This paper presents a new interpretation of Robert Salisbury's exchange theory of interest groups. The exchange theory contends that we can best understand interest group dynamics as the outcome of the exchange relationship between an entrepreneur/recruiter and prospective members. Recent research under the label "population ecology of interest groups" has claimed otherwise, arguing that these individual-level phenomena are unimportant.

In order to show that the individual-level model is a necessary ingredient of a useful theory of interest groups, this paper extends the exchange theory by supplementing it with some more explicit mathematical elements and a computer model. In particular, the new ingredients are 1) a formal spatial model of expressive benefits, 2) an agent-based model of the recruitment process in which recruiters simultaneously search for prospects and adjust their political positions.

The simulation model is written in Objective-C with the Swarm Simulation Toolkit version 2.1 (http://www.swarm.org). The Swarm Toolkit is a general purpose library of classes and methods for creation of simulation models of complex adaptive systems.

This project has been supported by the General Research Fund of the University of Kansas and National Science Foundation award SBR-9709404

Prepared for presentation at the 2000 Annual Meeting of the Midwest Political Science Association.

The exchange theory of interest groups, proposed by Robert Salisbury (1969), holds that the growth or decline of membership in an interest organization depends on the nature of the exchange relationship between the organization's entrepreneur and the members and prospective members. Acting in the role of recruiter, the entrepreneur entices people to join by offering a mixture of material, expressive, and solidary incentives.

The exchange theory is a leading solution to the so-called logic (or illogic) of collective action. As Olson described it, the problem is that political interest groups are difficult to form because the changes for which they work--legislative changes--affect all members of society, whether or not they contribute to the lobbying effort. People are thus inclined to be free-riders. Widely held interests are likely to go immobilized unless there is some sort of economic link that binds people together and their political action is, according to Olson, a by-product of their linkage. Olson contended that small interests would be advantaged in the political process (1965), because they are more readily mobilized.

The reach of the exchange theory is wider than the logic of collective action because the exchange theory is intended to explain why organizations grow and die. A fundamental part of the exchange theory is the idea that the benefits offered by the recruiter vary in cost and the power of their appeal. Material selective incentives may offer the most powerful enticement, but they are also the most costly for a voluntary organization to provide. On the other hand, expressive benefits may be provided relatively cheaply, but their attention-grabbing effect is not so permanent.

As an alternative explanation for the growth in interest organizations and the nature of the interest group system, Gray and Lowery, (1996a,b), among others, have proposed a theory of interest groups that draws on some ideas from population ecology. Two contentions of the population ecology approach are especially relevant to the present inquiry. First, the individual-based theories of Olson and Salisbury do not lead to interesting or meaningful predictions about the overall nature of the interest group system that we are likely to observe. In other words, these micro level theories lack macro implications. Second, and more to the point, it is not necessary to understand the individual level goings-on because the structure of the environment plays a determining role.

The first contention is correct. The exchange theory, in its current form, describes a micro level relationship without providing much aggregate level insight. The second contention, however, is incorrect. It is not wise to develop a theory based on correlations observed at the aggregate level for a number of reasons. One might look, for example, at the literature in ecology, where there is currently much focus on the question of microfoundations (Judson, 1994; DeAngelis, and Gross, 1992; Booth, 1997; Schmitz and Booth, 1997; Kreft, Booth, and Wimpenny, 1998; Jones, Hraber, and Forrest, 1996; Huston, DeAngelis, and Post, 1988). A major theme is that, since life and death are individual-level events, we should seek to explain population aggregates in terms of the individual level. There is a suggestion, furthermore, that some aggregates are simply inexplicable except in terms of complicated individual level processes and that other observed patterns are misleading due to, among other things, the well known ecological fallacy (Robinson, 1950). Finally, one might look at the literature on complex adaptive systems (Waldrop, 1992; Holland, 1998). A complex adaptive system is a system composed of many autonomous elements that are referred to as agents. Furthermore, these elements are loosely interlinked, usually as a result of limitations on the information available to the agents. One of the principal goals of CAS research is to understand the implications of individual-level behavior for aggregates.

