Collective Intelligence and its Implementation on
`the Web: algorithms to develop a collective
`mental map
`
`Francis HEYLIGHEN*
`
`Center “Leo Apostel”, Free University of Brussels
`
`Address: Krijgskundestraat 33, B-1160 Brussels, Belgium
`E-mail: fheyligh@vub.ac.be
`home page: http://pespmc1.vub.ac.be/HEYL.html
`
`ABSTRACT.
`
`Collective intelligence is defined as the ability of a group to solve more
`problems than its individual members. It is argued that the obstacles
`created by individual cognitive limits and the difficulty of coordination
`can be overcome by using a collective mental map (CMM). A CMM is
`defined as an external memory with shared read/write access, that rep-
`resents problem states, actions and preferences for actions. It can be
`formalized as a weighted, directed graph. The creation of a network of
`pheromone trails by ant colonies points us to some basic mechanisms of
`CMM development: averaging of individual preferences, amplification
`of weak links by positive feedback, and integration of specialised sub-
`networks through division of labor. Similar mechanisms can be used to
`transform the World-Wide Web into a CMM, by supplementing it with
`weighted links. Two types of algorithms are explored: 1) the co-occur-
`rence of links in web pages or user selections can be used to compute a
`matrix of
`link strengths,
`thus generalizing
`the
`technique of
`“collaborative filtering”; 2) learning web rules extract information from
`a user’s sequential path through the web in order to change link
`strengths and create new links. The resulting weighted web can be used
`to facilitate problem-solving by suggesting related links to the user, or,
`more powerfully, by supporting a software agent that discovers relevant
`documents through spreading activation.
`
`1. Introduction
`
`With the growing interest in complex adaptive systems, artificial life, swarms and simu-
`lated societies, the concept of “collective intelligence” is coming more and more to the
`fore. The basic idea is that a group of individuals (e.g. people, insects, robots, or soft-
`ware agents) can be smart in a way that none of its members is. Complex, apparently in-
`telligent behavior may emerge from the synergy created by simple interactions between
`individuals that follow simple rules.
`
`* Research Associate FWO (Fund for Scientific Research-Flanders)
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`To be more accurate we can define intelligence as the ability to solve problems. A sys-
`tem is more intelligent than another system if in a given time interval it can solve more
`problems, or find better solutions to the same problems. A group can then be said to ex-
`hibit collective intelligence if it can find more or better solutions than the whole of all so-
`lutions that would be found by its members working individually.
`
`1.1. Examples of collective intelligence
`All organizations, whether they be firms, institutions or sporting teams, are created on the
`assumption that their members can do more together than they could do alone. Yet, most
`organizations have a hierarchical structure, with one individual at the top directing the ac-
`tivities of the other individuals at the levels below. Although no president, chief executive
`or general can oversee or control all the tasks performed by different individuals in a
`complex organization, one might still suspect that the intelligence of the organization is
`somehow merely a reflection or extension of the intelligence of its hierarchical head.
`This is no longer the case in small, closely interacting groups such as soccer or foot-
`ball teams, where the “captain” rarely gives orders to the other team members. The
`movements and tactics that emerge during a soccer match are not controlled by a single
`individual, but result from complex sequences of interactions. Still, they are simple
`enough for an individual to comprehend, and since soccer players are intrinsically intelli-
`gent individuals, it may appear that the team is not really more intelligent than its mem-
`bers.
`Things are very different in the world of social insects (Bonabeau et al. 1997;
`Bonabeau & Theraulaz 1994). The way that ants map out their environment, that bees
`decide which flower fields to exploit, or that termites build complex mounds, may create
`the impression that these are quite intelligent creatures. The opposite is true. Individual in-
`sects have extremely limited information processing capacities. Yet, the ant nest, bee hive
`or termite mound as a collective can cope with very complex situations.
`What social insects lack in individual capabilities, they seem to make up by their sheer
`numbers. In that respect, an insect collective behaves like the self-organizing systems
`studied in physics and chemistry (Bonabeau et al. 1997): very large numbers of simple
`components interacting locally produce global organization and adaptation. In human so-
`ciety, such self-organization can be found in the “invisible hand” of the market mecha-
`nism. The market is very efficient in allocating the factors of production so as to create a
`balance between supply and demand (cf. Heylighen 1997). Centralized planning of the
`economy to ensure the same balanced distribution would be confronted with a “calculation
`problem” so complex that it would surpass the capacity of any information processing
`system. Yet, an efficient market requires its participating agents to follow only the most
`simple rules. Simulations have shown that even markets with “zero intelligence” traders
`manage to reach equilibrium quite quickly (Gode & Sunder 1993).
