R. Robert Huckfeldt, University of Indiana (

Paul E. Johnson, University of Kansas (

John D. Sprague, Washington University in St. Louis John (

Michael C. Craw, University of Indiana (

August 17, 2000



            This paper combines results from survey research and simulation to address questions about the nature and impact of interpersonal political communication.  The first part of the paper integrates the results of recent surveys about political discussion and the nature networks in which political ideas are discussed.  While long-standing theories predict that people will not generally interact with others when their political attitudes differ, the accumulating evidence points to a different conclusion, namely that interactions of people with distinct political views occurs and, while persuasion occurs, it does not completely eliminate diversity.


            The formation of discussion networks and their impact on political opinions is difficult to study empirically because most of the important variables are endogenous.  Following Axelrod's suggestion that an agent-based model can be a useful tool for "thought experiments" and clarification of theory, we have used the Swarm simulation toolkit to investigate the formation of discussion networks and implications of theories about persuasion and information exchange.


Prepared for delivery at the annual meeting of the American Political Science Association, Washington, DC, Aug. 31-Sept. 2, 2000.  The authors would like to thank Marcus Daniels of the Swarm Development Group and Rick Riolo of the Center for the Study of Complex Systems at the University of Michigan.




            A central issue in the study of democratic politics is the capacity of citizens and electorates for tolerating political disagreement.  The model of a free, open, and democratic society is one in which political issues are fully explored and political debates are fully aired.  In such a society, citizens are open to persuasion, the social boundaries on political viewpoints are fluid and shifting, and individuals encounter the full spectrum of issue positions and political viewpoints.

How does this model correspond to contemporary analyses of citizens and democratic politics?  At one analytic extreme, citizens play the role of individually autonomous actors, oblivious to the experience of political disagreement.  Individual preferences inform individual choices, and these preferences are idiosyncratic to particular, socially self-contained individuals.  Hence, the preferences and choices of one person become irrelevant to the preferences and choices of another, and political disagreement among citizens becomes irrelevant to political outcomes. 

At an opposite extreme, inspired by a conformity model of social influence (Asch 1956), some analysts see citizens as the individually powerless dupes of an irresistible social influence process. The psychic discomfort of disagreement causes individuals to reduce dissonance through various means (Festinger 1957).  In particular, individuals adopt socially prevalent viewpoints and, just as important, they avoid disagreement in the first place by censuring their patterns of social interaction to create politically homogeneous networks of political communication. 

Neither of these analyses is able to accommodate the survival of disagreement in patterns of meaningful communication and deliberation among citizens.  In the model of the self-contained citizen, communication is not meaningful because it is extraneous to the formulation of individual choice.  In the conformity model, disagreement is extinguished through censured patterns of interaction and powerful mechanisms of social influence.

The strategy of this paper is twofold.  First, we evaluate empirical evidence regarding the survival of political disagreement among citizens within their naturally occurring patterns of social interaction.  Second, we evaluate a dynamic, agent-based model of political persuasion to assess the mechanisms that might sustain disagreement among citizens.  In both instances we assume that communication among citizens is politically consequential - that citizens are politically interdependent in the sense that they rely on one another for political information, expertise, and guidance.  The primary question becomes, what are the conditions under which diversity of opinion is likely to be sustained?




In their pioneering studies of social influence among citizens, Lazarsfeld and his colleagues (Lazarsfeld et al. 1944; Berelson et al. 1954) argue that political communication among citizens becomes less frequent during the period between election campaigns, and hence political preferences tend to become individually idiosyncratic.  As the frequency of political communication increases in response to the stimulus of the election campaign, these idiosyncratic preferences become socially visible, and individuals are correspondingly brought into conformity with micro-environmental surroundings. 

These arguments were based, at least implicitly, on the micro-level foundations of group conformity and its effects.  In the context of an election campaign, the dynamic logic of group conformity pressures is quite compelling.  Before the campaign begins, people are less concerned about political affairs, and hence their conversations focus on other, nonpolitical topics: baseball, gardening, etc.  As long as their political preferences are socially invisible, they are immune to conformity pressures, and hence preferences become individually idiosyncratic.  As the campaign accelerates, so does the rate of political communication among associates, and individual political preferences are increasingly exposed to social scrutiny.  The stage is thus set for the introduction of conformity pressures that bring individual preferences into line with the preferences that are dominant within networks of social relations.

Carried to its extreme, the logic of group conformity suggests that political disagreement should disappear within networks of social relations.  Pressures toward conformity might drive out disagreement in several ways (Festinger 1957; Huckfeldt and Sprague 1995).  First, the discomfort of disagreement might encourage people to modify their patterns of social relations so as to exclude people with whom they disagree, or in a less extreme form, to avoid political discussion with associates who hold objectionable preferences.  Second, and partially as a consequence of discussion avoidance, people might incorrectly perceive agreement among those with whom they actually disagree.  That is, a well-documented bias exists in which people over-estimate the extent to which others hold their own political preferences (Huckfeldt and Sprague 1995; Fabrigar and Krosnick 1995).  Finally, and perhaps most importantly, individuals might bring their own preferences into correspondence with the preferences that they encounter within their networks of social relations - they may be influenced by the preferences of others.


Contrary Evidence Regarding Disagreement


As compelling as the group conformity argument may be, it suffers from one major shortcoming - disagreement is not typically extinguished within networks of social relations, even at the end of high stimulus presidential election campaigns.  At the end of the 1984 election campaign, Huckfeldt and Sprague (1995) interviewed discussants who had been identified by a sample of respondents from South Bend, Indiana.  And at the end of the 1992 election campaign, Huckfeldt et al. (1995) interviewed discussants who had been identified by a nationally drawn sample of respondents.  In both instances, no more than two-thirds of the discussants held a presidential candidate preference that coincided with the main respondent who named them.

