Comprehending uncertainty in fitness landscape modeling for
collective decision-making
Peter Marks & Lasse Gerrits
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Why modeling fitness landscapes?
Originating in evolutionary biology, fitness landscapes have been developed as graph-theoretical
representations of the reproduction success of genotypes, i.e. the fitness or replication rate of
particular genotypes. Kauffman introduced the simple formal model called the NK-model (e.g.
Kauffman & Levin, 1987; Kauffman & Weinberger, 1989; Kauffman, 1993), in which N genes
interact K with each other. In its most basic form the fitness of the genotype is just the sum of the N
independent fitness contributions divided by N (Kauffman, 1993: 41). However, in a system with N
genes most often the fitness contribution of one gene is depending on the other N – 1 genes. In
three-dimensional representations, see figure 1, the distance between genotypes, i.e. whether they
are more or less similar or very different, and the interactions between the genotypes define the
fitness in the landscape, which is represented by the height in the landscape.
Figure 1: Examples of fitness landscapes (single-peaked and rugged) from Levithal & Warglien (1999)
Fitness landscapes have been adopted and adapted to the social sciences to suit a wide variety of
purposes (see Gerrits & Marks (2013a) for an extensive survey on the uses of fitness landscapes).
The allure of using fitness landscapes in the social sciences is two-fold. First, it allows the
researcher to explore the relationships between actors, strategies, interactions and outcomes in
different configurations. Second, it provides a relatively accessible way to present the results and
conclusive narratives to readers (Gerrits & Marks, 2013b). The number of applications of fitness
landscapes to issues in public administration and public policy are relatively small in comparison to
for instance economics and organization and management sciences. This suggests that there is an
opportunity for the deployment of fitness landscapes to analyze persistent issues in our domain.
The current research project aims to develop and operationalize a three-dimensional fitness
landscape in such a way that it allows the mapping and analysis of real-world cases of collective
decision-making. This particular paper focuses on the modeling process itself and how we dealt
with issues such as model uncertainty and measurement during that process. In other words, the
paper features in two lines of reasoning; the first concerns the development of a fitness landscape
model for collective decision-making, the second concerns our reflection on the modeling process
itself and the ways we dealt with requisites and uncertainty in our modeling attempt. We will
present our considerations and will illustrate them using a case study.
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1.1
From modes of inquiry to modeling
In Gerrits & Marks (2013a) we conducted a literature survey on the interpretations and
applications of fitness landscapes in the social and behavioral sciences. We identified 162 relevant
sources, which we categorized in six more or less common different modes of inquiry. These are:
metaphors, sense-making, modeling, simulations, theorizing and mapping cases. For each mode we
identified the advantages and drawbacks. For example, while metaphors are necessarily vague, they
are powerful tools for story-telling (e.g. Plutynski, 2008). Conversely, modeling methods are strong
on operationalization but are usually weak on external validity. The six different modes can be
found to diverging, perhaps even contradicting. This ostensible lack of coherence can be
understood in terms of Althusser’s classification of social theories into Generalities II and
Generalities III (1969). In short, Generalities II concerns conceptual approaches that inform the way
a certain phenomenon can be understood and explained. Generalities III concerns theories as
provisional end-products that generate substantive claims that can be falsified. As such, the two
kinds of theories inform each other. One needs the testable hypotheses to uncover causal
relationships and the proverbial dictionary to explain the patterns that were found. This
classification helps understanding how diverging approaches can co-exist in a theory under
development (Gerrits & Marks, 2013b). In modeling the fitness landscape for the current research,
we will borrow from the existing approaches identified in Gerrits & Marks (2013a) in order to
further our argument.
1.2
Modeling requisites
One recurring theme in using fitness landscapes in research is the trade-off between generality and
specificity. Models that are not very specific and that use broad categories and ambiguously
operationalized variables tend to be easier to model and allow for efficient communication. Such
models serve primarily as heuristic devices because what they lack in specificity in fact helps them
to further a more generalized narrative, e.g. that cooperation will lead to improved fitness. Models
that try to capture case-specific dynamics are much more difficult to model because they require an
unambiguous operationalization of variables that should remain measurable under different
circumstances. While such models may lack the engaging narratives because of the many nuances
build into them, they offer more analytical depth and more accurate representation of social reality.