While it has been known, at least since Robinson observed the ecological fallacy (1950) and Schelling's research on segregation (1971), that aggregates do not necessarily yield information about individual level tendencies, the tools with which to investigate models of this kind have not been available until recently. In the remainder of this paper, I attempt to show that the aggregate level implications of various individual-level theories of interest groups can be explored within the paradigm of complex adaptive systems. The computer models are written in Objective-C using the Swarm Simulation System, a general purpose simulation toolkit and library (Minar, Burkhart, Langton, and Askenazi, 1996; see also http://www.swarm.org). The usage of a standard "workbench" is intended to address some common shortcomings in simulation modeling by providing high-quality numerical routines.

The next section provides an overview of the individual-based model. It is followed by description of a complicated issue space in which the artificial agents "live" and, after that, some observations about the implications of the model will be discussed.

In the agent-based model, there are two kinds of political agents: interest group entrepreneurs/recruiters and citizens.

1. Citizens. The citizens can best be described as "rationally ignorant." They have opinions about politics, but they don't know what interest organizations exist or what they stand for. Unless they are individually contacted, citizens do not join any organizations. When citizens are invited to join, and they have the resources and inclination to do so, they always choose the organizations with the policy stances that are closest to their personal views.

The expressive benefits of membership in an organized interest are the main focus in the current inquiry. The basic idea is that an interest group takes positions in a policy space and citizens will join when they are offered a tolerable policy package. As in the spatial models of voluntary organization participation and decision making that have been presented elsewhere (Johnson, 1996), each citizen has a favorite policy position as well as a personal notion of which organizational positions might be tolerably close. The set of tolerable policies depends on individual characteristics, such as the pleasure of being a member of an organization and the attractiveness of alternative uses of time and money. It also represents the strength of the individual's drive for self expression and affiliation. Presumably, if an organization offers an extremely appealing material selective incentive, then the set of policies that the citizen can tolerate from that organization should be more inclusive.

The current project extends the previous model to cover situations in which there are many interest organizations and the citizen may join any number of them. The maximum number of organizations that a agent might join is called the budget. The budget reflects not only financial scarcity but also the citizen's general proclivity to join organizations.

During a period of time, the citizen might receive invitations from a number of recruiters. Any invitations that contain offers that lie outside the tolerable interval are simply thrown away. The tolerable offers are kept in a list where they are sorted in order of their proximity to the citizen's ideal. When it comes time decide about these invitations, the citizen begins with the most appealing organization and expends the allocated budget. The citizen chooses randomly among equally appealing offers.

One of the most important elements of the exchange theory is that expressive benefits are short-lived and, generally speaking, people are not driven by powerful urges to obtain them. As Aldrich has observed in the context of electoral politics, participation is a low-cost, low-benefit affair (AJPS, 19XX). In order to take this into account, some factors are added to the model. First, each agent is created with a "free rider coefficient," a number which indicates how likely that person is to ignore an organization's offer even if its proposal is tolerable. People for whom this coefficient is 0 will always join an organization if its proposal suits them, but people for whom it is 0.5 will free-ride on the organization's activities one half of the time. Of course, someone for whom this coefficient is 1 is a free-rider, pure and simple.

Second, random defections from organizations are possible. One side-effect of the mild nature of expressive benefits is that their effect is limited in duration. Interest group recruiters face the problem that many members decline the invitation to renew their memberships. It may be that the individual's thirst for self expression and membership has been satiated, for example. In the aggregate, the recruiter observes a "retention curve," a relationship between the number of years that a person has been in an organization and the probability of getting a renewal from that member. Among people in their first year of membership, the renewal rate is low. As a cohort of members is winnowed down by resignations, a core of more-loyal members remains. This phenomenon is taken into account by designating a "loyalty coefficient" for each citizen. The loyalty coefficient indicates the probability that the agent will renew a tolerable offer when it is within the budget.

2. Recruiters. The entrepreneur/recruiters want citizens to join their organizations, so they formulate policy stances and advertise them to the citizens. The details of the policy stances are to be discussed below. The advertising process is modeled as a direct mail advertising campaign. In its first periods of existence, the recruiter is given a start-up fund with which to contact a number of citizens and ask them to join the organization. After the start-up funds are exhausted, then the recruiter is required to "pay" for its recruiting efforts.

