Caucuses in Collaborative Governance: The Effects of ...€¦ · Caucuses in Collaborative Governance: The Effects of Structure, Power, and Problem Complexity Taehyon Choi Ph.D. and

Caucuses in Collaborative Governance:

The Effects of Structure, Power, and Problem Complexity

Taehyon Choi

Ph.D.

and

Peter J. Robertson

Associate Professor

School of Policy, Planning, and Development

University of Southern California

Los Angeles, CA 90089-0626

Prepared for the

11th

National Public Management Research Conference

June, 2011

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Abstract

It is important to identify approaches that can be used to promote egalitarian decision processes

in which all stakeholders’ concerns and interests are given serious consideration in deliberations

regarding how best to address challenging social problems. One approach that has been used to

deal with the issues of problem complexity and power imbalance is to structure the collaborative

forum into smaller caucuses reflecting relatively distinct categories of issues and/or interests.

Despite their successful use in practice, a lack of research on this topic has precluded the

development of a good understanding of the conditions under which a caucus structure is likely

to be effective. The purpose of the present research is to contribute to the task of developing

theory pertinent to collaborative governance by exploring the effects of using a caucus structure

in a collaborative forum when problems are complex (i.e., considerable interdependence among

interests) and/or a power imbalance exists among participants. In particular, we used agent-

based modeling to examine the consequences of alternative caucus structure designs under

varying conditions of problem complexity and power imbalance. We evaluated the effects of the

different structures on various decision outcomes in an effort to better understand how the use of

caucuses may or may not enhance decision dynamics in a real-world collaborative governance

forum. The simulation results indicate that even when some caucuses’ autonomy is constrained

by a coordinating structure, the acceptability of the final decision may be higher than when there

is no such a restriction. This effect may be contingent on the number of caucuses into which a

forum is divided. The results also indicate that power-balancing decision rules within caucuses

are a key factor affecting the probability and speed of reaching agreement as well as the

acceptability of the decision. The analysis contributes to an understanding of collective decision-

making in the context of collaborative governance by identifying complex interactions among

caucus coordination structures, balance of power among decision-makers, and problem

complexity.

Keywords: collaborative forum, caucus structure, problem complexity, decision-making

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Collaborative governance generally refers to a group of interdependent stakeholders,

usually from multiple sectors, who work together to develop and implement policies to address a

complex, multi-faceted problem or situation (Robertson & Choi, forthcoming). Recent research

on collaborative governance has focused on the structures, processes, and contextual conditions

that facilitate and/or constrain collaborative dynamics among diverse participants (Ansell &

Gash, 2008; Bryson, Crosby, & Stone, 2006; Gray, 1997; Huxham & Vangen, 2005; Mandell,

1999). Collaborative governance is typically used to address complex rather than simple social

problems (Imperial, 2005; Moynihan, 2005; Weber & Khademian, 2008), which call for

collective solutions generated through collaborative decision-making among diverse stakeholders.

More complex issues typically require a more inclusive collaborative governance forum in order

to respond to pertinent political, financial, and informational needs (Feldman & Khademian,

2007; Olsson, Folke, & Hahn, 2004). As the size of the forum increases, however, participants

are likely to face greater difficulty making collective decisions. A key question for those

interested in developing effective collaborative governance systems is how to facilitate decision-

making dynamics among diverse stakeholders confronting complex problems.

A common concern about collaborative governance is that, despite inclusion of a broad

range of stakeholders, the decision process may still be dominated by the most powerful actors

and interests pertinent to the situation being addressed. For example, it is not unusual for

government agencies or large business firms to wield greater influence on the process than

citizens or community-based organizations; for wealthier land owners to have more impact than

the working poor; or for mainstream concerns to be given more weight than more fringe or

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radical perspectives. The goal of achieving consensus among participants can help to balance

their power, but those with more resources, information, legitimacy, and/or prestige have

considerable capacity to shape the consensus-building process in a direction that favors their

interests. Thus, it is important to identify approaches that can be used to promote egalitarian

decision processes in which all stakeholders’ concerns and interests are given serious

consideration in deliberations regarding how best to address the problem.

One approach that has been used to deal with the issues of problem complexity and

power imbalance is to structure the collaborative forum into smaller caucuses reflecting

relatively distinct categories of issues and/or interests. For example, in the Sacramento Water

Forum, stakeholders were grouped into four small caucuses reflecting the business interests,

environmental interests, public interests, and Sacramento water interests. This structure helped

stakeholders in each caucus to clarify their concerns and better understand the complex

environmental problem by working closely with a few stakeholders (Connick, 2006). Despite

their successful use in practice, a lack of research on this topic has precluded the development of

a good understanding of the conditions under which a caucus structure is likely to be effective.

When the interests involved in an issue are highly interdependent, for example, it is not clear that

dividing a forum into caucuses involving deliberation among a subset of the stakeholders will

enhance the decision process. Or, when efforts to reduce power imbalances among participants

are not made, it is not clear that the use of caucuses will have positive outcomes. More generally,

when a collaborative forum is divided into caucuses, each addressing some aspects of the issue

but not others, it is not clear how their separate deliberations and decisions should be integrated

into an overarching decision for the forum as a whole. In short, there is not yet a solid

theoretical or empirical basis for determining how best to create an effective caucus structure.

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The purpose of the present research is to contribute to the task of developing theory

pertinent to collaborative governance by exploring the effects of using a caucus structure in a

collaborative forum when problems are complex (i.e., considerable interdependence among

interests) and/or a power imbalance exists among participants. In particular, we use a novel

research method – computer simulation using agent-based modeling (ABM) – to examine the

consequences of alternative caucus structure designs under varying conditions of problem

complexity and power imbalance. Through an agent-based model, we performed a simulation in

which a real-world collaborative governance forum was represented conceptually in a virtual

world. Artificial agents representing diverse stakeholders tried to reach consensus on a decision

while operating according to a particular set of decision-making rules intended to reflect

alternative caucus structures. We evaluated the effects of the different structures on various

decision outcomes in an effort to better understand how the use of caucuses may or may not

enhance decision dynamics in a real-world collaborative governance forum.

In the first section below, we discuss some theoretical issues regarding the use of

caucuses in collaborative forums under varying conditions of problem complexity and power

imbalance. This information provides a foundation for developing a computational simulation

model of a collaborative forum, the details of which are provided in the next section where we

explain how the model was designed to reflect theoretical concepts and real-world practices

pertinent to collaborative governance. The simulation results and analyses are reported in the

following section, and the paper concludes with a discussion of the implications of these findings.