The trade-off between generality and specificity matters because one of the main issues in
fitness landscape modeling is whether such models can be generalized to the extent that they can
account for all variation. For example, in Altenberg (1995; 1996) extended the model into a
generalized version which can provide any number of elements and any number of functions in
biology. This generalized NK-model allows the number of fitness components to differ from the
number of genes, and allows genes to be added to the genome while keeping the set of fitness
components fixed. In our modeling process we have yet to discover the possibilities of a generalized
model for understanding collective decision-making without the pitfalls of generating clichés. This
results from the self-imposed limitation that the model should be able to process real-world data in
a meaningful way. Inevitably, this means that the model is tailor-made to suit case-specific
conditions. If we understand real-world cases as the conjunction of generic patterns and
idiosyncratic (i.e. local in place and temporal in time) events (e.g. Byrne, 2011; Gerrits, 2012;
Gerrits & Verweij, 2013; Verweij & Gerrits, 2013), it follows that a model rooted in such a situation
bears with it the specifics of the case.
Initially, we were held back in our modeling process because of the condition that the model
should be able to process real-world data. The review in Gerrits & Marks (2013a) shows that in
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instances where the fitness landscape was actually modeled, as opposed to just mentioned, they
were most often not calibrated or validated using real-world data. Arguably, this provides a shortcut because the modeler doesn’t need to consider the measurability of items in the real world or the
collection of empirical data when modeling. We couldn’t satisfy ourselves with such an approach
and understood that the ability to process real-world data was a requisite to the model we
envisaged. In other words: we wanted to build a model that accounts for the complexity of realworld cases.
Following this point of departure, we drafted four additional requisites besides the already
mentioned requisite of (1) processing real-world data. We also wanted the model (2) to allow for
unambiguous measurement, (3) to account for all possible combinations on the grid, (4) to be able
to uncover persistent patterns, and (5) to be not too simplified or generic to generate the obvious
without additional depth. These five requisites imply that modeling fitness landscapes is not just
about mathematical elegance but that external validity is as important as is internal validity. From
external validity follows that the model should be based on qualitative cases, which closes the circle
because such types of cases hold the key to uncover generic patterns and idiosyncratic events. We
find it important to lay out these requisites because each modeling iteration was tested against
them.
In our modeling attempt we used mathematical expressions to keep ourselves away from
approximate formulations and vagueness. As such, the mathematical expressions are used as a
heuristic to further our thinking, but we will not end with a mathematical model because that
would undermine our requisites for modeling fitness landscapes, as will become clear in the
remainder of the text.
1.3
Case Fyra
As our approach requires a qualitative case, we selected the Dutch Fyra high-speed train case as an
illustration for the modeling process. For this purpose, we focus on the tendering and operation of
the high-speed railway link and the problems with the V250 trains. We draw our data from 650
newspaper articles published in Dutch national newspapers and collected through the LexisNexis
database. A full list of all documents is available from the authors upon request. For this paper we
are mainly interested in the modeling process so the case serves as an illustration of our
considerations and will not be fully analyzed.
The origins of the plan to build and operate a high-speed railway link between Amsterdam
and Paris date back to the mid-1980s. The first section between Amsterdam and Rotterdam was
completed in September 2009 but it took longer before the connection with Belgium was made. A
tendering process favored operator NS Hispeed1 over competitors such as Deutsche Bahn. Once
track building was completed, NS Hispeed was unable to run the promised service because it had
yet to receive certified trains. Nevertheless, it launched the service under the brand of ‘Fyra’. In
reality the Fyra was not a high-speed train service but a make-shift service with leased locomotives
and second-hand carriages that could not run at high speeds. Meanwhile, there were severe
problems with the delivery of the new V250 train sets from Italian manufacturer AnsaldoBreda. An
extensive testing period started once the first new train sets were manufactured and delivered.