Suppose the ability to recruit new members depends on the existing number of members. Suppose the organization can afford to pay for a fixed number of contacts with the resources it collects from a single member. In "real life", for example, suppose an organization collects $20 from a member in the form of dues. Suppose $13 is required to run the organization and provide whatever benefits have been promised, so the recruiting effort can take $7. Then if it costs fifty cents to contact each new prospect, the recruiting arm of the organization can afford to contact 14 new prospect for each of the current members.

As explained elsewhere (Johnson, 1997), an organization that recruits at a fixed ratio of prospects to members will begin to "exhaust" its pool of potential members. How large will the organization become, and what will be its recruitment rate? In order to make this calculation, it is necessary to have some information about the organizations "retention rate", the proportion of current members that it is able to renew each time period. Suppose the organization gradually accumulates a base of loyal members, so its renewal rate rises to a relatively high value of 0.72. An organization in steady-state will need to replace 28 percent of its members, so if it contacts 14 prospects per member, the response rate will be 2 percent.

What if the response rate is less than 2 percent? It may be that the organization will face an inevitable decline and possibly death. When the number of recruits does not counterbalance resignations, then the organization will have fewer members and, as a consequence, it will be able to contact fewer prospects.

If the organization's recruiting department is left to its own devices, it seems likely it might crank up the recruitment volume to counteract the low level of response. This might bring the organization to a new steady-state value and the response rate will be forced down yet further.

Because of the financial cost of advertising, however, it is doubtful that an organization could afford to ramp up its recruiting activity in this way. It is more reasonable to expect that the "real life" recruiter might be constrained by cost pressures that force a reduction in recruiting, rather than an increase. For example, organizational leaders are typically not excited about paying the expense of a direct mail campaign unless it is likely to offer safe rate of return (Johnson, 1998). If organizational leaders indicate, for example, that the lowest financially acceptable response rate is 2.5 percent, then the scale of recruiting must be reduced.

The most frequently asked question about this model is the following: How would an interest group differ from a political party? The answer is this: The only inherent difference between political parties and interest groups the citizens are restricted to join only one party, while citizens may join many different organizations. All of the other differences we typically associate with parties and groups are epiphenomenal.

One might argue, for example, that there is a substantive difference between political parties and interest groups because parties are expected to take stances across a broad range of policy spaces while interest groups are not. Empirically, this claim might be true. Theoretically, it is an open question. At least in America, a political party is not legally compelled to take a given number of issue stances, and there is nothing restricting an interest group from staking out a position on all of them. Ideally, one would like to have a theory that explains why parties take some positions and not others.

1. The idea of a policy space. The political landscape described in this paper is unique. As far as I am aware, no model of this sort has been proposed before. The hallmark of the model--and the computer code that underlies it--is its generality. It can be used to represent an arbitrarily complicated political world in which organizations compete for the attention of citizens in tens or hundreds of policy arenas. This is quite a change from formal models of elections, which typically represent positions in a one or two dimensional space.

The policy universe is the set of all possible issue stances that can be taken. It is made up of policy spaces. Define a policy space is a set of interrelated issues. If an organization or a citizen takes a position on one of these issues, then it must take a position on all of them. For example, if a policy space deals with the question of welfare, then there are interrelated issues such as eligibility, benefit amounts, work requirements, and so forth. A policy space may have any number of issue dimensions.

2. Groups and Citizens may be selective. Suppose that there are many of these policy spaces, and that they are disconnected, in the sense that an organization or a citizen may have a position on one space and not the other. It has been a long-standing assertion in American politics that there are "issue publics," subsets of the populace that take stances on particular issues and overlook, or place decidedly less emphasis on, other possible spaces. If there are policy spaces that represent such diverse policy topics as air pollution, water pollution, the rights of disabled people, flag burning, labor union regulation, health care, immigration, and so forth, it seems plausible to assert that people and organizations can pick and choose among policy spaces.