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Theoretical Issues

Problem Complexity and Caucus Structure

The use of caucuses to organize a collaborative forum raises the issue of finding an

effective institutional design to facilitate their coordination in order for the structure to actually

improve decision outcomes. While “getting the institutions right” in support of collaboration is a

difficult process (Ostrom, 1990: 14; Thomson & Perry, 2006: 24), there are some advantages to

using a caucus structure. First, given that the size of a collaborative forum tends to get larger

over time (Feldman & Khademian, 2007), use of a caucus structure can help keep the size of the

basic decision-making unit in the forum at a manageable level. Second, it can help to relieve

stakeholders of the burden of excessive epistemic labor. People have limitations in dealing with

complex information and sometimes do not even recognize their real interests (Innes & Booher,

2010). Thus, an institutional setting through which they can narrow and clarify their interest

areas can facilitate successful collaboration. Third, since information sharing and decision

making in large forums are often monopolized by a few people (Stasser, 2000), smaller groups

can help to insure that stakeholders have equal opportunity to express their interests and exercise

their influence on the collective process. The Sacramento Area Water Forum case demonstrates

that organizing stakeholders into a few independent caucuses can help them develop a better

understanding of the situation and their interests and ultimately reach an integrated consensus

(Connick, 2006; Connick & Innes, 2003).

Despite these positive expectations regarding the use of a caucus structure, an important

theoretical issue to be considered is the nature and effect of problem complexity in the context of

collaborative governance. Although complexity is often described in such terms as irreducibility,

connectedness, and a state between order and chaos (Page, 2011; Waldrop, 1992; Wolfram,

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2002), the concept itself is vague and consensus on its definition is lacking. In the public

management and policy literature, complex policy problems have been referred to as “wicked”

(Conklin, 2006; Rittel & Webber, 1973). Weber and Khademian (2008) identified three

characteristics of complex social problems, namely, that they are unstructured, cross-cutting, and

relentless. Whichever characteristics may be emphasized, a relevant characteristic of problem

complexity with regard to the use of a caucus structure in collaborative forums is that

components of a complex system are interconnected (Kauffman, 1995; Levinthal, 1997) and thus

cannot be totally disaggregated into independent subsystems.

The interdependence of the components of a complex system is a key feature of the social

problems typically faced by stakeholders in collaborative governance. Under high problem

complexity, the process of collaboration must take into account the fact that stakeholders’

interests are mutual in the sense that realization of one actor’s goals depends on another actor’s

actions (Thomson & Perry, 2006). In other words, one actor’s choices can be constrained by

another’s pursuit of self-interest, or one actor’s pursuit of self-interest can be achieved by

another interdependent actor’s choices. In this situation, whether multiple actors’ interests can be

realized simultaneously may depend on the degree of interconnectedness of their interests. This

mutuality of interest, reflecting the level of interconnectedness among components of the

problem, calls attention to the type of coordination structure used to manage these

interdependencies.

On one hand, if the degree of interconnectedness is high, such that all components are

interdependent with each other, the problem is inseparable and it would be useless to try to

disaggregate these components into different caucuses, since all stakeholders would need to

build an integrated cognitive map of the problem. Conversely, if the degree of interdependence is

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negligible, with components relatively independent from each other, there is no need for any

coordination among them. When there is a medium level of interconnection, a coordination

structure is necessary to deal with the need for compatibility among the interconnected parts. At

this point, however, there has not been sufficient empirical investigation of the relative

performance of different coordination mechanisms.

Thus, the question remains as to what kind of coordination mechanism would perform

best given a moderate degree of problem complexity. When a collaborative forum is structured

into caucuses each addressing one or more components of the problem, two basic rules of

coordination can be considered. One approach would be to coordinate the decisions made by

separate caucuses sequentially. Using this rule, a decision made by one caucus earlier than others

would be taken as a “given” such that subsequent decisions made by other caucuses would need

to be consistent with the first decision in those areas in which they are interdependent. Since

reaching agreement itself is often a valuable outcome in a collaborative forum, this coordination

rule essentially rewards a caucus for reaching consensus relatively quickly, in the sense that its

decision then constrains the viable solutions for other caucuses addressing other components of

the problem. The downside of this rule is that there is no other logical rationale for giving an

advantage to the fastest decision made, and the constraints it imposes on subsequent decisions

may undermine the overall quality of the integrated solution.

A second approach would be to give all caucuses an equal opportunity to reach a decision,

with a coordination mechanism being utilized only when decisions made by separate caucuses

are not compatible with each other in those areas where they are interdependent. In this case, all

caucuses would be given another opportunity to modify their decisions so as to make them

compatible with those of other caucuses. This approach is more consistent with the notion that

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collaborative governance reflects an egalitarian process in which all stakeholders are able to

influence the decision in the sense that an integrated solution would better reflect the interests of

all caucuses and stakeholders rather than being biased in the favor of those who managed to

reach agreement on how to address their part of the problem more quickly. The downside of this

rule is that, when problem complexity is high, it may be very difficult to reach an overarching

collective decision that successfully integrates the preferences of the separate caucuses. Given

the limitations of these two approaches, it may also be possible to consider a third type of rule

that reflects a compromise between the ease of reaching an integrated decision associated with

the first approach and the equity of an integrated decision associated with the second approach.

In any case, investigation of the effects of alternative institutional designs under varying

conditions of problem complexity can enhance our knowledge about how best to manage the

process of making effective decisions in a collaborative governance forum.

Power Imbalance and Decision-Making Rules

A prominent feature of collaborative forums as compared to traditional decision-making

mechanisms is their explicit or implicit pursuit of a relative balance of power among the multiple

stakeholders involved in the decision process. This balance of power can be established in at

least two ways. First, it can be designed in through the application of a decision-making rule,

such as a requirement for unanimity or supermajority, which serves to distribute relatively equal

voting power to all the stakeholders. Second, power can be balanced through mutual learning

processes that take place during the deliberations about the nature of the problem and potential

solutions. To the extent that stakeholders acknowledge each other’s interests and strive to find

mutually beneficial solutions based on a common cognitive ground, the negative effects of a

power imbalance can be mitigated.

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Despite their importance for creating an egalitarian decision context, theoretical issues

regarding the effects of decision-making rules that shape power dynamics in collaborative

forums have not been addressed much in the collaborative governance literature. In contrast, the

consequences of different decision-making rules have received considerable attention in other

fields, such as social choice and group research that has explored the effects of decision-making

rules on jury verdicts (cf. Ohtsubo, Miller, Hayashi, & Masuchi, 2004). Findings from that

research suggest that a unanimity rule supports the egalitarian orientation of collaborative

governance. For example, Kameda (1991) found that use of a majority rule shortened the

deliberation process and left those in the minority unsatisfied with the decision. In contrast, a

requirement for unanimity can facilitate a more thorough hearing of minority views in the course

of deliberation (Kameda, 1991; Mendelberg, 2002). According to Miller (1985) and Kaplan and

Miller (1987), the extreme opinions of participants – which would likely constitute a minority

perspective in a collaborative forum – had to be listened to under a unanimity rule, resulting in

compromises from other group members, whereas under a majority rule they could simply be

ignored.