These levels of disagreement become even more important when we recall that they are based on dyads rather than networks.  If the probability of dyadic disagreement within a network is .7, and if the likelihood of disagreement is independent across the dyads within a network, then the probability of agreement across all the relationships within a three-discussant network drops to .73 or .34.  In other words, disagreement and heterogeneous preferences are the rule rather than the exception within the micro-environments surrounding individual citizens. 

The pervasiveness of disagreement within networks of social relations forces a reassessment of social conformity as a mechanism of social influence, as well as a reconsideration of the dynamic implications that arise due to politically interdependent citizens. In the analysis that follows, we assess the conditions that give rise to socially sustained disagreement.  Our argument is, quite simply, that complex patterns of communication among citizens might sustain as well as extinguish patterns of disagreement among citizens.



The 1996 Indianapolis-St. Louis election study was conducted by the Center for Survey Research at Indiana University.  Its primary focus is on patterns of communication over the course of the campaign, and thus interviews began late in February of 1996 and stopped in early January of 1997.  The study includes two samples: a sample of main respondents (N=2,174) drawn from the lists of registered voters, combined with a one-stage snowball sample of these main respondents' discussants (N=1,475).  The main respondent samples are drawn from two study sites: (1) the Indianapolis metropolitan area defined as Marion County, Indiana; and (2) the St. Louis metropolitan area defined as the independent city of St. Louis combined with the surrounding (and mostly suburban) St. Louis County, Missouri.  Our pre-election main respondent sampling plan was to complete interviews with 40 main respondents each week before the election, equally divided between the two study sites.  After the election, an additional 800 respondents were interviewed, once again divided between the St. Louis and Indianapolis metropolitan areas.  Discussant interviews were completed at a rate of 30 interviews each week during the pre-election period, with an additional 500 interviews conducted after the election.  In the pre-election period, the discussant interviews for a particular main respondent were completed within two weeks of the main respondent interview.

            Every respondent to the survey was asked to provide the first names of not more than 5 discussion partners.  A random half of the sample was asked to name people with whom they discuss ``important matters''; the other half was asked to name people with whom they discuss ``government, elections, and politics'' (Burt 1986; Huckfeldt et al. 1998b).        At the end of the interview, we asked the main respondents for identifying information that we might use to contact and interview their discussants.  Based on their responses we interviewed nearly 1,475 discussants, employing a survey instrument that was very similar to the instrument used in the main respondent interview. 

            Table 1 shows the self-reported voting preferences for main respondents and discussants, and the results closely parallel those of earlier studies.  Nearly 60 percent of Clinton respondents name discussants who report supporting Clinton, and nearly 70 percent of Dole respondents name discussants who report supporting Dole.  The level of shared preference drops off dramatically for respondents who support Perot, but these results are coincidental with other results for individuals who hold preferences that constitute a minority (Huckfeldt et al. 1998a).  Hence, while substantial agreement is present within these dyads, the disagreement is far less than complete.

            Do these individuals recognize the presence of disagreement among their associates? Either because they avoid the discussion of political topics, or because they misperceive in effort to avoid cognitive dissonance, or because they myopically generalize on the basis of their own preferences, it is not uncommon for individuals to infer incorrectly that others hold their own preferences.  This tendency is present among the Indianapolis-St. Louis respondents - 66 percent of the Clinton supporters perceive that their discussants support Clinton, and 73 percent of the Dole supporters perceive that their discussants support Dole.  Thus, while perceived levels of agreement are higher than the actual levels, the differences are not great.  And regardless of whether we consider the perception or reality of disagreement, it becomes clear that these communication networks are not characterized by political homogeneity. 

            Other analyses of these data demonstrate a variety of factors that enhance or inhibit political influence among and between citizens.  In particular, the influence of any given discussant is enhanced to the extent that other discussants within the network hold preferences that are the same as the discussant (Huckfeldt, Johnson, and Sprague 2000).  That is, the political influence of a Democratic discussant is enhanced to the extent that the citizen is imbedded in a communication network that is homogeneously Democratic. 

Results such as these, which suggest that minority preferences are less likely to be politically influential within networks of communication, add to a significant body of evidence suggesting that political minorities operate under pronounced disadvantages in democratic politics (Miller 1956).  Other efforts show that minority preferences are less likely to be communicated effectively, and hence less likely to be recognized, even by fellow members of the minority (Huckfeldt et al. 1998a; Huckfeldt and Sprague 1995). In other words, the influence of the discussant's preference is weighted by majority-minority standing within networks of social communication.  Hence, the preferences of those in the political majority count more heavily in the deliberative process than the preferences of those in the minority. 


Majoritarian Biases and the Survival of Disagreement


            Regardless of the cumulatively bleak picture for the communication and influence of minority preferences, there is no evidence here to suggest that minorities tend to be eliminated as part of the deliberative process (see Moscovici, Mucchi-Faina, and Maass 1994).  This is especially striking because we are defining minority and majority preferences relative to closely held social environments created through the communication networks of individual citizens.  Within this context, only 36 percent of the main respondents who support Dole or Clinton perceive that all their discussants hold the same candidate preference.  In other words, a lack of political agreement is the modal condition among our respondents, even within enduring networks of communication and association.