The positions that are taken by interest organizations may change. If a position is taken on one policy space and not the rest, the organization might decide to drop its position on that one space and take up positions on all of the rest. As a result, position taking has these two separate phases, the selection of a position in a space and then the decision about whether or not to take any position whatsoever. In the models described below, these adjustments are represented as a democratic process in which the agents that currently belong to an organization are allowed to decide whether to jettison positions on some spaces or taken up positions in new spaces.

The adjustment in the organizational position begins at a randomly assigned initial position. In some simulations, the organizations are assigned positions on all spaces, while in others they are limited to positions in one or a small number of spaces. Similarly, the interests of the citizens may be broad ranging and encyclopedic, meaning they have ideal positions on all spaces, or they may have interests in only one, or possibly none, of the spaces.

Although the positions of organizations are treated as flexible quantities that adjust to the composition of the organization, the positions of citizens themselves are not treated as moving targets. The ideal points of the citizens, as well as their tendencies to free ride or remain loyal, are fixed. The computer model is able to incorporate changes in the parameters that describe citizens if necessary.

3. The recruitment process. Many interest groups may exist in the model and each citizen may receive offers from several of them. As a result, the model has to deal with a number of questions that have not been discussed in much detail in the interest group literature. One problem is how citizens compare "apples and oranges" when different organizations take positions on different policy spaces. Since, in the current model, each citizen might care about only a few policy spaces, and each recruiter might take positions in only a few spaces, there are some very significant logical problems to be overcome. I have worked with the following premises:

1. If a citizen does not have an opinion about any of the policy spaces on which a recruiter takes a stand, then the citizen will not join that organization.

2. A citizen ignores positions taken by recruiters on policy spaces that it does not care about.

3. If a recruiter does not take a position on an issue in which the citizen is interested, the citizen assumes the recruiter's stand is the average. This assumption is surely open to debate, but one argument that supports it the empirical finding that voters tend to assume parties are in the center when information about their positions is not available (Alvarez and Franklin, 1994).

During the "recruiting period", the citizens will accumulate invitations from interest groups. Any offers that are so far from the citizen's preferred policy as to outside the tolerable region for that citizen are simply thrown away. The tolerable offers are kept in an ordered list. Each citizen has a budget that allows a certain number of memberships. The citizen takes that number of offers from the top of the list of offers and processes them, which means that, with given probabilities, the citizen will either join or renew its membership.

This model is represented formally in the following way.

1. Characterizing the political world. There are N spaces:

The number of issue spaces within each dimension is given by a N-tuple of integers,

There will be d_j dimensions within a space j, in other words.

The subscripts used to keep track of the positions of the agents in the model are specified in this order: agent, space, dimension. If a recruiter r takes a stance on all of the spaces, then its position will be represented by a full N-tuple,

and each item in this array in turn reflects positions on the individual sub-dimensions within the space. Consider the first space, for example, which has d₁ sub-dimensions:

An organization might, however, take a stance on only one space. To allow that possibility, in place of a position we insert the symbol "nil" into the N-tuple of stances. (The word "nil" is used in the Objective-C language to refer to a an object that has not been created.) If an organization takes a position only on the first space, for example, its stance would be described by:

The citizens have opinions about public policy as well. The citizen's ideal policy is described with the same tools that describe the entrepreneur's stance. A citizen i's ideal point in a particular subspace is called

If the citizen does not care about a space, then a nil value is assigned to that space. So, for example, if a citizen i cares about spaces 2 and 4, the ideal array for that citizen would look like:

2. Recruitment.

Each recruiter begins with an initial position, s_r⁰ as well as the ability to contact C_r⁰ prospects out of the society. The prospects are selected at random without replacement from the list of all citizens. The number of members in the organization is referred to as M_t.

In order to probe the importance of advertising and various assumptions about the rate of contacting allowed to recruiters, three specifications have been considered. First, a model in which recruiters can contact all citizens at all times points. Second, there is a model in which the number of contacts is kept at a fixed proportion of the current membership base of the organization, or If C_r^t=k*M. Typically, k is set at a value between 8 and 14 for empirical reasons. Third, there is a model in which the recruitment rate can be adjusted by the recruiter in light of the response rate achieved on past efforts and on the organization's overall growth rate. Suppose that recruiters have "tempered greed" to build their organization. As long as their response rate is at or above the "break even" point, they will increase their volume (in this case, by 0.5 contacts per member per period). However, if the response rate is lower than the break even point, then the volume will be reduced by 0.5 per member. It idea there is that the organization has "saturated" its market and should seek a lower, stable level of members.