These tests revealed many major issues with the sets, including problems with the train protection
system and the software. This delayed the acceptance trials and certification from the Ministry of
Transport once again. When the trains were finally found fit to run late 2012, they were withdrawn
We use the brand name of the operator, i.e. NS Hispeed. However, the winning consortium was initially
named High Speed Alliance or HSA because the Royal Dutch Airline company had a 10% share in the
operation, next to NS as the main shareholder. NS Hispeed is now the common name to denote HSA.
1
3
from service after a few months because of persistent problems with the technology and build
quality. As of spring 2013, NS Hispeed attempts to restart its Fyra service again using the leased
locomotives and carriages used earlier.
2
Modeling a three-dimensional landscape for visualization
As is obvious from the previous section, fitness landscapes come in many shapes. No matter what
way they are used, the visual representation of fitness landscapes has a convincing nature. This
visualization puts forward a concise, quick and convincing picture of the dynamics of the decisionmaking process. However, a three-dimensional fitness landscape is limited to two variables
whereas mathematically fitness landscapes can be extended to any amount of variables, but they
will lose their visual persuasive powers. Regardless, we choose to first model a three-dimensional
landscape as a first attempt to explore what the model should entail and where its explanatory
power lies. In this process we have to define the N & K and the fit that is produced by them.
2.1
Problem-and-solution combinations
In our initial thinking about which two variables would form the basis for the x and y-axis in the
visual representation, we focused on the question which process could be measured in real-world
cases, e.g. exploitation vs. exploration (Becker, Knudsen, & Stieglitz, 2006; Bocanet & Ponsiglione,
2012), or search strategies (Baumann & Siggelkow, 2012). However, the biological fitness
landscape model is quite clear in the N being a substantive gene, in other words: content; and the K
is interaction between genes, in other words: process. This made us define two measurable
variables of which one is about content and the other about processes (requisite 1, 2 & 3).
Collective decision-making, as the term implies, concerns two or more ‘competing’ actors.
As such, public decision-making is a subset of collective decision-making. Collective decisionmaking could cover for instance a married couple deciding about whether to go out at night or not
but also the interaction between several governmental organizations that want to make a certain
city district safer. Decision-making here means that n actors have ideas about the issue they are
concerned with. This means that as modelers we have discerned the issues on which collective
decisions are reached.
The content variable builds on the idea that issues resolve around two idea categories that
actors have about the issue. Firstly, actors have certain perceptions about what the issue really is
about, i.e. issues are perceived and framed in certain ways creating actor-specific problem
definitions. Secondly, actors have certain specific ideas about the way their problem definition
should be dealt with, i.e. they formulate their own specific solution definition. We use the
abbreviation ‘PSC’ to denote the specific problem-and-solution combination as used by each actor.
Actors make decisions based on the prevailing PSC. Consequently, PSC’s provide us with a core
variable N that is represented on the x-axis of the visualization.
Problem
definition
PSC
Solution
definition
4
As can be observed in practices of collective decision-making, problem definitions and
solution definition are often completely intertwined (see e.g. Parsons, 1995 for an extensive
discussion; John, 1999). When engaging in decision-making, actors may share certain problem and
solution definitions while disagreeing on others. Following Kingdon (1984), solution definitions
may precede and perhaps even determine problem definitions. This is exemplified in the Fyra case
where the solution definition, i.e. running a high-speed railway service at relatively short intervals,
preceded the problem definition. The latter was more ambiguous and revolved around the question
how to deal with the trade-offs of expected growth in mobility.
In the process of operationalizing this variable we immediately recognized that the set of
problem and solution definitions by the different actors could never be empty because otherwise
the actors would not be involved in the issue. In other words: on the x-axis there could be no origin.