`The examples we discussed show relatively low collective intelligence emerging from
`highly intelligent individual behavior (football teams) or high collective intelligence
`emerging from “dumb” individual behavior (insect societies and markets). The obvious
`question is whether high collective intelligence can also emerge from high individual in-
`telligence. Achieving this is everything but obvious, though. The difficulty is perhaps
`best illustrated by the frustration most people experience with committees and meetings.
`Bring a number of very competent people together in a room in order to devise a plan of
`action, tackle a problem or reach a decision. Yet, the result you get is rarely much better
`than the result you would have got if the different participants had tackled the problem
`individually. Although committees are obviously important and useful, in practice it
`appears difficult for them to realize their full potential. Let us therefore consider some of
`the main impediments to the emergence of collective intelligence in human groups.
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`1.2. Obstacles to collective intelligence
`First, however competent the participants, their individual intelligence is still limited, and
`this imposes a fundamental restriction on their ability to cooperate. Although an expert in
`his own field, Mr. Smith may be incapable to understand the approach proposed by Ms.
`Jones, whose expertise is different. Even if we assume that Mr. Smith would be able to
`grasp all the ramifications and details of Ms. Jones’s proposal, he probably would still
`misunderstand what she is saying, simply because he interprets the words she uses in a
`different way than the one she intended. Both verbal and non-verbal communication are
`notoriously fuzzy, noisy and dependent on the context or frame of reference. Even if
`everyone would perfectly understand everyone else, many important suggestions during a
`meeting would never be followed up. In spite of note taking, no group is able to
`completely memorize all the issues that have been discussed.
`Another recurrent problem is that people tend to play power games. Everybody would
`like to be recognized as the smartest or most important person in the group, and is there-
`fore inclined to dismiss any opinion different from his or her own. Such power games
`often end up with the establishment of a “pecking order”, where the one at the top can
`criticize everyone, while the one at the bottom can criticize no one. The result is that the
`people at the bottom are rarely ever paid attention to, however smart their suggestions.
`This constant competition to make one’s voice heard is exacerbated by the fact that
`linguistic communication is sequential: in a meeting, only one person can speak at a time.
`It seems that the problem might be tackled by splitting up the committee into small
`groups. Instead of a single speaker centrally directing the proceedings, the activities might
`now go on in parallel, thus allowing many more aspects to be discussed simultaneously.
`However, now a new problem arises: that of coordination. To tackle a problem collec-
`tively, the different subgroups must keep close contact. This implies a constant exchange
`of information so that the different groups would know what the others are doing, and
`can use each other’s results. But this again creates a great information load, taxing both
`the communication channels and the individual cognitive systems that must process all
`this incoming information. Such load only becomes larger as the number of participants
`or groups increases.
`For problems of information transmission, storage and processing, computer tech-
`nologies may come to the rescue. This has led to the creation of the field of Computer-
`Supported Cooperative Work (CSCW) (see e.g. Smith 1994), which aims at the design
`of Groupware or “Group Decision Support Systems”. CSCW systems can alleviate many
`of the problems we enumerated. By letting participants communicate anonymously via the
`system it can even tackle the problem of pecking order, so that all contributions get an
`even opportunity to be considered. However, CSCW systems are typically developed for
`small groups. They are not designed to support self-organizing collectives that involve
`thousands or millions of individuals.
`But there is a technology which can connect those millions: the global computer net-
`work. Although communities on the Internet appear to self-organize more efficiently than
`communities that do not use computers, the network seems merely to have accelerated
`existing social processes. As yet, it does not provide any active support for collective in-
`telligence. The present paper will investigate how such a support could be achieved, first
`by analysing the mechanisms through which collective intelligence emerges in other sys-
`tems, then by discussing how available technologies can be extended to implement such
`mechanisms on the network.
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`2. Collective Problem-Solving
`
`To better understand collective intelligence we must first analyse intelligence in general,
`that is, the ability to solve problems. A problem can be defined as a difference between
`the present situation, as perceived by some agent, and the situation desired by that agent.