This raises an important question - how is the minority able to survive?  At an aggregate level, perhaps the most important factor maintaining political minorities is the Markov principle.  That is, a small defection rate operating on a large (majority) population will at some point be at equilibrium with a large defection rate operating on a small (minority) population.  Hence, minorities survive due to the stochastic logic of mathematical equilibria.

Minorities are also more likely to survive when the micro-environments created through networks of communication are not closed systems.  In particular, even if Joe and Bill are reciprocally related to one another as discussants and close friends, their micro-environments may be almost completely independent.  Hence, Joe and Bill may hold different political preferences, and yet both may be part of a political majority within their own respectively defined networks of political communication.

Several simple network structures, as well as their implications for the survival of disagreement, are considered in Figure 1.  Individuals are represented as ovals, discussant relationships as connecting lines, and the presence of a particular political preference as the presence or absence of shading in the oval.  In Part A of the figure, each individual is connected to each of three other individuals in a self-contained network of relations.  In such a situation, disagreement is quite likely to disappear, and only the heroic individual is likely to sustain an unpopular belief.  In contrast, Part B of Figure 1 shows two sub-networks of four individuals each, where every individual is connected to every other individual within the sub-network.  In addition, one individual within each sub-network is connected to one individual in the other sub-network, thereby providing a bridge that spans a structural hole between sub-networks (Burt 1992).  In this setting, while agreement is likely to be dominant within each of the sub-networks, disagreement will be socially sustained between the individuals who bridge this particular type of structural hole.

How important are such networks to the survival of disagreement?  One way to address this question is by examining the networks of both main respondents and their discussants.  The interview with the discussants included the same network name generator that was employed in the interview with the main respondents.  Thus we are able to compare (1) the main respondent's perception regarding the political composition of the main respondent's network with (2) the discussant's perception regarding the political composition of the discussant's network.  Guided by Part B of Figure 1, we are particularly interested in the composition of the residual networks - the networks that remain when the two members of the dyad are removed.[1]  Two questions arise.  First, how closely related is the political composition of the discussant's residual network to the political composition of the main respondent's residual network?  Second, does this relationship depend on the existence of political agreement or disagreement between the main respondent and the interviewed discussant?

In Part A of Table 2, the percentage of the discussant's residual network supporting Clinton is regressed on the percentage of the main respondent's residual network supporting Clinton.  The regression is estimated twice - once for all dyads in which interviewed discussants and main respondents each name at least two discussants, and a second time for all dyads in which the main respondent and the discussant each identify more than two discussants.  In both instances we see a positive slope with a large t-value and a small R2.  In short, the political composition of the main respondent's residual network generally resembles the political composition of the discussant's residual network.

These simple regressions are repeated in Parts B and C of Table 2, first for main respondents and interviewed discussants reporting the same candidate preferences, and then for main respondents and interviewed discussants reporting different candidate preferences.  For the agreeable dyads, we see an enhanced relationship in the form of a larger regression slope, as well as a larger coefficient t-value and an enhanced R2.  In contrast, for the disagreeable dyads, we see a reversed slope of smaller absolute value with a nearly non-existent R2, but with a coefficient t-value that supports the presence of a discernible negative relationship.

What do these results suggest?  Agreement within dyads is typically sustained by larger networks of communication that simultaneously support the preferences of both individuals within the dyad.  In contrast, we see at least some evidence to suggest that disagreement is also socially sustained, but by politically divergent networks that serve to pull the two members of the dyad in politically opposite directions.  At the very least, disagreement within dyads is characterized by political independence between the two participants' larger networks of association and communication.

In summary, the survival of disagreement within dyads is profitably seen within larger patterns of association and communication.  The logic of social influence creates a bias in favor of majority sentiment, thereby making it difficult for disagreement to be sustained.  Indeed, to the extent that networks of communication and influence constitute closed social cells, characterized by high rates of interaction within the network but very little interaction beyond the network, we would expect to see an absence of disagreement among and between associates.  Indeed, the survival of disagreement depends on the permeability of communication networks crated by "weak" social ties (Granovetter 1974) and the bridging of structural holes (Burt 1992).  At the same time that these ties lead to the dissemination of new information (Huckfeldt et al. 1995), they also bring together individuals who hold politically divergent preferences, thereby sustaining patterns of interaction that produce political disagreement.

Where has this review and analysis led?  Two tentative conclusions seem warranted:

1. Disagreement is more likely to survive to the extent that networks of political communication are characterized by low density levels - to the extent that associates do not share identical sets of associates.  To the extent that the friends of your friends are not necessarily your friends as well, a situation is created in which disagreement as well as agreement might be socially sustained.

2. These low density networks expose individuals to higher levels of disagreement in their closely held communication networks.  And the potential for such disagreement to be sustained is further enhanced by a mechanism of influence that places disproportionate weight on preferences that are widely held.  For example, you and your coworker are more likely to sustain your disagreement if your remaining friends share your political preferences and her remaining friends share her political preferences.

How are we to evaluate the implications of these conclusions?  We certainly do not possess the data that would be needed for a full evaluation of political homogeneity and diversity among and between the networks of communication within which citizens are imbedded.  Indeed, such a body of information is, as a practical matter, quite nearly inconceivable.  And hence our efforts point in a different analytic direction.



            In the remainder of this paper, we pursue a modeling strategy inspired by Axelrod in his analysis of cultural dissemination (1997).  Axelrod constructed an agent-based model which explored the emergent properties of small scales social interaction.  Axelrod's model conceptualizes interactions among agents in the following way.  A square grid of agents, described as villages, is created.  Each village has a culture, represented by an array such as (0,1,2,1,4), where each “trait” is randomly assigned at the outset.  Each element of the array is called a “feature.”  These represent cultural issue dimensions or topics. 