In addition to contacting new prospects in each period, each recruiter also automatically sends a renewal notice to existing members. If the recruiter's invitation had described a policy stance that was either dishonest or has since been changed, then the member's renewal invitation reveals the organization's correct stances on all policy spaces.

3. How citizens evaluate their offers. The citizens want to join organizations that are close to their ideals. They evaluate the offers they get by aggregating the distances across the spaces.

The distance between two points in space j is the simple Euclidean distance between the points,

The attractiveness, or utility, or an organization's policy position depends on the combined distance between the organization's positions and the citizen's ideal points in the various spaces. If the recruiter's offer includes stances on all spaces for which the citizen has interest, then the calculation of the distance between the recruiter and the citizen is straightforward: the distances within the individual subspaces are summed:

The desirability of an interest group recruiter's offer depends only on non-nil entries in the citizen's preference array. The citizen ignores any group positions taken in spaces that are nil in the citizen's ideal array.

The citizen simply ignores any recruiter positions on spaces that the citizen does not care about. However, if the citizen's ideal point is not nil on a space and the recruiter takes no position there, then the citizen proceeds as if the recruiter has taken an average position. So one can conceive of an "augmented" array that describes the recruiter's offering in the eye of the citizen, namely

The ideal positions of the citizens and the initial positions of the recruiters on each space are drawn from random number generators that conform to various statistical distributions and the expected values are used when the recruiter's offer is nil in a space.

The organization's policy offering has to be "close enough" to the individual's ideal before the citizen will even give the invitation serious consideration. Suppose each individual has a tolerance level, T_i, which indicates "how close" an organization's proposal must be to the citizen's ideal if that citizen is to join up. The tolerance level is the maximum amount of policy discord that a person can tolerate. A necessary condition for joining an organization is that U_i(p) > T_i. T_i can be thought of as an "exit level" of utility that a person can obtain by joining no organizations. To take into account the variable number of spaces on which citizens might take positions, the tolerance level is calculated by beginning with a base level of tolerance for each dimension, and then multiplying that by the number of spaces on which positions are taken to arrive at T_i.

Each citizen has a budget, b_i, that specifies the number of organizations that it can afford to join. At the end of a time period, the citizen is told to process the invitations it has received since the previous time step. Given a budget, b_i, the b_i most attractive offers are processed. Invitiations from organizations to which the individual does not currently belong are rejected with probability FR_i, the probability that this individual will be a free-rider. This is a number FR_i in [FRMin,FRMax] which determines the probability that the citizen will choose to not join an organization that is otherwise acceptable. Invitations for renewal are accepted with probability equal to the "loyalty coefficient," L_i in [LoyaltyMin,LoyaltyMax]. The loyalty coefficient gives the probability that a citizen will renew membership in an organization.

The model is designed to help us investigate the strong form of the environmental determinism argument. One major question is whether it is possible to conceive of a world in which individual traits are totally unimportant, so that one can proceed to build a theory based purely on environmental aggregates. The evidence below indicates that the environmental parameters do have an important impact on the evolution of the interest group system, but the specifics of our models about individual behavior and adaptation are likely to be just as important.

The models described below reflect a great deal of experimentation. There are certain "obvious" things that can be done to emphasize the importance of the individual level variables. For example, one might suppose that some organizations are able to offer better material selective incentives that others. This would give them a recruiting advantage because prospects might be willing to tolerate group positions that are less than ideal. One might also suppose that some organizations have more efficient recruiting departments than others, winning higher retention rates. These obvious strategies are not explored here.

Result 1. Communication matters.

It makes a great deal of difference whether we begin with the idea that information about all organizations is not known automatically by all citizens. If all citizens know about all organizations, then more organizations are likely to survive and they are more widely dispersed and more representative of the general population.