This research sheds light on the theoretical issue of the effect of power imbalance in

collaborative forums and the practical question of how best to organize a forum to address power

dynamics. One implication of the research is that an important purpose of collaborative forums –

enabling minority opinions to be considered in the decision process – can be facilitated by the

use of a power-balancing decision-making rule such as a requirement for unanimity or

supermajority when reaching decisions. In the Sacramento Area Water Forum, for example, a

three-quarters (75%) voting rule was employed to help balance power among stakeholders within

caucuses (Connick, 2006). However, since the balance of power is also related to the probability

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of reaching consensus, the effect of such decision rules should be investigated in a broader

context. More specifically, a better understanding is needed as to whether organizing a

collaborative forum into small caucuses should be accompanied by decision rules that balance

power but might hamper consensus formation, and what institutional designs and decision rules

can be used to reduce this negative effect.

Design of the Computational Model

To explore the issues raised above, we employed an agent-based computational modeling

method. Given that the purpose of this study is to explore the relationships among caucus

structure, power balance, and problem complexity so as to contribute to theory-building on this

topic, agent-based modeling is an effective research tool. The merits of the method are manifold.

First, agent-based modeling is a tool for rigorous thought experiments (Levitt, 2004). One can

deduce propositions regarding the relationships among power, complexity, and decision-making

dynamics through thought experiments, but ABM provides a tool to do the same thing with

greater precision and breadth. When investigating a number of factors that simultaneously shape

relevant outcomes, ABM enables the researcher to investigate complex interactions among these

variables. Second, agent-based modeling allows researchers to conduct virtual experiments

(Harrison, Lin, Carroll, & Carley, 2007) by manipulating focal variables at different levels while

also controlling for the effects of other variables not of interest to the researcher. With the use of

a parsimonious experimental design, the causal relationships between variables of interest can be

clearly identified. Third, ABM is effective when research focuses on complex processes. Agent-

based models assume that complex social systems can be understood as emergent phenomena

resulting from local interactions among heterogeneous actors and basic rules that govern these

interactions (Arrow, McGrath, & Berdahl, 2000; Holland, 1995). Complex processes like the

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deliberative dynamics in a collaborative forum can be clearly modeled using ABM through a

precise specification of actors and rules. Finally, ABM is useful for exploring new areas of

research or to clarify research foci that have not been defined well by existing theories (Levitt,

2004). This last benefit is particularly relevant in this study.

Simulation Design

In this study, we developed an agent-based computational model of collective decision-

making in the context of collaborative governance. What the model tries to simulate is a

collaborative forum in which stakeholders with different interests make a collective decision

through the identification of a mutually acceptable alternative. When the problem is complex and

there are many stakeholders involved, a collaborative forum can be organized into smaller

subgroups (i.e., caucuses) for effective information sharing and decision-making regarding

particular components of the problem. However, when a collaborative decision structure is

organized into caucuses, interdependence among the issues the caucuses address results in the

need for some kind of central coordination mechanism that helps to integrate the decisions made

by the separate caucuses. The computational model developed for this study simulates this kind

of decision-making situation. Details of the simulation, including the definition of agents,

problem complexity, power balance, decision-making process, caucus structures, and the

experimental design, are described below.

Agents. Agents in the computational model were designed to represent participants in a

collaborative forum. Agents possessed a set of potential policy alternatives, each of which was

associated with a certain level of acceptability. A policy alternative was defined as an 8-digit

binary string (e.g., 1/0/0/1/1/1/0/0), with which 256 (i.e., 28) different policy alternatives can be

defined. All agents shared the same set of 256 alternatives, but the level of acceptability

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associated with each alternative varied across agents, to reflect the fact that agents represented

different constituent groups with different concerns and priorities. The level of acceptability

assigned to each alternative was extracted from a normal distribution with a mean of zero and

standard deviation of one. (The negative values in the distribution turned into the corresponding

positive values.) It was assumed that the acceptability of each alternative was known to agents

in advance, and agents were designed to act so as to reach a collective decision with a

sufficiently high level of acceptability.

Agents were designed to take the following actions. First, at the beginning of each

iteration of the decision process, they looked at their own set of alternatives and identified the

one with the highest acceptability score. Second, if and when their turn came to make a proposal

to the caucus, they proposed their preferred alternative. Third, they were designed to be learning

agents, such that when an alternative was proposed by another agent, they adjusted their own

level of acceptability of the proposed alternative to be more similar to the level of acceptability

of the agent proposing that alternative. The degree of adjustment was one tenth of the difference

between the two levels of acceptability. Finally, whenever a proposed alternative did not receive

sufficient support from a group of agents to be selected, this alternative was deleted from each

agent’s set of alternatives so that it was not proposed again at some point in the future.

Problem complexity. Problem complexity refers to a situation in which the components

of the problem a collaborative forum is attempting to resolve are interdependent with each other.

In other words, when the components are interconnected, the decision made with regards to one

part of the problem affects other parts of the problem as well. This interdependence among

problem components was defined as follows. Recall that each alternative was defined as an

eight-digit binary string. Let caucus A’s problem component be defined as PA = {p1-p8} and

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caucus B’s component defined as PB = {q1-q8}, with p and q denoting the eight dimensions of a

problem to which the alternatives correspond. First, a lack of interdependence meant that the PA

and PB are independent, such that caucus A and caucus B could each identify an acceptable

solution to their part of the problem without any need to coordinate their decisions. Second, a

low degree of complexity meant that p1 and q1 are interdependent such that p1 = q1, i.e., the

solutions selected by caucuses A and B had to match in the first dimension. Finally, a high

degree of complexity meant that p1 is interdependent with q1 and p2 with q2 such that p1 = q1 and

p2 = q2, i.e., the solutions selected by caucuses A and B had to match in the first two dimensions.

In short, greater complexity reflected greater interdependence and thus greater need to coordinate

the decisions made by caucuses on separate components of the problem.

Power balance. The balance of power among the agents was defined by four different

decision-making rules used in the simulation. First, under the unanimity rule, all agents

possessed the same level of power since the collective decision had to be made unanimously and

thus any agent could veto a decision. Second, under the balance rule, all agents again possessed

the same level of power (i.e., one vote), but a collective decision could be made when 75 percent

of the agents accepted a proposed alternative. So, for example, when a caucus consists of four

members, consent of three of them is sufficient to make a decision. Third, under the imbalance

rule, agents possessed different levels of power, but no single agent could monopolize the

decision. Under this rule, fewer than 75 percent of the agents could make a decision if the sum of

their power exceeds 75 percent.1 Finally, under the unilateral rule, a randomly selected agent

possessed sufficient power to be able to make a decision unilaterally.