            The Axelrod simulation proceeds along these lines.  Each village is conceived of as a unitary actor.  An agent (village) is randomly selected and given the opportunity to interact with a randomly chosen neighbor.  The set of neighbors is a truncated von Neumann neighborhood.  Except for agents on the edge of the grid, the neighbors are found on the on the east, west, north, and south borders.  Cells that lie on the outside boundaries are only allowed to look into the grid for neighbors (in other words, Axelrod does not employ a model in which the space “wraps around” to form a torus on which agents are situated (in contrast, see Epstein and Axtell, 1996).  After a random neighbor is selected, an interaction occurs with probability equal to the similarity of the traits of the two agents.  If the interaction occurs, then an issue on which the two disagree is selected at random and the agent's opinion on the issue is changed to match the other.  Hence, influence automatically follows whenever interaction occurs.

            Axelrod made a number of observations on the basis of his model, the most striking being that, over the long run, there is not likely to be very much cultural diversity.  While the tendency toward homogeneity is greater for some parameter settings than others, it is powerful in all cases. 

            When diversity survives in the Axelrod model, it is a diversity of the most extreme sort.  Different cultural clumps are completely homogeneous and totally isolated from one another.  If a village interacts, it interacts with villages that are identical to it.  As Axelrod shows, separate groups do not form in some conditions, but they are more likely to form if the number of traits per feature is high.  Under those conditions, two agents are less like to have anything in common and so they never interact.  He shows that the number of clusters decreases as the number of features increases, and the number of clusters increases as the number of traits increases. 

            Axelrod's conclusion poses a challenge for the current modeling exercise.  If we are to formulate a useful model of political communication within small networks of citizens, we do not want the major implication of the model to be that diversity is unlikely to exist.  One solution is to create agents who are individually resistant to environmental influences, but that is not the route explored here.  Rather the emphasis is on developing a more intricate understanding of the formation of networks and the formulation of public opinion. Using an Axelrod-style model as a baseline, our own analysis turns elsewhere to consider the consequences of several other, newly introduced, model features.  

The model is implemented in Objective-C using the Swarm Simulation Toolkit (Minor, et. Al, 1996; we used version  Swarm is currently being supported by the Swarm Development Group, a nonprofit membership organization (  The modeling project we describe here introduces a raft of variables that can be inspected, including the basics like the size of the grid, the number of features and traits, the scheduling of agent actions, and so forth.  The substantively important additions concern the processes through which others are sought out for discussion and opinions are adjusted.  In Appendix 1, we present a summary of the features of the simulation as it currently stands.  In addition to introducing a number of system and individual level parameters, we also have introduced summary measures for the diversity of opinion (entropy) as well as measures of individual perceptions of diversity.  These are discussed below (see also, Johnson 1999).

We have pursued this agent-based approach as an alternative to cellular automata.  Projects by Latane, Nowak, and Liu (1994) and Nowak and Lewenstein (1996) have used a cellular model in which cells are subjected to influence of varying degree from neighbors to demonstrate some interesting emergent phenomena.  The agent-based model can incorporate the strengths of that approach, but it can add a variety of new features, perhaps most importantly the movement of agents within and across the grid and the development of individually distinct logics that govern network development.


1. A Baseline Model

Our baseline model is designed to replicate (nearly exactly) the results of Axelrod while building a structure for further study and comparison.  In the computer model, each agent in the model is conceived of as a separate “citizen” object, which has the ability to move about, initiate interactions, and adjust its opinions.  The baseline model is a restricted version, since the agents are distributed evenly over a 10 by 10 grid and they are fixed in positions.  In these models we describe in this paper, we have set the number of features at five and the number of traits at 3.

Our model is designed to incorporate agent movement.  We have done so with "dynamic scheduling" (see Johnson and Lancaster, 2000: Chapter 9.6).  Swarm is a discrete event simulator, meaning that time is broken-up into small time steps.  We have structured our model so that each agent plans its activities over the course of a “day”, which is a predetermined (in this case, 10) number of time steps.  At the beginning of each day, the agents are randomly sorted and each is told to schedule its movements throughout the day and to select (at random) a time during the day at which to initiate an interaction.  In the baseline model, the agents are not allowed to move.  In this baseline model, the agent looks for a discussion candidate in the way that Axelrod described, i.e., a discussion candidate is chosen at random from the neighborhood and interaction occurs with probability equal to the similarity of the two agents.  (If one sets the day to length 1, and selects only one agent for an interaction per day, then this model is identical to the original Axelrod model.)  When an agent finds a discussant, then the agent will copy one feature on which the two differ from the discussant.

            As the simulation proceeds, the agents are keeping records about the others they have encountered.  They note, first, what fraction of the discussion candidates they encounter agree with them about a randomly chosen feature (when they find such a common feature, we call them "acquaintances" because an interaction will follow).  Among the people selected for interaction, the agent makes note of the proportion of features on which it agrees with the discussant (the degree of "harmony"), and it also notes if the agent's features are identical to its own.  Each agent uses a 20 period moving average to tally these observations.  We can aggregate these individual perceptions by calculating various summary statistics.