`Problem-solving then means finding a sequence of actions that will transform the present
`state via a number of intermediate states into a goal state. Of course, there does not need
`to be a single, well-defined goal: the agent’s “goal” might be simply to get into any
`situation that is more pleasant, interesting or amusing than the present one. The only
`requirement is that the agent can distinguish between subjectively “better” (preferred) and
`“worse” situations (Heylighen 1988, 1990).
`To generalize this definition of a problem for a collective consisting of several agents it
`suffices to aggregate the desires of the different agents into a collective preference and
`their perceptions of the present situation into a collective perception. In economic terms,
`the aggregate desire becomes the market “demand” and the aggregate perception of the
`present situation becomes the “supply” (Heylighen, 1997). It must be noted, though, that
`what is preferable for an individual member is not necessarily what is preferable for a
`collective (Heylighen & Campbell, 1995): in general, a collective has emergent properties
`that cannot be reduced to mere sums of individual properties. (Therefore, the aggregation
`mechanism will need to have a non-linear component.) In section 3, we will discuss in
`more detail how such an aggregation mechanism might work.
`On way to solve a problem is by trial-and-error in the real world: just try out some
`action and see whether it brings about the desired effect. Such an approach is obviously
`inefficient for all but the most trivial problems. Intelligence is characterised by the fact that
`this exploration of possible actions takes place mentally, so that actions can be selected or
`rejected “inside one’s head”, before executing them in reality. The more efficient this
`mental exploration, that is, the less trial-and-error needed to find the solution, the more
`intelligent the problem-solver.
`
`2.1. Mental maps
`The efficiency of mental problem-solving depends on the way the problem is represented
`inside the cognitive system (Heylighen 1988, 1990). Representations typically consist of
`the following components: a set of problem states, a set of possible actions, and a
`preference function or “fitness” criterion for selecting the most adequate actions. The
`fitness criterion, of course, will vary with the specific goals or preferences of the agent.
`Even for a given preference, though, there are many ways to decompose a problem into
`states and actions. Changing the way a problem is represented, by considering different
`distinctions between the different features of a problem situation, may make an unsolvable
`problem trivial, or the other way around (Heylighen 1988, 1990).
`Actions can be represented as operators or transitions that map one state onto another
`one. A state that can be reached from another state by a single action can be seen as a
`neighbor of that state. Thus, the set of actions induces a topological structure on the set of
`states, transforming it into a problem space. The simplest model of such a space is a net-
`work, where the states correspond to the nodes of the network, and the actions to the
`edges or links that connect the nodes. The selection criterion, finally, can be represented
`by a preference function that attaches a particular weight to each link. This problem
`representation can be seen as the agent’s mental map of its problem environment.
`A mental map can be formalized as a weighted, directed graph M = {N, L, P},
`where N = {n1, n2, ..., nm} is the set of nodes, L (cid:204) N ·
` N is the set of links, and
`P: L fi
` [0, 1], is the preference function. A problem solution then is a connected path
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`C = (c1, ..., ck) (cid:204) N such that c1 is the initial state, ck is a goal state, and for all
`i ˛
` {1, ..., k }: (ci, ci+1) ˛ L .
`To solve a problem, you need a general heuristic or search algorithm, that is, a method
`for selecting a sequence of actions that is likely to lead as quickly as possible to the goal.
`If we assume that the agent has only a local awareness of the mental map, that is, that the
`agent can only evaluate actions and states that are directly connected to the present state,
`then the most basic heuristic it can use is some form of “hill-climbing” with backtracking.
`This heuristic works as follows: from the present state choose the link with the highest
`weight that has not been tried out yet to reach a new state; if all links have already been
`tried, backtrack to a state visited earlier which still has an untried link; repeat this
`procedure until a goal state has been reached or until all available links have been
`exhausted. The efficiency of this method will obviously depend on how well the nodes,
`links and preference function reflect the actual possibilities and constraints in the
`environment.
`The better the map, the more easily problems will be solved. Intelligent agents, then,
`are characterized by the quality of their mental maps, that is, by the knowledge and under-
`standing they have of their environment, their own capacities for action, and their goals.
`Increasing problem-solving ability will generally require two complementary processes:
`1) enlarging the map with additional states and actions, so that until now unimagined op-
`tions become reachable; 2) improving the preference function, so that the increase in total
`options is counterbalanced by a greater selectivity in the options that need to be explored
`to solve a given problem.