1 Power level was randomly assigned to each agent from a uniform distribution ranging from one to two,

i.e., an agent could possess power greater than or equal to one but less than or equal to two. Each agent’s power was

independently determined. In a four-agent caucus, for example, it was viable for the members to have power levels

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Decision-making process. With agents, problems, and power defined as described above,

the following process was executed in the simulated collaborative caucuses. First, an agent was

randomly selected to propose an alternative, and it proposed the alternative in its set with the

highest level of acceptability. The random selection of agents was intended to approximate a

situation in which each participant had a procedurally equal opportunity to speak. The other

agents in the caucus then checked their own level of acceptability associated with the proposed

alternative, and adjusted it in the direction of the level of acceptability of the agent that proposed

it. This was intended to reflect a process of mutual adjustment and shared understanding that can

develop in a collaborative forum. Next, each agent indicated whether or not it accepted the

proposed alternative, with the threshold for acceptance set to 1.5 (one and a half standard

deviations above the mean, which means that only about 14% of the alternatives in an agent’s

alternative space would meet this criterion). In other words, an agent would agree to an

alternative only when its own level of acceptability for that alternative was 1.5 or greater.2

Finally, whether and when the agents in a caucus reached a collective decision was shaped by

one of the four decision-making rules described above. However, the overall process of

proposing and assessing alternatives, and integrating decisions made by separate caucuses,

unfolded in different ways as a function of the type of caucus structure in place, as described

below.

of 1.2, 1.8, 1.9, and 2.0, and a decision could be made when the sum of the power of those voting for a proposal

exceeded three (i.e., 75 percent of four). For example, if two members possessed power levels of 1.6 and 1.7 (the

sum of which is 3.3) and they agree on an alternative, this is enough for the caucus to make a decision. 2 This threshold was set to reflect the fact that 1) alternatives that satisfy all stakeholders are rare, and 2)

given the cost of participating in collaborative governance, the threshold should be relatively high. Generally

speaking, a simulation with a low threshold does not generate sufficiently different results across factors to be able

to identify clearly their effects on the outcomes. Conversely, a simulation with too high of a threshold results in too

few of the forums reaching consensus.

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Caucus structures. Three different caucus structures were defined in terms of the

coordination mechanism used to integrate the decisions of separate caucuses into a collective

decision for the collaborative forum as a whole. These structures were intended to represent

simplified idealizations of complex real world decision-making structures and practices. First,

we defined a “sequential coordination” structure in which potential conflict between caucus level

decisions was coordinated by the criterion of “which decision was made first.”3 In other words, if

caucus A reached consensus on their decision first, it constrained the subsequent decisions that

could be made by any other caucus. For example, under a low level of problem complexity, with

one interdependent dimension, if caucus A reached agreement on an alternative with p1 = 0,

caucus B could reach agreement only on an alternative with q1 = 0.

Second, we defined a “referee coordination” structure. A sequential coordination

structure may not be attractive since it tends to undermine the egalitarian nature of collaborative

governance by privileging one caucus over others. Thus, the referee coordination structure was

designed to ensure equality between the caucuses.4 In this structure, a virtual referee (maybe

analogous to an overarching workgroup that includes representatives from all caucuses) waited

for each caucus to reach an agreement on a proposed alternative for its problem component.

Once all caucuses reached an agreement, the referee checked the compatibility of their decisions

on any interdependent dimensions. If the decisions were compatible, they were accepted as is. If

not, the referee sent the decisions back to each caucus for them to repeat the decision-making

3 When more than one caucus reached agreement at the same time, one of them was randomly selected as

the first caucus. Also, note that there was no possibility of conflict between caucus level decisions when there was

no interdependence among the problem components. 4 The level of equality within caucuses is manipulated through the power-balancing decision rules

described above.

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process. This iterative routine continued until all caucuses’ decisions were compatible with each

other.

Finally, we defined a “rational coordination” structure. As in the referee coordination

structure, each caucus first reached agreement on an alternative for its problem component, and

then the referee checked the compatibility of these caucus decisions. If these decisions were not

all compatible with each other, the referee compared their acceptability levels, retained the

caucus decision with the highest acceptability, and sent the other(s) back to the relevant

caucus(es) with the stipulation that their subsequent decision has to be compatible with the one

that was retained. These caucuses then started the decision-making process again, taking into

account the constraint imposed by the referee.

Experimental design. Four independent variables were manipulated in the model. First,

the degree of problem complexity was defined at three levels: none, low, and high. Second, four

decision-making rules that created four conditions of power balance were designed: unanimity,

balance, imbalance, and unilateral. As the rule changes from unanimity to unilateral, fewer

agents can dominate the decision process. Given that the unanimity and balance rules are

accepted as legitimate in real world collaborations, the imbalance and unilateral rules are

included for comparison purposes. Third, three different caucus structures were examined:

sequential, referee, and rational. Finally, the number of caucuses was varied in three levels: two,

three, and four. In all conditions, there were four participants in each caucus.5

Because it would be too complex to analyze all four independent variables

simultaneously through ANOVA, we designed two different virtual experiments. Experiment 1

5 Whether or not a caucus could reach consensus became very sensitive to the number of participants in the

caucus as the number approached ten. The number of caucus participants used in this study was determined to obtain

statistically stable results.

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focused on the effect of different structures, interacting with the problem complexity and power

balance. The number of caucuses for this experiment was set at two. With these three

independent variables, a 3 (structure) x 3 (complexity) x 4 (balance) factorial design was

employed. One thousand virtual forums were randomly generated in each of the 36 conditions,

for a total of 36,000 forums.6 Three-way analysis of variance was employed to analyze the

virtual data generated by the simulation. Experiment 2 focused on the effect of the number of

caucuses, interacting with caucus structures and problem complexity.7 A 3 (the number) x 3

(structure) x 3 (complexity) factorial design was employed, with four thousand virtual forums

randomly generated in each of the 27 conditions.8

Four dependent variables were used to measure the results of the decision-making

process. First, success rate was defined as the percentage of collaborative forums in each

condition that reached an overall decision that integrated the decisions of their separate caucuses.

Second, time to decision was measured as the average number of iterations it took the successful

forums in each condition to make a decision.9 A third measure was the mean level of

acceptability (across agents) of an alternative chosen in a successful forum, averaged across the

successful forums in each condition. Finally, the standard deviation of the level of acceptability

(across agents) of the alternative chosen in a successful forum, averaged across successful

6 The sample size was determined to be large enough to ensure the stability of the statistics derived from

the simulation results. 7 Analysis of the results of Experiment 1 indicated that the effect of power balance was very

straightforward, without any interesting interactions with other variables. Thus, we decided to omit this variable

from Experiment 2 and focus on the other three variables. 8 The four thousand forums included one thousand of each of the four decision-making rules (unanimity,

balance, imbalance, and unilateral). 9 Note that this measure does not correspond precisely to the amount of time in the real world. Instead, the

number of iterations it takes before a proposed alternative is accepted by a caucus might be seen as representing the

length of the deliberation, or even the amount of effort required to reach agreement.

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forums in each condition, was used to measure the overall equity of the decision, with greater

variance indicating that the decision was less equitable.