            The baseline model produces a pattern of interaction which is consistent with the original Axelrod results.  A graph depicting three summary measures calculated from one run of the model is presented in Figure 2.  The most obvious feature of Figure 2 is that all three measures converge to unity.  First, the "acquainted" line indicates the average proportion of random encounters that produce interaction.  A higher acquaintance rate reflects a higher level of shared preferences among individuals a neighborhood.  As time goes by, more and more neighbors find themselves open to interaction with a randomly chosen neighbor.  Second, the "harmonious" line indicates the level of agreement between people who interact.  It reflects perceptions within networks of interaction, which indicate that the chances of disagreeing about any particular issue are diminished over time.  Finally, the "identical" line indicates average of individual perceptions of the extent to which the people that they are identical to the people with whom they interact.  Here again, the focus is on those agents engaged in interaction, and particularly the proportion of interacting agents who hold identical positions on all five issues.  Not only are people open to more interaction, but also those interactions are increasingly likely to result in total agreement between the agents.

            This particular run is not significantly different from the others we conducted with these parameter values.  We set the model so that it would terminate the simulation if no opinion change was observed for 10 consecutive days, or 100 time steps.  The average number of steps to termination is 8972.9, and in each of the 100 runs, all diversity was eliminated.  Entropy, an index of diversity across the population of opinion, drops to 0 in all cases. 

            Quite clearly, this model does lead to the same outcome as the Axelrod model.  Equally clearly, does not correspond to our empirical observations.  Uniformity and a lack of disagreement are not standard features of the political landscape, and our objective in this analysis is to consider several changes in the specification of the model that would yield a more believable world.


2. The Impact of Self-Selection


            What if people are not so selective in political interaction?  We have investigated that question by relaxing the self-selection assumption by incorporating the early work of Coleman (1964: chap. 16).  In his effort to relax baseline assumptions of random mixing in patterns of interaction within populations, Coleman introduced a parameter that allowed individuals to interact even when the parameters which governed the model would ordinarily dictate otherwise.  Rather than ignore (with certainty) a person that is different from oneself in every respect, the Coleman model introduces the possibility of interaction between these different sorts of people.  Perhaps the homogenizing influences which drive the Axelrod model can be abated if individuals are not completely isolated from others with which they disagree about everything.

            We have adapted Coleman's logic to the current context.  As in the Axelrod model, the agent chooses a candidate at random from the neighborhood.  The candidate will be accepted with probability equal to the similarity of the agents.  However, if that discussant is rejected, then with a given probability (which we call the Coleman parameter), an interaction occurs.  Hence, as the Coleman parameter grows larger, the diversity of interaction increases.  If the interaction does not take place, the individual repeats the search process, until an interaction partner is located or ten efforts have been made.

Why would political communication take place with politically disagreeable individuals?  Perhaps the individual failed to recognize the absence of political agreement, or the individual does not care much about politics or political issues, or the individual enjoys political argumentation, or the individuals simply like the same baseball team, or the two individuals work together and political discussion is unavoidable.  The point is that selection is an imperfect, stochastic mechanism with systematic slippage, and by adding the Coleman parameter we are able to examine the consequences of relaxing self-selection.

            In Figure 3a, we illustrate one simulation of the model with the Coleman parameter set to .2, meaning that, if one were to reject a discussion candidate on the first pass, there is a .2 probability that an interaction will occur anyway.  The random numbers used in this simulation are the same as the baseline model, so the difference between these two runs results solely from the introduction of the Coleman logic.  The conclusion from Figure 3a is that reducing the level of self-selection serves to produce a more rapid convergence to political homogeneity.  That is, the presence of self-selection serves to sustain disagreement.  People who avoid interaction with politically disagreeable encounters are acting to sustain their own cluster of beliefs.  The attenuation of self-selection does not change the fact that, over the long haul, disagreement disappears.  But the preservation of these small clusters tends to delay the process of political homogenization.

            In Figures 3b and 3c the Coleman coefficient is increased to .5 and .8 respectively.  We present these graphs, partly for completeness, but also to illustrate something important about simulation research.  Claims about the impact of parameter changes should be made on the basis of many runs, rather than a few.  On the basis of these graphs, one would suspect that raising the Coleman coefficient would delay the eventual homogenization of opinion.  These models begin with conditions that are exactly the same—the same individual opinions—as the models we have illustrated in Figures 2, and 3a, and so that is a reasonable conclusion.  However, the overall pattern is in the opposite direction.  The duration of simulations with the Coleman parameter equal to .5 is greater in 45 of 100 simulations.  The average number of periods until the model terminates is 8040.8, 6776.4, and 5842.5, when the Coleman parameter is .2, .5, and .8, respectively.  The distribution of outcomes is shown in Figure 4,and it supports the contention that exposing agents to political interactions with others who are completely different can shorten the survival of political diversity.

            In summary, relaxing the self-selection effect does not transform the results of the model.  Indeed, the attenuation of self-selection only serves to accelerate convergence toward a politically homogeneous outcome.


3. The Impact of Geographic Dispersal

The model variations we have considered thus far are geocentric in their assumptions and organization.  In other words, the encounters that produce opportunities for social interaction are all spatially organized.  None of the agents have the ability to form associations with individuals who are located beyond the four cells that are contiguous to their own.  This is, of course, an imperfect and perhaps misleading abstraction.  The modern citizen sleeps in one neighborhood, works in another, plays softball in a third, and goes to church somewhere else.  Indeed, modern communication and transportation technologies may serve to minimize the importance of geographically defined proximity.

We accommodate geographic dispersal by incorporating the possibility of movement between grids.  For ease of discussion we refer to these as work grids, but they might be church grids, or softball grids, or even bowling grids.  There can be any number of home grids and work grids in the model.  In the specific examples below, the five work grids (size 5 x 5) are smaller than the home grid (size 10 x 10).  The agents are assigned coordinates in the work grids in a completely random way, so the work grids can have several agents in a single cell, and there can be empty cells as well.  (Multiple of occupancy of cells is allowed by a subclass of Swarm's Grid2d that we have created).  The important point is that interaction in these workplaces is completely independent of geographic location in the home grid.  Each individual is randomly assigned to one and only one position on one of the work grids, and hence the work grids provide a formal representation for geographically dispersed networks of social interaction.