As evidence of the importance of communication, compare figures 1 and 2. These figures are "screenshots" of two simulations with identical populations that are distributed Normally on a single two dimensional policy space. The top graph shows the membership levels of the organizations and the bottom figure, entitled "PolicySpace00" (because in C one counts beginning with zero), shows the spatial positions of the offers from the organizations as well as the ideal points of the citizens. Each ideal point is represented by a small dot and the organizational position is shown by the letter M followed by the organization's number. Each citizen has a budget of 1. The citizen's have free rider coefficients that are uniformly distributed between 0 and 0.5, loyalty coefficients between 0.6 and 0.9, and their tolerable intervals are distributed between a minimum of 3 and a maximum of 13. The organization's position in the space reflects a democratic process within the membership, in the sense that organizational policy is set equal to the median of current member ideal points in each time period. An organization is "killed" if its membership level drops below 10 after the 9th time step.

Figure 1 shows what happens when interest group positions are automatically known among the population. The group positions, after a relatively short period of time, reach positions that don't change much, and the membership levels of the organizations fluctuate within narrow bands. All 40 organizations survive.

Figure 2 shows what happens when each group is able to contact 1000 prospects in each of the first 4 periods and after that the recruiting rate is fixed at 14 contacts per existing member. There is a slow, long-term "settling out" process in which organizational positions adjust. The most important differences observed here are:

1. 15 out of 40 organizations do not survive when contacting effects are taken into account.

2. Surviving organizations have fewer members (the average is 1140, compared against 1431.0) and the variance among their sizes is much greater (standard deviation is 635.8, compared against 301..4). Note these numbers exclude the 15 organizations whose membership level was 0 at time 1000.

3. Positions taken by surviving organizations are more compactly placed in the space. The average distance between positions in Figure 1 is 31.25, while it is 26.60 in Figure 2.

Result 2. Ecology matters.

The theme of this presentation is that individual level parameters are important, but this does not mean that structural/ecological characteristics are unimportant. On the basis of a good deal of experimentation with these simulation models, I feel comfortable with the conjecture that "carrying capacity" might be a meaningful concept. The number of citizens, and their characteristics, create a framework that will not support more than a certain number of interest organizations. The individual level characteristics of the citizens determine the carrying capacity of the environment as it is experienced by the interest group recruiters.

One piece of evidence for the claim that there is such a thing as "carrying capacity" can be found by varying the number of interest organizations that are created in the model. When the number is small, below the capacity, all organizations survive. When the number exceeds the capacity, organizations are "weeded-out." We saw an example of that phenomenon in the previous section, and futher evidence can be seen in Figure 3. This figure shows what happens when the identical set of initial conditions is used in a model that starts with 60 organizations. When there are 60 organizations crowded into the space, the weed-out takes longer, but after 1000 time steps the interest group positions are not dramatically different from those seen in Figure 2.

The individual prospect's budget is an important factor that affects the carrying capacity and the aggregate environment experienced by the recruiters. A number of variations have been explored. Consider these two. First, suppose each citizen has a budget that allows them to join two interest organizations. The effect is shown in Figure 4, shows a simulation that is identical in every way with the one depected in Figure 2, except now each citizen has a budget of 2. The difference between the two is somewhat stark. When the budget is set at 1, the organizations at the periphery of the space are gradually squeezed out. In Figure 4, all 40 organizations survive, meaning the carrying capacity has been raised. There is another significant difference, however. The policy stances of the organizations are closer to the center (and closer to each other). The organizations with positions in the periphery of the space are not weeded out when the citizens have higher budgets for political action. Rather, the citizens participate and draw their positions into the center.

Second, observe what happens when bias is introduced to create spatially-related inequality. In Figure 5, all citizens with ideal points above 65 on both dimensions--that means the bottom right portion of the policy space display--are given budgets of 5 while all of the other citizens have budgets of 1. The effect is subtle, but noticeable when compared against Figure 2. In Figure 2, only organization 13, which attracted 450 members while offering position (70.4,67.0), has a position more extreme than (65,65). When citizens above 65 have a higher budget, by contrast, organizations 12, 13, 21, 30 have positions that extreme (21 and 13 are hidden). These organizations have a combined membership of 696. The effect of the bias in the budget is not confined strictly to the region more extreme than (65,65). There is a slight cascade effect, as organizations are drawn into the vacuum that these organizations leave behind.