`
`2.2. Coordinating individual problem-solutions
`Let us apply this conceptual framework to collective problem-solving. Imagine a group of
`individuals trying to solve a problem together. Each individual can explore his or her own
`mental map in order to come up with a sequence of actions that constitutes part of the
`solution. It would then seem sufficient to combine these partial solutions into an overall
`solution. Assuming that the individuals are similar (e.g. all human beings or all ants), and
`that they live in the same environment, we may expect their mental maps to be similar as
`well. However, mental maps are not objective reflections of the real world “out there”:
`they are individual constructions, based on subjective preferences and experiences (cf.
`Heylighen 1999). Therefore, the maps will also be to an important degree different.
`This diversity is healthy, since it means that different individuals may complement
`each others’ weaknesses. Imagine that each individual would have exactly the same men-
`tal map. In that case, they would all find the same solutions in the same way, and little
`could be gained by a collective effort. (In the best case, the problem could be factorized
`into independent subproblems, which would then be divided among the participating in-
`dividuals. This would merely speed up the problem-solving process, though; it would not
`produce any novel solutions).
`Imagine now that each individual would have a different mental map. In that case, in-
`dividuals would need to communicate not only the (partial) solutions they have found, but
`the relevant parts of their mental maps as well, since a solution only makes sense within a
`given problem representation. This requires a very powerful medium for information ex-
`change, capable of transmitting a map of a complex problem domain. Moreover, it re-
`quires plenty of excess cognitive resources from the individuals who receive the trans-
`missions, since they would need to parse and store dozens of mental maps in addition to
`their own. Since an individual’s mental map reflects that individual’s total knowledge,
`gathered during a lifetime of experience, it seems very unlikely that such excess process-
`ing and storage capacity would be available. If it were, this would mean that the individ-
`ual has used only a fraction of his or her capacities for cognition, and this implies an in-
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`dividual who is very inexperienced or simply stupid. Finally, even if individuals could
`effectively communicate their views, there is no obvious mechanism to resolve the
`conflicts that would arise if their proposals contradict each other. It seems that we have
`come back to our problem where we have intelligent individuals but a dumb collective.
`Let us see whether investigations of existing intelligent collectives can help us to over-
`come this problem of coordination between individuals.
`
`Stigmergy
`2.3.
`While studying the way termites build their mounds, the French entomologist Pierre
`Grassé (1959) discovered an important mechanism, which he called “stigmergy”. He ob-
`served that at first different termites seem to drop mud more or less randomly. However,
`the presence of a heap of mud incites other termites to add mud to that heap, rather than
`start a heap of their own. The larger the heap, the more attractive it is to further termites.
`Thus, the small heaps will be abandoned, while the larger ones will grow into tall
`columns. Since the bias to add mud in those places where the concentration of mud is
`highest continues, the columns moreover have a tendency to grow towards each other,
`until they touch. This produces an arch, which will itself grow until it touches other
`arches. The end result is an intricate, cathedral-like structure of interlocking arches.
`This is obviously an example of collective intelligence. The individual termites follow
`extremely simple rules, and have no memory of either their own or other individual’s ac-
`tions. Yet, collectively they manage to coordinate their efforts so as to produce a complex,
`seemingly well-designed structure. The trick is that they coordinate their actions without
`direct termite-to-termite communication. The only “communication” is indirect: the mud
`left by one termite provides a signal for other termites to continue work on that mud.
`Thus, the term stigmergy, whose Greek components mean “mark” (stigma) and “work”
`(ergon).
`The fundamental mechanism here is that the environment is used as a shared medium
`for storing information so that it can be interpreted by other individuals. Unlike a message
`(e.g. a spoken communication) which is directed at a particular individual at a particular
`time, a stigmergic signal can be picked up by any individual at any time. A spoken mes-
`sage that does not reach its addressee, or is not understood, is lost forever. A stigmergic
`signal, on the other hand, remains, storing information in a stable medium that is acces-
`sible by everyone.