Consequently, we had to find a different scale for the PSC-variable (requisite 2 & 3). We
operationalized the variance in PSC by deriving the differences between singular and composite
PSC’s (see Gerrits (2008) for a similar reasoning of singular and composite in policy action
systems). A singular PSC implies definitions of a limited scope, i.e. a singular problem definition and
singular solution definition. Conversely, a composite PSC takes a wider diversity of factors into
account, i.e. several elements are considered in the problem definition and several solutions are
defined (requisite 1). On the x-axis, singular PSC’s lie on the left-hand side and composite PSC’s on
the right-hand side. Other combinations, such as a composite problem definition with a singular
solution definition, can be positioned somewhere between the two extremes. In the Fyra case, it
was the operator NS who held onto a singular solution definition, i.e. running the Fyra service,
whilst at the same time switching problem definitions between singularity and a composite nature,
depending on the circumstances.
In terms of Kauffman’s NK-model, N = {psc1, psc2, …, pscn}; that is n actors have a PSC, where
n ∈ . We postponed thinking about the scales and values of the PSC’s (requisite 2) after we had a
clear idea on what the rest of the NK-model should look like, which we’ll demonstrated further
below.
Problem
definition
Singular
Composite
PSC
Solution
definition
Singular
Composite
By defining N as PSC’s that vary between singular and composite, K needs to feature similar
properties, i.e. having no origin and not being infinite. The three-dimensional representation of the
variables, including the fitness based on the N and K, will therefore be a so-called hypercube
(Kauffman & Johnsen, 1991). Our first and over-simplified inclination is that fitness is the
‘probability’ that an actor’s PSC ‘wins’. Fitness for player i can then be defined as fi, where
fi = w(N, K), i.e. the fitness function attaches a fitness value w to each combination of N and K. In the
biological NK-model of Kauffman (1993), K is permanently linked to N because the interaction
frequency that can take place between the different genes is N-1. This connection is not self-evident
in collective decision-making. In order to stick to requisites 1 & 5 about the real world data, we had
to find another variable that is measurable and links the PSC’s in a logical way.
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2.2
Distance between actors
When engaged in collective decision-making, actors perceive or experience a distance between
themselves and others, i.e. an actor may perceive the PSC of a different actor as similar or different,
and all shades in-between. The PSC’s are tightly related to actor interaction. In source models, such
as in Kauffman (1993; 1995) K represents the frequency of interaction, i.e. N-1. However, this
doesn’t suffice for our purpose. Interaction frequency lacks the differentiating power necessary to
distinguish between different types of interaction. For example, while the frequency of the
interactions between NS and the Ministry on the one hand, and NS and AnsaldoBreda on the other
hand, is high in both instances, the nature of the interactions differs greatly. Arguably, both types of
interaction can occur with the same frequency but they will yield very different results for PSC’s
and, consequently, the decisions reached (requisite 1, 2 & 5). We therefore defined K as the distance
between actors. This was potentially problematic as distance requires an elaborate set of variables
and individual weighing, which brings about practical issues of measurability (thus violating
requisite 2). Two of the main actors in the Fyra case, operator NS and the Ministry of Public
Transport, underwent a change in their mutual relationship. Where NS used to be a government
agency when the HST was first proposed, it had been formally put at a greater distance from the
Ministry by the time the operation was planned. However, the two kept working together in a
fashion reminiscent of the previous legal status.
A work-around would be to measure perceived distance, e.g. by using an ordinal scale. This
solves the aforementioned problems because perceived distance serves as a proxy for interaction.
However, in operationalizing perceived distance elements as behavioral records of actors, strategy
and ideas about strategies of other actors enter the scene, but also a complicating factor such as
interpretations of the other actor’s strategy sets and PSC.
history
ideas of
behavior
record
(dis)like
go-alone
perceived
distance
strategy
...
cooperative
ideas of the
strategy set of
others
(un)known
ideas of PSC's
(un)clear
This conceptualization points at the fact that perceived distance and PSC’s are intertwined in such a
way that treating the two as independent dimensions is artificial (requisite 2 & 5). Actors’
experience of distance regarding others is partly informed by the extent to which PSC’s converge or
diverge, i.e. the PSC’s of actors inform the perceived distance. Conversely, that convergence or
divergence in PSC’s is partly informed by the perception of the position of, and interaction with,
other actors, i.e. the perceived distance informs the PSC’s of actors. This is exemplified in the Fyra
case by the fact that the preferred solution was intimately tied to the roles and relationships NS and
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the Ministry had relative to each another. It contributed to the ostensibly permanent solution
definition despite changing conditions.