The allocation of time during the day makes use of the scheduling scheme described above.  Each agent begins the day in a "home" grid (this allows us to conduct a daily survey of their experience at the start of the day).  Each day has 10 periods, and during the first period agents are told to schedule their activities during the remaining 9 time periods.  No interactions take place during that scheduling period.  Agents first schedule their movement from home to work.  Then they can schedule themselves to interact at any time step during the day, except when they are “in transit” from one grid to another.  The number of time steps spent at home is governed by an individual trait called “home duration.”  This variable is set when the model begins by adding 1 to a draw from a Binomial distribution B(9,h), meaning 9 "trials" with probability of success equal to h.  If h=0.5, then most agents spend “about half” of their time at home, while some spend significantly more and some spend less.  If “home duration” is 1, then the agent is in the home grid only in the first time step of the day, and then moves to the work grid.  Conversely, an agent whose home duration is 10 will never go to work, and will thus never have direct exposure to that grid’s occupants.  At some randomly chosen time step during the day, possibly at home or at work, the agent will initiate an interaction.  The interaction can occur only with other agents who happen to be in that grid at that time, and thus a source of heterogeneity is created.  Since the work grids may have more than one citizen in each spot, a second sort of heterogeneity is created, because agents who look “up” might not always find the same discussant.  Hence, the difference between the baseline, as depicted in Figure 2, and this new scenario, as in Figure 5a, results from greater heterogeneity of exposure.

The intuition that guides the development of this model is that exposing agents to interaction with agents with different backgrounds can ameliorate the forces which homogenize opinion in the home neighborhood.  This intuition is not valid, however.  Recall that the average number of time steps to convergence in the baseline model is 8,972.9, but the average for this model is 6,275.  A comparison between Figure 5a and Figure 2 illustrates this phenomenon.  Figure 5a shows time paths that converge toward a homogeneous equilibrium over the long haul.   The observed path to convergence appears different, however, for the first 2000 time periods.  Figure 5a shows that the initial level of political diversity is much higher with geographically dispersed opportunities for social interaction.

What happens when people spend all their time at in the work grids?  The results we obtained mirror the results for multi-agent cells presented in Johnson (1999).  In Figure 5b, the home-grid probability is set to zero, which means that all opportunities for interaction occur at the work grid.  Perhaps not surprisingly, the pattern of convergence is similar to that of the baseline model, except in this case the rate of convergence is much quicker.  The average number of time steps is 1024.5, about one-eight of the baseline model.  This happens for several reasons, but we believe the two most important are the smaller size of the work grid (5x5) as well as the possibility of open cells that act as “firewalls” isolating agents from each other.

In summary, our imposition of geographically dispersed social interaction does not alter the outcome of the baseline model in any fundamental sense.  The end result continues to be a politically homogeneous community that is devoid of disagreement and diverse political opinions.  More analysis is clearly warranted, however.  In particular, a natural next step is to produce initially skewed distributions of opinion in several alternative home grids that are socially segregated from one another, combined with non-geographically based work grids that combine individuals from all the alternative home grids.  This would produce an opportunity to study the maintenance of political divergence between politically disparate communities, and the consequences of cross-cutting institutions on the survival of political diversity between and among geographically based communities (see Fuchs 1955).


4. Separating Persuasion from Interaction


            The baseline model conflates interaction with persuasion.  Every time agents who differ interact, one feature is copied from one to the other.  Agents are wholly indiscriminate in their adoption of opposing points of view.  For many purposes, this is perhaps a wholly adequate model.  If you need information regarding web sites for vacation alternatives, you might indeed seek out information from people with travel interests similar to your own and take whatever information they provide.

            In contrast, the value of political information taken through social interaction is problematic.  Even if you acquire information from a generally trustworthy individual suggesting that George W. Bush is just another rich fraternity kid who would make a terrible president, you might want to evaluate the worth of that information.  The important point is that communicated information does not necessarily translate into influence, and in this sense the influence of even effectively communicated information is quite problematic.

            How do people evaluate the worth and credibility of political information?  What makes for political information on the part of a communicated opinion or preference?  Indeed, a range of factors could be considered: the clarity with which individuals communicate, the imputed expertise of political discussants, and more.  In this analysis we build on earlier work (Huckfeldt, Johnson, and Sprague, 2000) to focus on the incidence of opinions within networks of political communication.

            If you think that George W. Bush is high quality presidential material, and one of your friends tells you that George Bush is just another rich fraternity kid, how might you respond?  According to the baseline model you would simply change your opinion, but an alternative strategic response is to contextualize the information provided by the discussant relative to information provided by other discussants.  Hence if you like Bush, but your friend Joe dislikes him, you might take account of other opinions about his capabilities.  If all your other information sources suggest that he is a good guy, you might downgrade the credibility that you place on Joe's opinion.  On the other hand, if all your other information sources agree with Joe, you might reconsider your own opinion on the matter (see McPhee 1963).

            In summary, we are suggesting that the influence of particular opinions held by particular discussants is proportional to the incidence of these opinions within larger networks of opinion.  If all my friends and I believe that Bush is an excellent presidential candidate, then I am highly unlikely to change my mind when someone tells me otherwise.  If, on the other hand, I increasingly receive reports that Bush is just another rich fraternity kid, then it becomes more difficult to dismiss the opinion, and I am more likely to revise my opinion.  Any single piece of information is seen within the context of all the information that is available.  The social influence of any single interaction ceases to be determinate, and the agent becomes an evaluator of information received through a successive process of social interaction.