Result 3. A Change in the number of spaces makes a big difference.

It seems undoubtedly true that some interest groups take positions across a broad range of issues while others focus their attention on just one. Simulation allows us some opportunity to explore different ideas about how organizational positions might be shaped over time.

Suppose there are 6 separate policy spaces, each is two dimensional. In the first four spaces, citizen preferences are distributed according to the same law that was used in the previous figures, i.e., the citizen ideal points are distributed Normally with a mean of 50 and standard deviation of 20. There is no correlation between spaces, which means that finding a citizen is in the top-left on one space has absolutely no implication for the position that citizen might take on the other spaces. In the following figures, these spaces are numbered 0, 1, 2, and 3.

In the next 2 spaces, my small tribute to the bimodal "sugarscape" (Epstein and Axtell, 1996) can be found. The ideal points are distributed in two "clumps" or "hills". One hill has a peak at the coordinates (30,30) and the other is at (70,70). These hills are created by assigning each citizen an "ideology" value, either 30 or 70, and adding to it a draw from a Normal distribution with a mean of zero and a standard deviation of 10. Then the x and y coordinates for the citizen's ideal point are determined by adding to the ideology variable a additional draws from the Normal distribution with a standard deviation of 10. The same ideology value is used in creating the two clumps of ideal points, so there is some correlation of preferences across these two spaces, since people in the "top left" hill in one are also likely to be located somewhere in the top left hill in the other.

Organizations can adopt or eliminate positions they take in each space. The simulations described here suppose that the current members of an organization have a say about what stances it takes. This is implemented by these rules.

1. In each time period, the organization revises its position on all spaces where it currently takes a position. The revision adopts the median of the member ideal point on each subdivision taken separately, taking into account only the members who have an opinion about that space.

2. For each space on which the organization does not currently take a position, the members are offered a chance to adopt a position at the median of the ideal points. If a majority of all members support the adoption of a policy, then the organization takes a position at that point. The people who do not have an opinion about a space are thus counted as "no" votes.

3. For each space on which the organization currently takes a position, the members are offered a chance to replace that position with nil. The members who do not have an opinion about this do not vote.

In Figure 6, there is a simulation with 40 recruiters and 100,000 citizens, all of whom have opinions about each of the spaces. The recruiters are assigned positions on all of the issue spaces according to the same random mechanism that creates citizens. There are some striking differences between this model and the model with a single space.

Perhaps the most striking difference is that the recruiter's positions do not exhibit the evenly-spaced pattern that is seen when there is only a single dimension. The failure of group positions to sort themselves evenly across the space is not due to a change in the nature of the citizens. In the first four spaces (labeled Policy Space 0 through 3), the citizen ideal points are distributed according to the exact same Normal random generator that was used in the previous simulations. Rather, the change is due to the fact that citizens have interests that reach across dimensions and they cannot so easily be sorted into homogeneous, isolated groupings. The recruiters have no way to stop citizens from joining their organizations, so a citizen who finds a recruiter's position on one space to be perfectly ideal may join and then exert influence to change policies in other spaces.

Another striking difference is the fact that membership levels do not settle down into a narrow range in the multidimensional model. Figure 6 extends for 500 periods, but even when the model runs for a much longer time frame, it does not exhibit the stability that is seen in figure

In the last two spaces shown in Figure 6, labeled 4 and 5, the recruiter positions are not a jumble. Rather, the policy stances of the organizations lie along the diagonal. The organizational positions are more strictly "ideological" than the citizens themselves.

Figure 6 includes a graph indicating the changes in spaces on which organizations take positions. After 500 time steps, the average organization has dropped and then added spaces about 8 times. This happens because, due to random fluctuations in membership interests, there are times at which a majority favors taking no position whatsoever, but membership turnover quickly reverses that decision. The average net number of changes is approximately 0.

Some variations on this theme yield valuable insight. First, suppose that the organizations are created as single-issue organizations, adopting a position in just one policy space. If all of the citizens have opinions on all of the spaces, the dynamic process leads quickly to a situation in which all organizations have adopted positions on most or all of the issues. The dynamics (not shown here) are not unlike the previous figure.