Results

Experiment 1

In this section, we analyze the effect of caucus structure and its interactions with

decision-making rules and problem complexity. We report the simulation results according to the

four outcome measures: success in reaching consensus, time to decision, acceptability of the

decision, and equity of the decision.10

Success. Table 1 summarizes the means of success rate in reaching consensus in each of

the manipulation conditions. First, regarding the main effect of structure, a sequential

coordination structure recorded the highest success rate (66.26%), followed by a rational

structure (65.53%) and a referee structure (62.39%) (F = 74.63, p<.001). Second, success rate

was negatively related to the balance of power in decision-making rules. Success rate of the

unanimity rule (1.11%) and the balance rule (65.54%) were quite a bit lower than that of the

imbalance rule (92.62%) and the unilateral rule (99.63%) (F = 26695.94, p<.001). Finally,

success rate was also negatively related to the degree of complexity (F = 964.62, p<.001). All of

these patterns are compatible with what would be expected or has been found in previous

research. This compatibility demonstrates the basic external validity of the model in its essential

structure.

In addition to this congruence with what would be expected in the real world, a couple

other results here are notable. First, a referee coordination structure was related to the lowest

success rate except for under the unanimity rule, and it was also negatively sensitive to problem

10

All results were statistically significant unless explicitly identified below as non-significant.

19

complexity. In particular, the mean success rate fell considerably from low (65.85%) to high

interconnectedness (56.84%). The relatively high success rates of a sequential structure (66.26%)

and a rational structure (65.63%) indicate that some guidance that constrains caucuses’ degrees

of freedom when making decisions can be useful for building consensus. As discussed below, the

restrictions articulated in the sequential and rational structures did not necessarily result in lower

acceptability. Finally, stakeholders in real-world collaborative forums are likely to deal with

problems with high complexity and to make decisions using rules that help to achieve power

balanced (the unanimity and balance rules in this study). It is thus interesting to note that this

particular condition was the only one in which the simulated forums had a success rate of less

than 50 percent. All in all, these simulation results suggest that the difficulty of reaching

consensus may be attributable to issues of power balance and problem complexity.

---------------------------------

Insert Table 1 around here

---------------------------------

Time. The amount of time to decision required by successful forums was measured by

the number of iterations (of proposing alternatives) until consensus was reached. As shown in

Table 2, a sequential structure recorded the shortest time to reach consensus (8.02), followed by

a rational structure (9.64) and a referee structure (12.03) (F = 57.51, p < .001). More time was

necessary for forums using a decision rule with a greater balance of power (F = 2851.11, p

< .001). The effect of problem complexity was not statistically significant using a strict criterion

(F = 4.33, p = .013).11

In addition to these main effects, an interesting interaction pattern was

11

This result may seem surprising, as one might presume that more complex problems would require more

time to resolve. However, the epistemic effort needed to solve a complex problem may take place in two stages. The

first is an analysis of the problem and its differentiation into component parts that can be assigned to relevant

caucuses, whereas the second is the process of making decisions regarding those components separately while

recognizing their inherent interconnectedness. This model reflects only the second stage of this process, yet the

difficulty of the first stage may be the key reason why it would take more time to resolve a complex problem.

20

found between structure and complexity, although the statistical significance was rather small (F

= 8.73, p < .001). First, a referee structure required more time as the degree of complexity

increased (9.11, 12.15, 15.88). Second, a sequential structure required less time as the degree of

complexity increased (8.82, 8.46, 6.58). Third, a rational structure (10.34) required most time

under a low level of complexity. In short, all three structures showed different patterns of

interactions with problem complexity.

---------------------------------


---------------------------------

Acceptability. Table 3 summarizes the results regarding the level of acceptability of the

decisions. Regarding the main effect of structure, caucuses with a rational structure reached the

most acceptable collective decision (1.69), followed by a sequential structure (1.67) and a referee

structure (1.65). A referee structure, even though it allowed all caucuses to pursue their most

acceptable decisions, recorded the lowest acceptability. This result indicates that sub-

optimization of the components of a complex problem does not necessarily lead to optimization

at a more global level. As indicated above, guidance that restricts caucuses’ autonomy to some

degree might be able to generate a better integrated result. On the other hand, these differences

were not statistically significant (F = 4.20, p = .015), so structure may not be an important factor

determining the acceptability of the decision. The main effect of power balance on the

acceptability of the decision was positive (F = 1834. 27, p<.001), and it was the factor with the

strongest influence on level of acceptability. Complexity was negatively related to the

acceptability of the decision (F = 7.99, p<.001). The interactions between structure and both

power balance (F = 5.34, p < .001) and complexity (F = 3.15, p = .014) demonstrated weak

statistical significance and were simply consistent with the main effects of these factors.

21

---------------------------------


---------------------------------

Equity. In accordance with the small differences in acceptability across conditions, there

were no notable results regarding the equity of the decision. Table 4 summarizes these findings,

which indicate that the main effect of structure was statistically significant (F = 7.66, p < .001)

even though the practical effect was trivial. A referee structure recorded the highest equity,

which is to be expected considering the nature of the structure, which did not privilege any of the

caucuses in the decision process. There was no difference between the other two structures.

Furthermore, the interaction effects between structure and complexity (F = 3.07, p = .016) and

between structure and power balance (F = .96, p = .45) were insignificant. Overall, these results

suggest that the rule for making decisions is the sole factor that influences the levels of

acceptability and equity in this model.

---------------------------------


---------------------------------

Experiment 2

Through Experiment 1, the effects of different caucus structures were investigated.

Another important aspect of designing a collaborative forum into caucuses to cope with a

complex social problem is the question of how many caucuses to use. This decision is likely to

be related to, and maybe driven by, the scope and/or scale of the issue being addressed. As the

breadth of the problem increases, it is usually necessary to include more stakeholders in the

process, for political, financial, and informational reasons (Feldman & Khademian, 2007). With

more extensive involvement in the collaboration, it may be useful to organize the forum into a

larger number of caucuses. Therefore, in Experiment 2, we included forums with two, three, or

22

four caucuses and investigated how the number of caucuses interacted with caucus structure and

problem complexity to affect the four outcome variables.

Note that power was not included as a factor in this experiment. As indicated in the

previous section, greater power balance reduced the success rate and increased the time to

decision as well as the acceptability and equity of the decision. Furthermore, none of the

interactions between power balance and the other variables changed any of the patterns found in

the main effects of power. In short, because the main effects of power balance and its

interactions with caucus structure and problem complexity were very straightforward, our

analysis of the results of Experiment 2 focus on a three-way ANOVA among the number of

caucuses, caucus structure, and problem complexity.

In an effort to model social problems that would require use of more than two caucuses,

we specified the problems and levels of complexity differently in Experiment 2 that in the first

experiment. As in Experiment 1, a relatively simple problem was defined as an eight-digit binary

string, and the number of caucuses used in these forums was maintained at two. A broader

problem was defined as a ten-digit binary string, and forums addressing these were organized

into three caucuses. A twelve-digit binary string represented the broadest problems in our

analysis, and four caucuses were utilized in these forums. Since broader problems also tend to

be more complex, we adjusted the number of interdependent dimensions associated with low and

high levels of complexity. As in Experiment 1, low and high complexity were represented by one

and two interdependent dimensions, respectively, for an eight-digit problem. These numbers

increased to two and three for ten-digit problems and three and four for twelve-digit problems.