These considerations made us realize that our model is about configurations rather than
about discrete variables and their individual weight in relation to the whole (see e.g. Ragin, 1987;
Byrne & Ragin, 2009; Ragin & Amoroso, 2011 for an extended argument). Among others, this means
that we have to consider interdependent and sometimes confounding variables. Stronger still,
thinking in configurational terminology (cf. Gerrits, 2012) means we have to let go of the term
variable and start thinking in constituent components. Real world cases are emergent wholes of
internal and external interactions. Therefore, it is not possible to assign a discrete impact to each
individual variable that influences an event or process. Dividing the case in discrete variables
compromises the case's integrity. Thinking in terms of components that produce the case in
configurations solves that issue (Gerrits, 2012).
2.3
From independence to configurations
The issues mentioned above all come back to the issue of (in)dependence between dimensions in
the landscape. Theoretically speaking, independence implies that each coordinate on the grid is a
possible empirical manifestation (requisite 1, 3 & 4). However, there are two main constraints to
this reasoning. First, it is extremely unlikely that all combinations (i.e. coordinates) can occur
empirically. Second, in terms of modeling, independence would mean that a large distance between
two or more actors on one axis could coincide with zero distance on the other axis, which in any
case would be an inaccurate representation. In short: what may be a possibility theoretically
becomes an impossibility when confronted with real-world cases (thus violating requisite 1).
Understanding such cases as configurations implies that a case is not a product of discrete variables
but as nested and emerging from the specific conjunction of all constituting components that give
rise to structures and processes (Gerrits & Verweij, 2013; Verweij & Gerrits, 2013). A variablebased approach, as opposed to the case-based configurational approach, would be helpful to
uncover certain patterns but can’t account for the complexity of emergence in cases, which would
violate requisites 1 & 5.
The difference between variables and configurations is important in understanding how the
case is brought about, i.e. the nature of causation that drive real-world cases. Following Sayer
(2000), we understand that in nested cases, the same causal power can produce different outcomes
and that different causal mechanisms can produce the same result. To us, this implies that the
fitness landscape represents a configuration where fitness is related to a particular configuration as
a whole instead of being the outcome of two independent variables (requisite 3).
2.4
Back to K
So how does thinking in configurations lead to the operationalization of K? Taking the perceived
distance as our point of departure, we again looked at how others in the social and behavioral
sciences have operationalized the elements we mentioned there. For instance, ‘propensity to work
together’ is an (sub)component that could bridge the gap between PSC’s on the grid by coalition
formation (Axelrod & Bennet, 1993); independence and dependence between decisions and their
relation with the environment (Rhodes, 2008); or interdependence between actors’ beliefs
(Bocanet & Ponsigline, 2012). What it boils down to is that all these perspectives try to give an
approximate empirically measurable connotation to the element of interdependence; i.e.
Kauffman’s original K as interaction. In real-world collective decision-making, interaction is not
independent but a consequence of the propensity to work together, coalition formation,
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collaboration, interdependence between beliefs/ideas/decisions et cetera. In other words, in
attempts to (un)knowingly fulfill requisite 1 workarounds have been created that violate requisite
2.
If we now look back at K not as a single independent variable but as a configurational
component of NK, we have returned where we started but initially thought of as impossible. That is,
K is all about distance and its affiliated interaction. However, the aforementioned steps make clear
that instead of just registering interaction frequency, which is associated with contradicting
meanings, we have different substantial measurable components (requisite 1 & 2), i.e. distance can
be measured by:
 Content:
 Factual differences and resemblances of (elements of) PSC’s; i.e. divergence and
convergence on elements in PSC’s, ranging from the singular to the composite.
 Actual history of actors; i.e. the track records of actors on same collective decisionmaking issues.
 Issue-related working history; i.e. the known working relation history between actors
on same collective decision-making issues.