`The philosopher Pierre Lévy (1997) has proposed a related concept to understand
`collective intelligence, that of a shared “object”. For example, a typical object is the ball in
`a soccer game. Soccer players rarely need to communicate directly, e.g. by shouting di-
`rections at each other. Their activities are coordinated because they are all focused on the
`position and movement of the ball. The state of the ball incites them to execute particular
`actions, e.g. running toward the ball, passing it to another player, or having a shot at the
`goal. Thus, the ball functions as a stigmergic signal, albeit a much more dynamic one than
`the mud used by termites. Another typical “object” discussed by Lévy (1997) is money. It
`is the price, i.e. the amount of money you get for a particular good, which incites pro-
`ducers to supply either more or less of that good. Thus, money is the external signal
`which allows the different actors in the market to coordinate their actions (cf. Heylighen
`1997).
`The difference between Lévy’s “object” and Grassé’s stigmergic signal, perhaps, is
`that the former changes its state constantly, while the latter is relatively stable, accumulat-
`ing changes over the long term. The stigmergic signal functions like a long-term memory
`for the group, while the object functions like a working memory, whose changing state
`represents the present situation. In fact, you do not even need an external object to hold
`this information. The soccer players are not only influenced by the position and move-
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`ment of the ball, but also by the position and movement of the other players. This per-
`ceived state of the collective functions as a shared signal that coordinates the actions of the
`collective’s members. The coordinated actions exhibited by the individuals in a swarm
`(flocks of birds, shoals of fish, herds of sheep, etc.) are similarly based on a “real-time”
`reaction to the perceived state of the other individuals.
`
`2.4. Collective Mental Maps
`In the examples of stigmergy or shared objects we discussed until now, the problem-
`solving actions seem to be purely physical: amassing mud, kicking a ball towards the
`goal, producing goods. We might wonder whether stigmergy could also be used to sup-
`port problem-solving on the mental plane, where sequences of actions are first planned in
`the abstract before they are executed in reality. Again, insect societies can provide us with
`a most instructive example. Ants that come back from a food source to their nest leave a
`trail of chemical signals, pheromones, along their path. Ants that explore the surround-
`ings, looking for food, are more likely to follow a path with a strong pheromone scent. If
`this path leads them to a food source, they will come back along that path while adding
`more pheromone to the trail. Thus, trails that lead to sources with plenty of food are con-
`stantly reinforced, while trails that lead to exhausted sources will quickly evaporate.
`Imagine two parallel trails, A and B, leading to the same source. At first, an individual
`ant is as likely to choose A as it is to choose B. So, on average there will be as many ants
`leaving the nest through A as through B. Let us assume that path B is a little shorter than
`A. In that case, the ants that followed B will come back to the nest with food a little more
`quickly. Thus, the pheromones on B will be reinforced more quickly than those on A,
`and the trail will become relatively stronger. This will entice more ants to set out on B
`rather than A, further reinforcing the gains of B relative to A. Eventually, because of this
`positive feedback, the longer path A will be abandoned, while the shorter path B will at-
`tract all the traffic. Thus, the ants are constantly tracing and updating an intricate network
`of trails which indicate the most efficient ways to reach different food sources. Individual
`ants do not need to keep the locations of the different sources in memory, since the
`collectively developed trail network will always be there to guide them.
`This example may seem similar to the mud collecting termites. The difference is that
`the ants leaving pheromone are not making any physical contribution to the solution of
`their problem (collecting food), unlike the termites whose actions directly contribute to the
`mound building. They are merely providing the collective with a map to guide them
`through the terrain. In fact, the trail network functions like an external mental map, which
`is used and updated by all ants. We will call such an exteriorized, shared, cognitive
`system a collective mental map (CMM). Let us investigate this concept in more detail.
`A collective mental map functions first of all as a shared memory. Various discoveries
`by members of the collective are registered and stored in this memory, so that the infor-
`mation will remain available for as long as necessary. The storage capacity of this mem-
`ory is in general much larger than the capacities of the memories of the individual partici-
`pants. This is because the shared memory can potentially be inscribed over the whole of
`the physical surroundings, instead of being limited to a single, spatially localized nervous
`system. Thus, a collective mental map differs from cultural knowledge, such as the
`knowledge of a language or a religion, which is shared among different individuals in a
`cultural group but is limited by the amount of knowledge a single individual can bear in
`mind.
`In human evolution, the first step towards the development of a CMM was the inven-
`tion of writing. This allowed the storage of an unlimited amount of information outside of
`individuals brains. Unlike a real CMM, however, the information in books is shared only
`to a limited extent. Not all books can be accessed by all individuals. This was particularly
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`true before the invention of printing, when only a few copies of any given book existed in
`the world. Although libraries now provide a much wider access for people wishing to
`read books, there is still a very limited access for writing books. Although everybody
`could in principle write a book, very few books actually get published in such a way that
`they become accessible to a large number of people.