Table 5 summarizes the specification of the levels of complexity in forums with the different

numbers of caucuses.

23

---------------------------------


---------------------------------

Success. Table 6 summarizes the results regarding the rate of success in reaching

consensus. First, the use of more caucuses resulted in less success (F = 955.83, p < .001). In

addition, the results regarding structure in this experiment were consistent with those from

Experiment 1: sequential and rational structures performed better than the referee structure did.

The effect of the level of complexity was also statistically significant (F = 4719.51, p < .001),

demonstrating a negative relationship with success rate.

As for the interaction between number of caucuses and level of complexity, when there

was no interdependence, more caucuses resulted in a higher success rate. This result may reflect

the positive effect of having more alternatives to consider when there were more caucuses

working on a broader problem. Note that, by design, the number of alternatives available to the

agents increased along with the length of the binary digit strings used to define the problems they

addressed (8, 10, and 12 for 2, 3, and 4 caucuses, respectively). With this result providing a

baseline success rate in the absence of interdependence among caucuses, the results regarding

low and high complexity illustrate that greater interdependence leads to less success. In essence,

these findings illustrate that the positive effect of having more alternatives to consider can be

attenuated by the negative effect of increased problem complexity.

The results regarding the interaction between number of caucuses and type of

coordination structure show that, with a sequential or rational structure, there is not a lot of

variance as a function of the number of caucuses. In contrast, a referee structure was very

sensitive to the number of caucuses, with the success rate falling from 62.39 (two caucuses) to

33.39 (three caucuses) to 25.27 (four caucuses). Finally, the interaction between structure and

24

complexity was notable. A referee structure was very sensitive to the level of complexity,

dropping from 73.27 to 29.93 to 17.85 as the number of interdependent dimensions increased.

The sequential and rational structures were less sensitive to a change in the level of complexity

from none to low (73.16 to 70.17 for sequential and 73.17 to 66.07 for rational), but more

sensitive to a change from low to high complexity (70.17 to 53.63 for sequential and 66.07 to

52.64 for rational).

---------------------------------


---------------------------------

Time. Results concerning time taken to reach consensus are presented in Table 7. First,

the number of caucuses was associated with longer time to decision (9.86, 12.57, and 13.49; F =

315.56, p<.001). Second, the main effect of complexity was curvilinear (9.96, 12.90, and 9.97; F

= 386.48, p<.001). This finding suggests that the constraints imposed by some interdependence

among the components of a problem can increase the time required to find a solution. Beyond a

certain point, however, too much interdependence may exclude too many alternatives from

consideration, with the unintentional effect of reducing the time required to identify a mutually-

acceptable solution. Third, the main effect of structure demonstrated the same pattern as in

Experiment 1. Consensus formation was fastest in a sequential structure (9.19) and slowest in a

referee structure (12.23). However, this pattern varied a bit depending on the number of caucuses.

In particular, the time required in sequential and rational structures increased along with the

number of caucuses, whereas this was a curvilinear relationship in the referee structure. The

interaction between structure and complexity demonstrated an irregular pattern. First, the overall

curvilinear effect of the level of interdependence did not hold for the referee structure. Instead,

the time required to reach consensus continued to increase along with the amount of complexity

25

(9.97, 15.45, and 16.12). Furthermore, using a sequential structure, the amount of time decreased

significantly between low (10.35) and high (6.74) levels of complexity. Only the rational

structure showed the strong curvilinear relationship demonstrated by the main effect of

complexity (10.03, 14.45, and 11.18 for no, low, and high interdependence, respectively).

---------------------------------


---------------------------------

Acceptability. Findings from the analysis pertaining to acceptability of the decision are

provided in Table 8. First, the use of more caucuses served to increase the acceptability of the

decisions made by these forums (F = 923.13, p < .001). This may point to a key benefit of

organizing a large collaborative forum into smaller caucuses. Considering the interaction effect

between the number of caucuses and problem complexity, the results clearly show that using

more caucuses is a good strategy when there is a low level of interdependence. Second, the main

effect of increased complexity was a decrease in the acceptability of the decision (F = 1135.82, p

< .001). Finally, and consistent with the results from Experiment 1, the rational (1.78) and

sequential (1.77) structures performed slightly better than a referee structure (1.76). These

differences were fairly trivial even though they were statistically significant (F = 41.90, p < .001).

However, it is notable that, while a referee structure performed worst in the two-caucus

collaborations, it performed best in three- and four-caucus forums. This result suggests that the

positive effect of imposing constraints on caucuses in the decision process may yield decreasing

returns as the number of caucuses increases, ultimately being outperformed by a structure that

does not entail these constraints. Overall, these results may indicate that 1) dividing stakeholders

into more caucuses according to the size of the problem may enhance acceptability of the

decision, but that 2) the positive effect of doing so may be mitigated by the negative effect of

26

greater problem complexity and 3) constraining guidance might reduce acceptability as the

number of caucuses goes up.

---------------------------------


---------------------------------

Equity. Finally, Table 9 summarizes the results for equity of the decision. Looking at the

main effects, decision equity decreased as the number of caucuses increased (.89, .99, and 1.09

for two, three, and four caucuses, respectively). The level of complexity was positively related to

equity (1.04, .95, and .92 for no, low, and high complexity, respectively). Although statistically

significant (F = 82.28, p < .001), the main effect of structure on the equity of the decision was

practically trivial. In contrast, the interaction between the number of caucuses and the level of

complexity was notable. With only two caucuses, the difference between high complexity and no

complexity was only .03 (.88 versus .91, respectively), yet that difference increased to .15 (1.00

versus 1.15) when four caucuses were used. However, these results should be interpreted

cautiously. In the absence of any complexity, caucuses could essentially act independently when

making their decisions. So this condition could result in greater inequity, i.e., higher variance in

the level of acceptability across participants, since there was no constraint on their decision that

would reduce this variance. In the same vein, a referee system, which resulted in a high level of

acceptability, also yielded high variance when there were four caucuses. These results share a

similar interpretation, that the more acceptable a decision is, the less equitable it is likely to be.

Overall, a greater number of caucuses results in more acceptable decisions with higher variance

in its level of acceptability.