 Process:
 General history of actors; i.e. ideas actors have on each other’s track record in similar
cases
 Belonging; i.e. liking or disliking actors
 General working history; i.e. the collaboration history in previous similar situations
K can now be defined as dij, i.e. distance between actors i and j, (i, j
). In line with PSC, K as
distance is on the one extreme singular, i.e. no connection and interaction with others / no ideas
about other actors; and on the other extreme composite, i.e. belonging to others / high interaction /
sophisticated ideas about others. Quite clearly even though we’ve turned full circle and stay truer to
Kauffman’s (1993) K, they are not the same. Where K = N – 1 in Kauffman’s model, we’ve tried to
operationalize it by giving the component (and not variable) different measurable content
characteristics (requisite 2 & 3).
The Fyra-case shows how content and process are intimately linked in determining distance
between actors the real world. Definition and scope of the project were set in interaction between
the Ministry of Public Transport and NS in the time when NS was still an agency of the Ministry.
When the operation was put out to tender, the history of cooperation between the two during the
previous stages meant that the Ministry wanted to favor NS in winning the contract and that NS felt
obliged to offer a substantially higher sum for the contract than rivaling bidders. This won NS the
concession, thus continuing the close relationship between the two. However, the Ministry grew
weary with NS over time because it was forced to postpone revenue service a number of times. But
while the distance between the two increased because of the mutual dissatisfaction, the Ministry
couldn't act as a proper principal and replace NS because of the shared history in defining the
project's scope and the shared decision-making leading up to the tendering process.
2.5
Fitness
We have now defined the two core components of the NK-configuration as PSC and distance, which
allows us to group different actors relative to each other. So far, we have not yet discussed the
concept of fitness in-depth. Originally, fitness – the extent to which a species fits a particular niche –
had a clear and dichotomous indicator: survival or not. In collective decision-making, things are
less clear-cut. For example, even though AnsaldoBreda had violated its contract with NS because of
the late delivery of faulty train sets, it didn’t disappear from the landscape. One reason for the
8
delays was ambiguity about safety standards, for which NS, the Ministry and the European
Commission was at least partly to blame. It can be argued that a dichotomous indicator doesn’t do
justice to the complexity of such a situation. In collective decision-making, it is the matter of which
actor reaches its goals, i.e. who gets what, when, and how, as per Lasswell’s thinking (Laswell,
1936).
Fitness can now be defined as the probability of an actor achieving its PSC, i.e. the actor’s
desired goal. An actor’s ability to achieve its goal depends on its position relative to other actors,
not just its intentions or deliberate design. Over time, actors will converge and diverge in their
attempts to gain a better position or fitness (cf. goal-alignment by Venkatraman, 1999). The extent
to which actors succeed in aligning their PSC with these characteristics is expressed with a higher
position on z-axis, i.e. a higher level of fitness. A higher position indicates that an actor is closer to
achieving its goals, i.e. the realization of its PSC, and a lower position means that an actor is further
away from achieving its goals (requisite 4).
In the original NK-model “the two main parameters […] are the number of genes N and the
average number of other genes K which epistatically influence the fitness contribution wi of each
gene.” (Kauffman, 1993: 42) That means that the fitness of an entire genotype is the average of the
contributions, or as Kauffman (1993; 42) puts is:
∑
Because in many cases the K inputs can be chosen at random (e.g. Kauffman & Levin, 1987;
Kauffman & Weinberger, 1989; Kauffman, 1993; Hordijk & Kauffman, 2005) the general properties
of NK-landscapes are then as follows. When K = 0, the landscape has a single peak, whereas the
landscape is completely random and rugged, i.e. with many peaks, when K = N – 1. Thus, by
changing K (relative to N) the ruggedness of the fitness landscapes changes. How can this strict
model with variables be translated to our NK-configurational approach? The question confronting
us is whether the probability of achieving a PSC (i.e. the individual fitness) is relative to the overall
fitness of all PSC’s, or whether these individual fitnesses are only relative to each other and not to
the field? Taking all averaged PSC contributions to make up the fitness of the entire configuration
creates the advantage that the success rate of particular actor PSC’s is higher, same or lower than
the field fitness. In the three-dimensional representation this means that hills (the higher
probabilities) and valleys (the lower probabilities) are created within the condition-setting
environment in which the selection takes place (requisite 4 & 5). The fact that the Ministry and NS
were working closely together during the initial phases meant that NS got closer to realizing its PSC
than potential rivals such as Deutsche Bahn. When NS and AnsaldoBreda failed to deliver, the
probability of other operators realizing their PSC’s increased due to the possibility of them granted
a second chance. The shift in balance between all actors was the sum of their own actions (e.g. the
stressed relationship between NS and AnsaldoBreda) and external conditions (e.g. the European
Union setting the standards for train safety).