`In a CMM, such as the ants’ trail network, on the other hand, all individuals can
`equally contribute to the shared memory. They can in particular build on each others’
`achievements by elaborating, reinforcing or providing alternatives for part of the stored
`information. Books, on the other hand, are largely stand-alone pieces of knowledge, with
`very limited cross-references. It would be very difficult for me to take an existing book
`and start commenting, correcting or reinforcing on its content. If I want to add to the state
`of the art, I would rather need to write and publish a book from scratch, a very difficult
`and time-consuming affair.
`The need for a universally and dynamically shared memory has been well understood
`by researchers in Computer-Supported Cooperative Work (e.g. Smith 1994). Discussions
`over a CSCW system will typically keep a complete trace of everything that has been said,
`which can be consulted by all participants, and to which all participants can at any
`moment add personal annotations. This collective register of activities is often called a
`shared “blackboard”, “white board” or “workspace”. However, a record of all
`communications does not yet constitute a mental map. The more people participate in a
`discussion and the longer it lasts, the more the record will grow, and the more difficult it
`will become to distil any useful guidelines for action out of it. Of course, you can allow
`the participants to edit the record and erase notes that are no longer relevant, as you would
`do with scribbles on a blackboard. But this again presupposes that the participants would
`have a complete grasp of all the information that is explicitly or implicitly contained in the
`record. And that means that the size of the “controlled” content of the blackboard cannot
`grow beyond the cognitive capacities of an individual. This obviously makes the shared
`blackboard a poor model for an eventual Internet-based support for collective intelligence.
`A mental map is not merely a registry of events or an edited collection of notes, it is a
`highly selective representation of features relevant to problem-solving. The pheromone
`network does not record all movements made by all ants: it only registers those collective
`movements that are likely to help solve the ants’ main problem, finding food. A mental
`map consists of problem states, possible actions that lead from one state to another, and a
`preference function for choosing the best action at any moment. These are all implicit in
`the pheromone network: a particular patch of trail can be seen simultaneously as a location
`or problem state, as an action linking to other locations, and as a preference, measured by
`the concentration of pheromone, for that action over other available actions. As it is clear
`that a CMM cannot be developed by merely registering and editing individual contribu-
`tions, we will need to study different methods to collectively develop a mental map.
`
`3. Mechanisms of CMM Development
`
`3.1. Averaging preferences
`Probably the most basic method for reaching collective decisions and avoiding conflicts is
`voting. This method assumes that all options are known by all individuals, and that the
`remaining question is to determine their aggregate preference. In the simplest case, every
`individual has one vote, which is given to the options that this individual prefers above all
`others. Adding all the votes together determines the relative preferences of the different
`alternatives for actions. (Usually, after a vote only the highest scoring option is kept, but
`this is not relevant for our model, where all options remain available). This is to some
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`degree similar to the functioning of ant colonies, where the pheromone trail left by a
`particular ant can be seen as that ant’s “vote” in the discussion of where best to find food.
`In a more sophisticated version of the voting mechanism, individuals can distribute
`their voting power over different alternatives, in proportion to their individual preference
`functions. For example, alternative A might get a vote of 0.5, B 0.3, C 0.2 and D 0.0. In
`that case, the collective preference function Pcol becomes simply an average of the n indi-
`vidual preference functions Pi:
`
`(1)
`
`Pcol(l j ) = 1
`n
`
`n(cid:229)
`i=1
`
`Pi
`
`(l j ) = 1
`n
`
`n(cid:229)
`i=1
`
`i
`p j
`
`Johnson’s (1998; see also Johnson et al. 1998) simulation of collective problem-solving
`illustrates the power of this intrinsically simple averaging procedure. In the simulation, a
`number of agents try to find a route through a “maze”, from a fixed initial position to a
`fixed goal position. The maze consists of nodes randomly connected by links. In a first
`phase, the agents “learn” the layout of the maze by exploring it in a random order until
`they reach the goal. They do this by building up a preference function which attaches a
`weight to every link in the network they tried, but such that the last link used (before
`exiting the maze) in any given node gets the highest weight. In a second, “application”
`phase, they use this