---------------------------------


---------------------------------

27

Discussion

A rationale for using collaborative governance despite the political, social, and cognitive

costs involved in the process (Innes & Booher, 2010; Termeer, 2009) is that more egalitarian

decisions are expected from the process than from hierarchical or judicial decision-making,

through the participation of diverse actors who bring varied knowledge, resources, and

alternatives to the process (Feldman & Khademian, 2007). This inclusive approach, however,

inevitably increases the size of these decision forums, which in turn readily increases the number

of challenges likely to arise involving the structure of the forum and the division of cognitive

labor among participants. In this study, we modeled the effects of different types and numbers of

caucuses, power balance through decision-making rules, and problem complexity defined in

terms of interdependence of issues. We explored the effects of these factors on rate of success in

reaching a decision, time (i.e., number of iterations) required to make a decision, and the

acceptability and equity of the collective decision. In this section, we provide a comprehensive

summary of the results and discuss their theoretical and practical implications.

Summary of the Results

Structure. We simulated three different caucus structures. What is eminent in the results

is that some guidance or leadership constraining the caucuses’ decision-making autonomy can be

beneficial to the whole collaborative system. Specifically, a sequential coordination structure and

a rational coordination structure performed well across all four measures of performance. While

the former gives advantage to a lead caucus that made its own decision more quickly, the latter

gives advantage to a lead caucus that made a decision with the highest level of acceptability to its

participants. The sophistication of the rational structure also resulted in greater collective

acceptability of the system-level decision, except under the limited condition in which there were

28

three or four caucuses using a referee structure. These results highlight the importance of some

kind of central coordinator – or what might be thought of as facilitative leadership – when a

caucus structure is used in a collaborative decision-making. A caveat is that such a role,

manifested in the form of constraining some caucuses’ autonomy, may not be as effective as the

number of caucuses grows.

Whether timing or acceptability of a caucus’ decision should serve as a basis for

constraining other caucuses’ decision may depend on the criteria being used to assess the

performance of the collaborative forum. Our results suggest that giving preference to those who

make their decisions more quickly can facilitate the process of reaching consensus, as both

success rate and time to decision were better in the sequential structure. While the decisions

made in this structure had lower levels of acceptability and equity when there were only two

caucuses, this was not the case when there were four caucuses and acceptability levels equaled

those of the rational structure. In other words, the benefits of the sequential structure grew along

with the number of caucuses.

Despite its high performance, a sequential coordination structure runs counter to the

egalitarian ideal of collaborative governance by giving preference to one caucus versus the

others. Thus we included the use of a referee structure that was designed to ensure equality

between caucuses by not imposing constraints on any of their decisions. Overall, this structure

did not demonstrate very good performance. The decision success rate was consistently lowest

among the three structures, and was particularly sensitive to the number of caucuses and problem

complexity. Since this structure also took the most time to make a decision, this kind of “laissez-

faire” approach may not be the most appropriate when it is critical that the collaborative forum

reach some kind of consensus. For that matter, the referee structure did not usually result in

29

better acceptability or equity of the decisions made. Only as the number of caucuses increased

was the acceptability of decisions made in these structures higher than those made in the other

structures.

In summary, the simulation results indicate that ensuring caucus level autonomy and

equality may not result in the best outcomes at the system level. Depending on what is most

important to the collaborative, broadening the consensus or increasing decision acceptability,

structures that impose some constraints on the process may result in desirable outcomes at the

system level.

Power balance. The results regarding the effects of decision-making rules used to

balance power among caucus participants were straightforward. Power imbalances made it

easier to reach a decision, and power balances led to greater acceptability of the decisions made.

A comparison of the size of the effects of the four independent variables clearly shows that the

decision-making rule in use was the most powerful factor determining the performance of these

collaborative forums. An obvious implication of these results is that, if the major purpose of

using a caucus structure is to help ensure that all interests have the opportunity to be heard

through effective and egalitarian deliberation processes, an effective way to do this is to utilize

decision-making rules that prevent a coalition of interests from being able to dominate those with

minority perspectives.

Problem complexity. Problem complexity is usually expected to add difficulty to

collective decision-making processes. Our simulation results for the most part confirm this

expectation. Problem complexity was negatively related to decision success rate and

acceptability, and these relationships were not moderated by any other variables considered in

the model. In contrast, problem complexity was positively related to decision equity, or the

30

variance of acceptability across participants. However, this result does not necessarily reflect a

positive outcome in more practical terms. When taking into account the negative effect on

acceptability, the lower variance here essentially means “equity by leveling down.” Finally, the

effect of problem complexity on time taken to reach a decision was not consistent across

structures or the number of caucuses simulated. Overall, the simulation model generated results

consistent with what could be readily anticipated concerning the consequences of problem

complexity regarding consensus success rate and acceptability, with less straightforward results

regarding equity and time.

Number of caucuses. Regardless of structure, the use of more caucuses resulted in a

lower success rate, longer time to decision, higher acceptability, and lower equity. This result

raises a question about the usefulness of dividing a collaborative forum into many small caucuses.

On one hand, a structure that is too fragmented would likely incur greater transaction costs to

coordinate their decisions, which can be inferred from the difficulty these forums had in reaching

a decision. On the other hand, despite this difficulty, the results suggest that participants in

successful forums with a larger number of caucuses may be more satisfied with the collective

decision ultimately made. This finding is consistent with the premise that dividing stakeholders

into smaller groups of common interests would better serve each of their interests in the context

of collaborative governance (Innes & Booher, 2010). A caveat here is that the positive effect of

more caucuses on decision acceptability diminished significantly as problem complexity

increased. This suggests a dilemma: problem complexity provides some motivation to organize a

collaborative forum into a number of small caucuses, but use of this strategy may not have the

expected benefits in terms of facilitating the decision process.

31

Implications

The simulation results provide tentative theoretical and practical answers to relevant

questions about how to structure a collaborative forum. In this section, we raise those questions

and provide possible answers based on the findings from the simulation.

Does problem complexity affect the performance of different structures? When the

problem is complex, what structure is best? The effect of the structure is contingent on problem

complexity. When a decision is divided into components with interdependent dimensions, this

condition will generally reduce the probability of reaching agreement as well as the acceptability

of the decision, regardless of the type of coordination structure utilized. Given the general

negative effect of problem complexity, a coordination structure with a central authority may save

time in reaching a decision when there is high interdependence, while not necessarily sacrificing

the acceptability of the decision or the likelihood of success.

Should power be balanced when using a caucus structure? Power (im)balance created

through the use of a decision-making rule is a key factor affecting the probability and speed of

reaching agreement and the acceptability of the decision. The design of the coordinating

structure used may not significantly moderate the overarching effect of these decision-making

rules. Therefore, if a collaborative forum desires to make an egalitarian decision in terms of both

process and substance, power should be balanced within caucuses regardless of which caucus

structure is used.

Should we care about the design of a caucus structure? The balance of power might be

the single most important factor the leaders of a collaborative forum would want to care about.

Balanced caucuses generate more acceptable decisions, but they have a harder time reaching

consensus the necessary consensus. The particular type of caucus structure used may not modify

32

very much the effects of power balance. However, this does not mean that caucus structure does

not matter. To the extent that the egalitarian nature of collaboration should be respected, efforts

to design an appropriate structure may need to focus not so much on improving decision

acceptability as on attenuating the negative effects of power-balancing decision rules on the

consensus formation process.