Mathematically expressed our initial formula fi = w(N, K) can be transposed, through the
definition of N into problem solution combination and K into distance between actors, to
, where the fitness for the complete collective decision-making field is
∑ (
9
)
This mathematical expression summarizes our take on how fitness is obtained or lost in collective
decision-making whilst adhering to the requisites we laid out at the start of the paper. However, to
us the expression was a means, not an end. It helped focusing our ideas and cutting through the
ambiguities of conceptualization and operationalization. The expression may suggest more than it
does. First, it bears with it the impression of a definite formula that assumes mechanistic causality.
This may or may not be the case and that is something that can only be learned through empirical
testing. Second, although the formula is rooted in configurational thinking, it in itself doesn’t
express configurations, which could be deceiving.
2.6
Adaptive walk
Collective decisions made in a certain period will create new situations to which the decisionmakers might have to respond again, i.e. they may have to reconsider their PSC in the light of the
new situation. Making decisions based on the PSC means exerting selection pressures on the
situation. Responses from the environment in turn mean exerting pressures on the PSC and
decision-making. Such feedback loops carry information for actors, which is assessed and acted
upon (Dopfer, 2005; Foster & Hölzl, 2004; Gerrits, 2011). Which particular PSC comes out on top of
the competition is therefore not a given (John, 1999). It depends on the feedback loops and their
cumulative effects, as well as the strategies followed by actors, e.g. the support they manage to
amass by cooperating or going for a stand-alone strategy if they think this will bring them closer to
their goals. In other words, whom actors interact with affects the results of the possible actions of
actors (Arthur & Durlauf, 1997). We already demonstrated such a movement by outlining how NS
had gained a competitive advantage over rivals by being the one operator who not only bid for the
tender but also had set up the conditions for that tender in close cooperation with the Ministry.
Having defined the components of the NK-model and its fitness it is time to return to the
fitness landscape model in its entirety. Actors engaging in collective decision-making have their
own specific problem-solution combination and have certain distances with the other actors
concerning a given collective decision-making issue, and this is true for all actors. The probability of
successfully attaining a PSC for an actor is relative to the probabilities of the other actors.
Divergence or convergence on PSC’s, extending or limiting the distance between actors, can
increase or decrease the probability of successfully achieving the PSC of actors. In other words,
actions by actors, based on their PSC’s and distance in the configuration, lead to interactions (here
we return to Kauffman again). Notice that the strategies that were initially an indicator of perceived
distance in section 2.2 and were left out as indicator for distance in section 2.4 are reintroduced, as
strategy is the reflected in the way the actions of actors lead to interaction. By taking snapshots of
the configurations at different moments in time it is possible to trace the patterns of behavior by
the actors in the field, i.e. the adaptive walk across the landscape (requisite 4 & 5). Thus, if we want
to map the dynamics of decision-making in the Fyra project in order to understand how the current
situation came about, we would need to generate a time series of fitness landscapes that would
show how the constituent actors diverge and convergence, thus trying to enhance the probability of
obtaining their PSC. In this particular case, it would show how the initial distance between the
Ministry and NS favored the latter in its quest to reach its PSC. But this favorable position would
become a burden later on as NS saw itself confronted with a too expensive concession and lack of
revenues because it had no proper trains to run. What appeared an advantage at first became a
disadvantage later on.