            In our final model, we consider the consequences of this model, which, for lack of a better term, we are calling the "friends from the network" model.  The discussants are selected in the same manner as previous models, but agents keep records on the contacts they have experienced and use those records when formulating their response to new points of view.  The current scheme is somewhat coarse, but it captures the essence we are trying to capture.  Each time an agent interacts, it counts the number of features it holds in common with the other.  When an interaction occurs, the agent polls the people that it agrees with on more than one-half of the issues, and if more than one-half of those “friends” agree with the new point of view, it is adopted.  Thus, new ideas or novel preferences should take longer to catch on, and individual agents should be less susceptible to persuasion.  What are the results?

            As Figure 6 shows, when the influence of an opinion is proportional to its incidence within an individual's network of contacts, diversity is maintained within both the larger population and within networks of political communication.  First, the level of acquaintanceship is lower than in the previous models, reflecting the fact that the opinions of the agents are not so homogeneous.  People are regularly put in contact with others with whom they disagree.  Second, only a relatively small proportion of networks are composed of dyads with identical preferences.  Finally, the average proportional agreement with any discussion partner (harmony) is only slightly above .6.  This can be interpreted as the probability that two discussants will agree on any particular issue, and hence the level of agreement in Figure 6 roughly parallels the earlier empirical results. 

            We hasten to add that this figure is very much representative of the 100 runs we performed with these settings.  The number of steps averaged 732.1 with a standard deviation of 148.  However, the averages (and standard deviations) of the acquainted, harmony, and identical variables were .44 (0.03), .36 (0.05), and .6 (0.04).  Entropy is not zero at the end of any of the runs.

            What do these results suggest?  Much more work clearly remains to be done, and we have only begun to address the complex political processes that yield sustained disagreement and diverse preferences in democratic politics.  But these first results point to the importance of separating the communication of information from the persuasiveness of information.  Even effectively communicated messages may lack influence, and this analysis points to the importance of interdependent citizens as discriminating consumers of political information.


Summary and Conclusion

            A substantial body of evidence has accumulated regarding the distribution of preferences within citizens' networks of political communication.  Contrary to a great deal of conventional wisdom, these networks are not safe havens from political disagreement.  Quite to the contrary, it would appear that disagreement is the modal condition among citizens - most citizens experience disagreement and divergent political preferences within these networks.  Indeed, this conclusion is based on the closely held, self-reported relationships of the citizens themselves, and on the most visible of contemporary political choices - support for a particular presidential candidate.

            Hence the question becomes, what is the nature of the dynamic process that sustains disagreement among citizens?  A number of different analytic strategies can be used to address this problem.  In the current paper we employ an agent-based model of social interaction and political influence.  The model shows that political diversity is maintained for longer periods of time to the extent that individuals are able to seclude themselves from disagreement by self-selecting their political discussants to create politically censured clusters of like-minded individuals.  Over the long haul, even this strategy loses out, ultimately giving way to a process of political homogenization that creates uniformity in political preferences across the population.

            It is important to remember that, in the real world, transient responses may be more important than long-term equilibrium responses.  This is doubly true in political processes that are constantly being bombarded by stochastic events - Monica Lewinsky, fund raisers at Buddhist temples, unforeseen reactions to vice presidential candidates, and the like.  In such a stochastic world, initial conditions are continually being reset.  Hence the transient, short-term response may end up being most important, and the speed of recovery to equilibrium becomes especially crucial.

            In this context, a number of factors related to the social structure of interaction appear to affect the speed of the homogenization process.  First, to the extent that self-selection is attenuated, convergence toward homogenization is accelerated.  Second, to the extent that a set of geographically dispersed institutions and structures create a network of communication that overlaps the geographic organization of social life, convergence toward homogeneity is further accelerated.  This latter result is wholly in keeping with classic studies of contagion (Bartholomew 1967), and with more recent studies of the communication consequences that arise due to structural holes (Burt 1992) and weak ties (Granovetter 1974) within networks of communication.

            As long as persuasion is the inevitable consequence of interaction within discrete dyads, the elimination of political diversity and disagreement may be a foregone conclusion, at least over the long haul.  In contrast, a far different outcome emerges when we redesign the model to make persuasion within dyads the problematic and less than automatic consequence of interaction across an individual's entire network of contacts.  Based on earlier empirical results, we conceive the probability of persuasion as a function of an opinion's incidence within an individual's network of relationships.  That is, individuals are less likely to be persuaded by opinions that win only limited support among the participants within their communication networks.  Indeed, this model of persuasion serves to maintain diversity and disagreement both in the short run and over the long haul.

            In many ways this is a surprising outcome.  The model of influence we are describing rewards majority opinion at the same time that it punishes the political minority, but it produces an aggregate outcome in which the minority does not disappear.  The potential of this mechanism for maintaining political disagreement is that the influence of majorities and minorities are defined according to the distribution of opinion within closely held micro-environments of political communication.  Hence, people are able to resist divergent viewpoints within the network because every opinion is filtered through every other opinion. 

            Finally, the power of the mechanism we are describing is wholly dependent on the low levels of network density that are built into the model.  If the network densities were high - if networks were wholly self-contained so that all members shared the same interaction partners - then disagreement would disappear even though diverse preferences would be sustained in the larger environment.  That is, no one would ever encounter diverse preferences because every particular network is wholly self-contained and entirely homogeneous.  In contrast, low network densities, combined with influence that is predicated on the incidence of particular opinions within networks, serve to sustain political diversity in the larger environment as well as the experience of disagreement within citizens' closely held networks of political communication.

