using linear decision rules) can provide a local critical mass large enough to generate widespread diffusion (Chwe 1999;Watts and Dodds 2007). Clustering of influentials has successfully encouraged reductions in tobacco use among teens (Valente et al. 2003) and the growth of new businesses (Stoneman and Diederen 1994). In situations where initial activity falls short of the critical point, nascent innovations cannot build substantial support if the influence of first movers is diluted. Therefore, small groups, kept effectively smaller by inward-turning ties, best support new ideas or behaviors under these circumstances. Successful diffusion here requires either planning or luck in sampling, clumping together first movers or early adopters who reinforce each others’ behavior. Self-sustaining clusters can be created deliberately by handpicking individuals who are already committed to an action and isolating them in small, close-knit groups—a strategy employed by armed forces and terrorist organizations.
The location of influentials relative to social cleavages can also affect the course of decision-making in a group. In a continuous-opinion model with unconditional actors, Friedkin and Johnsen (1997) show that two friends who influence one another but lie along the cleavages of two cliques will develop divergent opinions. This is precisely the pattern of political disagreement found along partial cleavages within personal networks (Huckfeldt, Johnson, and Sprague 2004). As mentioned earlier, uncompromising influentials who police group boundaries may preserve cultural diversity by insulating minority groups from outside forces.
Human decision makers are inherently social: what most people do, say, or believe depends on what those around them do, say, or believe, even when individuals (p. 438) do not consciously frame their choices with reference to social pressure, desire to help others, or other social motives. Given that conditional decision-making is an omnipresent fact of social life, what sorts of general mechanisms can explain variation in observable social activity? As a formal approach to decision-making, conditional choice provides a systematic framework for examining links between social action and individual behavior when individual decisions are conditional or interdependent. Whereas rational choice explanations rely on variation in costs, benefits, probabilities, and information to generate variation in predicted outcomes, the conditional choice framework points toward variation in the factors detailed above: the initial activity or distributions of decision rules that constitute the basic dynamic, resistance to influence, social network structure, and the location of key actors in those networks as means of explaining variation in outcomes and trajectories.
Thus, conditional choice as described in this chapter is neither a stand-alone theory nor a set of specific empirical mechanisms; rather, it is a framework for explanation of social action. From this formal framework researchers can develop precise more mid-range theories of particular phenomena by drawing links between the formal mechanisms identified in this chapter (initial activity, decision rules, resistance to influence, network size) and empirical variables in the real world. How might this work in practice? Strang and Soule (1998) show that new management practices often diffuse from prestigious firms to more peripheral ones. The conditional choice framework suggests several possible explanations for this phenomenon, drawing on several of the formal mechanisms it identifies. Does the pattern of diffusion occur because leaders of prestigious companies are more likely to be first movers? Or do the innovations of less-prestigious firms fail to spread, either because the status of the early adopter leads to a different distribution of decision rules or because less prestigious firms are less favorably located in the relevant network structure? By identifying the range of possible formal mechanisms at play, the conditional choice framework encourages the development and testing of mid-range theories across different substantive areas that nonetheless fit into a coherent explanatory framework, while pushing research towards a precise treatment of theoretical issues.
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(*) Special thanks for comments or special assistance go to Scott Blinder, Peter Bearman, Adrienne LeBas, Michael Dawson, Tom Snijders, Anne Shiu, and Nick Collier. Portions of this chapter are based upon work supported by the National Science Foundation under Grant No. 0453076.
(1.) Although I borrow the terminology of dynamical systems, I describe individuals (not systems) as following rules determining change over time (as in agent-based modeling). Individual decision-making is better suited to social-science research, and it is fairly easy to translate from one form of expression to the other (López-Pintado and Watts 2006).
(2.) Axelrod (1997) claims that culture (as he defines it) is more likely to emerge when actors face nominal choices along several dimensions. However, this claim is misleading, as it attributes the impact of non-robust modeling assumptions to an intrinsic property of nominal choices (Klemm et al. 2003; Flache and Macy 2006). Nominal choices modeled as linked binary actions produce complete conformity in both herding models (Banerjee 1992) and the Sznajd opinion model (Sznajd-Weron and Sznajd 2000), unless the number of nominal choices is exceedingly large in proportion to the size of the group. When actions are ordinal, the basic dynamic occupies a middle ground between continuous- and binary-choice models (Amblard and Deffuant 2004; Stauffer and Sahimi 2006).
(3.) Despite the empirical appeal of categorical actions, this chapter will focus on binary and continuous actions—the relevant formal mechanisms work in similar ways across the action types, and more research exists on binary and continuous actions.
(4.) Conditional responses may take on other functional forms, such as: exponentially increasing (Banerjee 1992; Dodds and Watts 2004), decreasing, or unimodal (hump-shaped) (Elster 1989; López-Pintado and Watts 2006).
(5.) Thanks to Jeff Grynaviski for this point.
(8.) Semi-stable diverse states are produced when actors get ‘stuck.’ For example, take an audience member facing a standing ovation decision. He has 8 neighbors, 4 of them standing up and 4 remaining seated. This actor is stuck if using a majority threshold-decision rule, he will never sit down if he is standing, or vice versa.
(10.) Thanks to Michael Dawson for this point.
(11.) Face-to-face contact is more effective at increasing turnout than other forms of mobilization (Gerber and Green 2000; Green, Gerber, and Nickerson 2003). Face-to-face contact also changes contributions in social dilemmas, even when there is no opportunity to reward or punish group members (Ostrom, Walker, and Gardner 1992).
(12.) An obvious exception is complete geographic isolation, or the reproduction of variation associated with historical cleavages rooted in geographic isolation.