ArticlePDF Available

The Diversity-Ability Trade-Off in Scientific Problem Solving

Authors:
forthcoming in PSA2020/2021
The diversity–ability trade-off in scientific
problem solving
Authors:
Samuli Reijula
Theoretical Philosophy, University of Helsinki
Jaakko Kuorikoski
Practical Philosophy, University of Helsinki
15 Jan 2021
The diversity-ability trade-off in scientific problem
solving
Reijula, Samuli1and Kuorikoski, Jaakko2
1Theoretical Philosophy, University of Helsinki
2Practical Philosophy, University of Helsinki
15 Jan 2021
Abstract
According to the diversity-beats-ability theorem, groups of diverse problem solvers can
outperform groups of high-ability problem solvers. We argue that the model introduced by
Lu Hong and Scott Page (2004; see also Grim et al. 2019) is inadequate for exploring the
trade-off between diversity and ability. This is because the model employs an impoverished
implementation of the problem-solving task. We present a new version of the model which
captures the role of ‘ability’ in a meaningful way, and use it to explore the trade-offs between
diversity and ability in scientific problem solving.
Keywords— social epistemology of science; group problem solving; cognitive diversity;
agent-based modeling; distributed cognition
1. Introduction
Modern science is a deeply collaborative enterprise. Most genuinely important intellectual
challenges cannot be tackled by a single scientific discipline, let alone by individual researchers.
1
The diversity-ability trade-off in scientific problem solving
Science needs diversity – solving scientific research problems requires attaining specialized
expertise and resources from a variety of perspectives.
Problem-solving groups in general are taken to benefit from diversity (Reagans and
Zuckerman 2001; Mannix and Neale 2005; Jeppesen and Lakhani 2010; Steel et al. 2019).
Among other important benefits, it is assumed that differences in how members of a group see a
problem, in the cognitive resources they have at their disposal, and in the kind of heuristics they
use, make it more likely that the the group as a whole has the resources to solve the problem. An
important question, therefore, is whether the diversity of a group is in itself epistemically
valuable, over and above the epistemic abilities of the group members.
Besides the empirical evidence cited above, a particularly influential argument in favor of
diversity has been presented in the form of a mathematical theorem and an agent-based
simulation. According to the diversity-beats-ability (DAB) theorem, groups of diverse problem
solvers can outperform groups of high-ability problem solvers. This means that in assembling
problem-solving teams, functional group diversity should sometimes be prioritized over selecting
the most able individual members. Although they originate in computational social science, in
management and organization studies, the DAB results have recently been also discussed in the
philosophy of science (Grim et al. 2019; Singer 2019; Holman et al. 2018).
We argue that the "can" in the DAB theorem is ambiguous between several different
modalities: in some of its uses, it is only a claim about conceptual possibility, whereas in its
much advertised practical applications, it is clearly regarded as a more substantial possibility.
This raises the question of when and under which exact conditions diversity really beats ability.
We examine whether the original model by Hong and Page, and its further developments by Grim
and associates, actually support the existence of the diversity-beats-ability phenomenon.
We show that due to their impoverished task implementation, these models cannot capture
2
The diversity-ability trade-off in scientific problem solving
interesting trade-offs between functional diversity and individual ability: the problem-solving
tasks portrayed in the models are too difficult (i.e., random noise) for ability to make any
difference to the outcomes. We develop a new version of the model with an improved
problem-solving task. The new task representation allows our model to capture the role of
individual ability in problem solving. Only when both diversity and ability really affect the
outcome can the trade-off between them be studied.
We start by briefly presenting the DAB theorem and the associated simulation models,
focusing on the latter. In Section 2, we highlight the "bait-and-switch" argumentative strategy
used by Page to argue for DAB, showing that many of the modeling results supposed to support
the theorem are problematic and do not replicate well. In Sections 3 and 4, we present our main
argument: the model template used by Hong and Page as well as Grim and colleagues is ill-suited
for exploring the trade-off between diversity and ability, because the problem-solving task is
computationally implemented in a way that does not afford any advantage to individual ability or
expertise. We introduce our version of the model, the stairway landscape, and demonstrate how it
captures a substantial trade-off between diversity and ability. We draw two potentially interesting
conclusions concerning the trade-off.
In this article, we are only concerned with the purely instrumental value of cognitive
diversity; we are not arguing against the DAB phenomenon as such. We only ask whether the
particular models we discuss are an informative and reliable way of exploring the possible
trade-off, and provide what we regard as a better alternative way for doing so.