Appendix 1

Brief summary of model features


Structural Features.

1. Toroidal World or Square World.  (runtime "wrap-around" toggle)

2.  Multiple Scheduling Options (compile-time preprocessor flags and runtime options).  Axelrod "random one-at-a-time" simulation or Knight's tour through all agents (optionally, in random order) during each "day".  A "day" is an adjustable number of time steps.  CPP flag "NO_MASTER_SCHEDULE" compiles in fully autonomous dynamic scheduling by individual agents.  Otherwise, all agents place their actions onto a single master schedule, in which actions at any particular time step may be randomized.

3.  Multiple neighborhoods "home grids" in which people live and multiple "work grids" where they might interact.  All grid sizes can be adjusted at runtime.

4. Agent movement and access.   An agent's location at any time is controlled by individual movement parameters.  After the "home duration" is completed, the agent removes itself from that neighborhood and takes its position in the work environment.  As currently designed, each agent initiates an interaction once per day, and the probability of initiating an interaction in a grid is proportional to the total number of time steps per day spent there.  At the beginning of each day, each agent finds itself at home, and it then can schedule itself to go to the other environments and to initiate an interaction at some point during the day.


Behavioral Features:

The model separates agent actions into two groups of  interchangeable modules, "discussant selection" and "opinion adjustment)

1. Discussant selection: a method fulfilling this role returns either another agent or a missing value.

            A. Axelrod's Selection method: randomly choose a neighbor from the von Neumann neighborhood, then choose that person with probability equal to the proportion of identical features between the two agents. 

            B. Parochialism variant: Axelrod's method, except that when there are multiple people per cell, choose a discussant from within own cell with probability "parochialism" and otherwise select randomly from each of the 4 neighbors.

            C. Coleman variant: Same initial selection of discussion candidate as model A.  The candidate is selected for discussion with probability

            D. Selective exposure models: Agents build a list of others by random sampling from own cell and neighbor cells, then choose the one they expect to be most "agreeable" as discussant.  Variants on this theme explore assumptions about strangers and the way agents keep records on each other.

2. Opinion adjustment: response to an interaction.

            A. Axelrod method: find a feature on which the discussant differs from the agent who initiates interaction.  Copy that feature from the discussant. (Runtime variants in our model allow the possibility that either agent or both may adjust)

            B. Social network model: find a feature on which the discussant differs, then consider adopting his opinion if a sufficiently high proportion of "friends" supports that opinion.  (Runtime variables can adjust the criteria for considering someone a friend and whether or not friends are polled or rather a recollection of their opinions is used).


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Table 1.  Discussant's candidate vote preference by main respondent's

          candidate vote preference in 1996 Indianapolis-St. Louis study.


Discussant's           Main Respondent's Self-Reported Preference


Preference                 Clinton    Dole     Perot     Total


Clinton                     59.7     20.5       38.6      39.5 


Dole                        25.0     68.6       33.3      46.7 


Perot                        2.6      2.3       14.0       3.0 


Don't Know,                 12.7      8.6       14.0      10.8

  No vote


     Total                   573      605         57      1235


Table 2. The proportion of the respondent's network perceived (by the

         respondent) to support Clinton regressed on the proportion of

         the discussant's network perceived (by the discussant) to support

         Clinton, conditional on whether the main respondent perceives

         agreement within the respondent-discussant dyad.



                          number of discussants named by both the

                              respondent and the discussant:


                            2 or more              more than 2



              constant          .31                    .29

                             (20.07)                (15.48)


              slope             .19                    .27

                              (6.20)                 (6.78)


                R2              .04                    .07

                s.e.            .38                    .35

                N              1006                    640




              constant          .26                    .22

                             (13.46)                 (9.61)


              slope             .36                    .47

                              (9.23)                 (9.78)


                R2              .12                    .19

                s.e.            .37                    .34

                N               605                    401




              constant          .39                    .42

                             (16.03)                (14.24)


              slope            -.08                   -.15

                              (1.73)                 (2.34)


                R2              .01                    .02

                s.e.            .36                    .34

                N               378                    223



Note:  In constructing perceived network support for Clinton, the  

       interviewed discussant is extracted from the respondent's network,

       and the respondent is extracted from the interviewed discussant's

       network. Hence, the resulting measures index the political

       composition of the residual microenvironments absent the preferences

       of the particular dyad.
Figure 1. Patterns of social connection and implications for electoral  change.



A. Conformity and the socially heroic holdout.
















B. Socially sustained disagreement.




















Figure 2. Baseline model of communication and influence.




Figure 3a. Baseline model with Coleman parameter = .2.





Figure 3b. Baseline model with Coleman parameter = .5.



Figure 3c. Baseline model with Coleman parameter set to .8.




Figure 4: Histograms summarizing the duration of simulations and the effect of the Coleman parameter

Figure 5a. Multi-grid model with 1 :home grid and 5 work grids, h = 0.5.





Figure 5b. Multi-grid model with 1 home grid and 5 work grids, h = 0.0.




Figure 6. "Friends from the Network" model.



[1] Removing the interviewed discussant from the main respondent's network is a straightforward task.  Removing the main respondent from the interviewed discussant's network is not straightforward because we do not have a direct measure of reciprocity - we do not know with certainty whether the discussant names the main respondent as one of her discussants.  We adopt the procedure of assuming that the main respondent is included in the discussant's network if the main respondent reports a candidate preference that is perceived by the discussant to be present in the network.