10
3
Conclusions and a dual reflection
This paper aimed to develop a fitness landscape model for collective decision-making whilst being
constraint by five requisites. We also wanted to map the process of modeling to get a better
understanding of the trade-offs of modeling for cases. Looking back at the model, it is interesting to
note how Kauffman's NK-model provided the starting point for our model, how we moved away
from these ideas and ended up with a model that bears close resemblance with the original model.
There are a number of important differences. First, our model is rooted in configurations instead of
being build up by discrete variables. Second, the model deals with the ambiguities of measuring
social reality, which meant we had to find solutions for items such as distance and content. Third,
the implications that Kauffman and others derive from their NK-model is absent in our model
because the model is purely descriptive.
In modeling, we clearly constrained ourselves by the five requisites laid out in Section 1.2.
These requisites came from our observation that many modeling attempts perform strongly on
internal validity and coherence but weak on processing data from the real world, such as collected
from interviews or policy documents. Our point of departure, that the model should be able to
process real-world data, proved to determine the possibilities and constraints of our effort because
each iteration was tested against that requisite. As such, much attention was given to the second
requisite, namely to allow for unambiguous measurement in the real world. By meeting these two
requisites, the model should be able to meet the fourth and fifth requisites as a consequence. It
should be noted that the fifth requisite, i.e. to be able to generate in-depth insight beyond generic
statements, is something that needs to be proven in practice. In addition, it hints at the difference
between a three-dimensional landscape and a generalized NK-model for particular cases on
collective decision-making (cf. Altenberg Altenberg, 1995; Plutinsky, 2008).
The one requisite that we couldn't maintain in the present form was to account for all
possible coordinates on the grid. The premise of this requisite is that research is variable-based. In
reality, some coordinates would never be observed. Once we shifted to the configurational
approach, which was necessary to meet the other requisites, the third requisite became obsolete. In
hindsight, this requisite contradicted the other requisites.
In reflecting on the model and the requisites it is interesting to contrast our requisites with
those set out by Axelrod & Bennett (1993). These concern: (1) to provide an explanation for the
occurrence of convergence of actors; (2) to provide a deeper understanding of such convergence;
(3) to cross domains in society and politics by being generic; (4) to be simple enough to illuminate
the fundamentals of convergence; and (5) to have predictive capacity. We have noticed in our
survey that these requisites are typical for the kind of models found in fitness landscapes research
and we concur with some of them. We also aim to understand convergence or divergence as a
subset of collective decision-making and we also want to obtain a deeper understanding. However,
our version is also very different in that we do not know whether a generic model across domains is
possible. Also, thinking in terms of configurations is at odds with looking for the simplest
explanation. In addition, we are uneasy with the demand of predictive capacity. It appears that the
differences can be brought back to the ontological differences. We would like to think that real life
should be modeled and not the other way around that models show how real life should be, even if
that makes us different from mainstream modelers.
The reflections above concern the construction of our model. We also feel the need to reflect
on the modeling process. About a year has passed between our initial idea to build a fitness
landscape model and the current text. We started off with a literature survey to find the different
interpretations and applications of such models in the social and behavioral sciences. The vast and
diverse interpretations and applications led to the five requisites we used in this paper. Our
modeling effort has been iterative. At certain moments we thought we had a clear idea about what
constituted the model's variables, but in testing cases we found out that one or more of the five
11
requisites would be violated. Consequently, we kept on refining and specifying, where a big change
came from changing the variable-based approach to configurations.
All in all, in the iterative process we clearly felt a constant, admittedly sometimes very little,
progress towards a better fitness landscape model for collective decision-making. At this moment
in time we cannot uphold the idea that our model can be put into a singular mathematical formula
because that would violate requisites 4 & 5, i.e. the model would not allow for the real-world data to
surprise us. The constant balance that needs to be sought with the requisites kept us focused but at
the same time also restrained us. If we would be able to build a mental model on the process we
went though it would maybe look similar to our collective decision-making NK-configuration
model; there has been a clear diverging and converging of problem definitions and even more so on
solution definitions. The resulting model is another step in our thought process. The next step is to
test it thoroughly.
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