Something quite different happens, however, if the citizen interests are distributed more haphazardly. In the simulation depicted in Figure 7, the preferences are created according to the same laws that were used in the previous figure, except that each citizen will have an opinion on a space only 30 percent of the time. With that probability, the ideal points within the spaces are created according to the same logic used in the previous figure. This create a society that has a mixture of citizens with broad-based interests and single-issue (or no) interests. The expected percentage of citizens with no opinions whatsoever is 11 percent, while a very small .073 percent are expected to have opinions on all spaces.

The impact of the change in the density of citizen opinions is shows up clearly in the aggregates. Membership levels are lower, and fewer organizations survive.

One of the interesting insights from exploring this model is that the initial positions taken by the organizations have a significant long run impact on their membership levels. In Figure 8, a simulation in which each recruiter is created with a position on only one space is presented. As in the previous models, if a majority of members support adopting a positions in additional spaces, then the organization's stance becomes more broad based. Only a handful of organizations survive in this case. Organizations that initially take a stand in only one space have trouble because most people see them as average on most issues. Some organizations survive and branch out to take positions in other spaces, but some do not do so because there is not a majority of members who support taking on a new position.

In Figure 8, the placement of the organizational positions is particularly interesting because, on the last two dimensions, the organizational positions do not mirror the underlying distribution of citizens. Organization 15 holds the top-left "hill" by itself in policy space 04 while organization 11 is in a no-man's-land between the peaks in space 05.

Result 4. Recruiting Levels Matter

In the models described so far, the recruitment level is "pegged" at a multiple of the membership levels. In order to be more realistic, consider the following change. After a recruiting effort, the organizer looks at the response rate. If the response rate is extremely low, then the organization will lose money. In order to avoid this danger, the recruiter sets a "target" response rate below which the organization does not wish to drive the response rate.

The recruitment rate is adjusted as follows. All organizations have their recruiting multiplier--the number of contacts per current member--set at 14. When it is first founded, the organization finds many lively prospects. If the response rate is higher than the target, which is set at 2.2 percent for all organizations, then the recruitment multiplier is bumped up one-half unit. If the response rate is below 2.2, then the recruitment multiplier is reduced one-half unit. The minimum multiplier value is 1.

When the recruitment levels are adjusted in this way, there are some notable changes. For discussion purposes, consider Figure 9, which shows the full six dimensional model in which all 40 organizations begin with positions on all issues. Organizations that have initial low response go out of business more quickly than in the fixed recruitment rate models. As the organizations raise their recruitment rates, their membership rises to a saturation point, and then their membership levels fall off, and in the cases of surviving organizations, they rise again. An example of an organization with particularly wild, cyclic membership fluctuations is organization 24, which is highlighted in light gray. Organization 24 is highlighted in dark blue as an example of an organization whose membership 'burns brightly' and then it dies.

An agent-based model of interest group position-taking has been introduced and explored. It has been shown that aggregate level phenomena, such as the number of interest organizations and their political positions, may depend in a complicated way on our assumptions about the citizens and the way the individual recruiters go about their business. In particular, the information about organizations and the resources they have that allow them to join have a significant impact. Also, it has been shown that the nature of the policy universe--the number of separate policy spaces that make up the set of all possible political positions--can have a significant impact.

Some extensions of this model may deserve consideration. I have experimented with ways to model "intelligent" recruiters, group leaders that do not necessarily allow the group's policies to follow the will of the majority. Unfortunately, I've not found out much of interest. The "intelligent" recruiters, who search for policy positions by adaptive algorithms, are generally less fit than the majority dominated organizations I've described.

A second extension of the model concern the logic that leads to formation of organizations. In the models described so far, the recruiter has no initial membership base, but is created with an initial endowment of wealth with which it contacts prospective members. The current version of the computer code does not investigate the question of how these initial resources are gathered, but the introduction of foundations or other money granting entities would be well within its structure (see Walker, 1983). Given the ability to contact a number of citizens for a number of periods, the recruiter's initial support eventually stops and the recruiting level then depends on the number of people who are currently in the organization.

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