In summary, we can extract a few practical implications from our findings. First, it is

important to employ a power-balancing rule to fulfill the purpose of collaborative governance –

an egalitarian and mutually-beneficial solution-finding process. To overcome the low

probability of reaching consensus under a power-balancing rule, leaders should consider other

tools such as caucus structure and varying the number of caucuses. In this case, giving an

advantage to one caucus and constraining others’ autonomy could be beneficial to the forum as a

whole. Our simulation results indicated that even when some caucuses’ autonomy is constrained

by a coordinating structure, the acceptability of the final decision may be higher than when there

is no such a restriction. This conclusion runs counter to what may be a more common notion,

that constraints imposed on a decision process would likely result in an inferior solution. One

possible explanation is that this model simulated the collective decision-making process after

participants had accrued enough knowledge about viable alternatives and their payoffs. That is,

they had implicitly passed through an education phase of collaborative governance (Innes &

Booher, 2010), in which mutual learning takes place that is often an important factor enabling

successful collaboration. Further investigation of this issue in a real-world context certainly

seems warranted. Finally, when utilizing some form of coordination mechanism that puts

constraints on the decision process, the number of caucuses in the forum should be taken into

33

account. The benefits from constraining their autonomy could disappear quickly as the number

of caucuses increases.

Conclusion

Combining agent-based modeling with constructs from real-world practices in

collaborative governance, this study explored the effects of different caucus structures in

collaborative decision-making forums. The analysis contributes to an understanding of collective

decision-making in this context by identifying complex interactions among caucus coordination

structures, balance of power among decision-makers, and problem complexity. In addition to

exploring interactions among these factors, which have not been the focus of much public

management research, we evaluated their effects by considering four different outcome measures:

success rate in reaching a decision, time taken to reach a decision, acceptability of the decision,

and equity of the decision. In short, we tried to explore some important themes relevant to the

successful organization of a collaborative forum, and to gain insights into the relative strengths

and weaknesses of alternative structuring principles contingent on problem complexity and

performance evaluation criteria. The conclusions we have drawn from our findings can be

understood as tentative hypotheses, and empirical evidence is now needed to determine whether

or not they are valid in the real world. Despite its limitations, this study contributes to a call for

greater theoretical attention to the organization of collaborative forums and a systemic

understanding of the effects of potential managerial tools in this context.

34

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36

Tables

Table 1. Success rate

Structure

Power sequential referee rational Power mean none low high

unanimity 1.30 1.03 1.00 1.11 1.50 1.20 .63

balance 69.27 60.97 66.40 65.54 85.87 67.47 43.30

imbalance 94.50 88.60 94.77 92.62 98.60 94.77 84.50

unilateral 99.97 98.97 99.97 99.63 100.00 99.97 98.93

Complexity sequential referee rational Complexity mean

none 71.60 71.30 71.57 71.49

low 67.38 63.97 66.20 65.85

high 59.80 51.90 58.82 56.84

Structure mean 66.26 62.39 65.53 Note. Numbers are means.

Table 2. Time to decision

Structure


unanimity 17.77 24.55 27.30 22.73 25.00 24.03 14.89

balance 15.42 19.72 18.36 17.74 17.01 18.91 17.38

imbalance 6.99 11.44 8.76 9.01 7.36 9.46 10.45

unilateral 3.75 7.68 4.50 5.30 3.51 5.09 7.34


none 8.82 9.11 9.08 9.00

low 8.46 12.15 10.34 10.29

high 6.58 15.88 9.53 10.43


37

Table 3. Acceptability

Structure


unanimity 2.03 1.97 1.98 2.00 2.02 1.96 2.03

balance 1.78 1.79 1.80 1.79 1.81 1.78 1.78

imbalance 1.68 1.67 1.70 1.68 1.72 1.68 1.65

unilateral 1.57 1.55 1.60 1.58 1.61 1.58 1.54


none 1.71 1.70 1.71 1.71

low 1.66 1.65 1.70 1.67

high 1.62 1.58 1.67 1.63


Table 4. Equity of the decision

Structure


unanimity .47 .40 .44 .44 .44 .42 .49

balance .76 .74 .75 .75 .77 .74 .74

imbalance .91 .89 .90 .90 .92 .90 .88

unilateral .99 .96 .99 .98 .99 .96 .99


none .91 .9 .91 .91

low .89 .88 .89 .89

high .89 .85 .89 .88

Structure mean .90 .88 .90 Note. Numbers are means.

38

Table 5. Manipulation of the number of caucuses and the level of complexity

None Low High

2 caucuses 0/8 1/8 2/8

3 caucuses 0/10 2/10 3/10

4 caucuses 0/12 3/12 4/12

Note. The numerator in each cell indicates the number of interconnected dimensions. The denominator indicates the

length of a problem string.

Table 6. Success rate Structure

Number sequential referee rational Caucus mean none low high

2 caucuses 66.26 62.39 65.53 64.73 71.49 65.85 56.84

3 caucuses 65.75 33.39 63.57 54.24 73.64 53.76 35.31

4 caucuses 64.95 25.27 62.77 51.00 74.46 46.56 31.98


none 73.16 73.27 73.17 73.20

low 70.17 29.93 66.07 55.39

high 53.63 17.85 52.64 41.38


Table 7. Time to decision

Structure

Number sequential referee rational Caucus mean none low high

2 caucuses 8.02 12.03 9.64 9.86 9.00 10.29 10.43

3 caucuses 9.41 13.70 12.57 11.53 10.25 14.58 9.55

4 caucuses 10.14 10.80 13.49 11.62 10.58 14.66 9.62


None 9.87 9.97 10.03 9.96

Low 10.35 15.45 14.45 12.90

High 6.74 16.12 11.18 9.97


39

Table 8. Acceptability of the decision

Structure

Number sequential referee rational Caucus mean none low High

2 caucuses 1.67 1.65 1.69 1.67 1.71 1.67 1.63

3 caucuses 1.77 1.81 1.78 1.78 1.85 1.77 1.67

4 caucuses 1.86 1.97 1.86 1.88 1.97 1.86 1.69


None 1.84 1.84 1.84 1.84

Low 1.77 1.67 1.79 1.76

High 1.66 1.59 1.67 1.65


Table 9. Equity of the decision

Structure

Number sequential referee rational Caucus mean none low High

2 caucuses .90 .88 .90 .89 .91 .89 .88

3 caucuses .99 1.01 .97 .99 1.03 .96 .94

4 caucuses 1.09 1.15 1.06 1.09 1.15 1.04 1.00


None 1.03 1.03 1.04 1.03

Low .97 .90 .95 .95

High .96 .86 .92 .93

Structure mean .99 .97 .98 Note. Numbers are means.

Documents

Caucuses in Collaborative Governance: The Effects of ...€¦ · Caucuses in Collaborative Governance: The Effects of Structure, Power, and Problem Complexity Taehyon Choi Ph.D. and