3
The diversity-ability trade-off in scientific problem solving
2. The diversity–ability trade-off in group problem solving
Consider design tasks such as designing an automobile, a space shuttle, or a piece of software, or
scientific tasks such as measuring the mass of an elementary particle or discovering the structure
of a macromolecule. Heterogeneous cognitive and material resources need to be applied to solve
all these problems, and as the set of solution candidates is not known beforehand, a search for
solutions is needed. Simon (1989) suggested viewing the scientific research process through the
lens of heuristic search. For instance, scientists search for formulations of problems,
experimental designs, patterns in data, mechanisms behind data, and implications of their
theories. On some occasions, these multi-dimensional search trajectories result in beneficial
epistemic design; in other cases, they yield research approaches of little cognitive value.
Importantly, most scientific problems worth solving lie beyond the capacities of a single knower,
and scientific progress relies on a successful division of labor and collaboration between
researchers, research groups, and sometimes even between scientific disciplines. Hence,
scientific research should be understood as a socially distributed problem-solving process.
Such a picture of collective search immediately suggests a possible trade-off. On the one
hand, as Newell and Simon (1972) suggested, expert performance often relies on highly specific
search heuristics. On the other hand, more diversity in the group’s cognitive resources is
beneficial, all other things being equal, as more varied resources provide access to larger portions
of the solution space. Diversity may, however, conflict with individual ability. Experts are often
more alike (in the relevant respects) than non-experts. Herein lies the trade-off: individual ability
and group diversity both contribute to group performance, but, at least in some circumstances,
the two factors may be in conflict.
Explicit modeling of the epistemic benefits of diversity in collective problem solving is
4
The diversity-ability trade-off in scientific problem solving
needed, because the phenomenon involves multiple group-level mechanisms as well as possible
interactions between different epistemic, processual, and social factors. Therefore, purely verbal
and conceptual theorizing is not a reliable tool for drawing out the implications of theoretical
assumptions, and empirical (experimental or case-based) evidence does not usually
unambiguously discriminate between alternative mechanistic explanations for why, in any
particular case, diversity may or may not facilitate successful problem solving. Group problem
solving has proved challenging to model, however. The computational implementation of the
problem (task), cognitive resources (and differences therein), problem-solving behavior and
cognition, and interaction between the group members all present difficult methodological and
theoretical choices for the modeler, easily resulting in complex and intractable models with too
many methodological degrees of freedom. Such models yield results which are hard to interpret.
We believe that the heuristic-search paradigm proposed by Newell and Simon (1972) still
provides the most promising approach for addressing these modeling challenges (see also
Kauffman and Levin 1987; March 1991; Darden 1997). The models discussed and developed in
this article join this tradition.
In a series of articles and books, Lu Hong and Scott Page have provided model-based
evidence for the existence of the diversity-ability trade-off (Hong and Page 2001, 2004; Page
2008). They, in fact, use two distinct models to investigate diversity. The first model, introduced
in Hong and Page (2001) and described in length by Page (2008) in the context of the diversity
theorem, represents the problem to be solved as a binary string of finite length, where each bit
could be seen as portraying a yes–no decision regarding a solution to a particular sub-problem
(Kauffman and Levin 1987). A group of problem solvers of limited ability attempts to maximize
a value function defined over the possible states of this string (potential solutions to the problem).
Diversity is represented in the model by each agent having a different set of possible ways of
5
The diversity-ability trade-off in scientific problem solving
Figure 1: High-ability vs. random groups in the bit string model. The vertical axis represents the
score differential between high-ability groups and random groups.
flipping the bits ("flipset heuristics") of the candidate solution string shared between the group
members. Measures of problem difficulty can be assigned to alternative value functions (see Page
1996), and so the model can be used to represent a range of problems of different difficulty and
complexity. This model template therefore corresponds well to pre-theoretic intuitions about how
cognitive diversity can facilitate collective problem solving.
It is therefore rather surprising that the influential diversity-beats-ability results are not
derived from this model. Our replication of the model in Hong and Page (2001) did not provide
evidence to support the diversity-beats-ability phenomenon (see figure 1).1As the figure
illustrates, no systematic difference emerges between groups of high-ability problem-solvers and
groups of randomly selected problem-solvers. A more careful look at Page’s 2008 argument
reveals that it is based on evidence for the diversity theorem from an altogether different model
introduced in Hong and Page (2004). We refer to this simplified model as the ringworld model.
In sum, the substantial intuitions about diversity and ability in collective problem solving are first
1.
For details about the bit string model, see Hong and Page 2001. All program code for the simulations and the gen-
erated data sets are available for download at https://osf.io/a6f5e/?view_only=fcee3f72db8643b9999ad19447f89886
6
The diversity-ability trade-off in scientific problem solving
formalized in one model, but the results are derived from a different model based on assumptions
which do not correspond as neatly to the original intuitions. We find such a "bait-and-switch"
argumentative strategy confusing, and not appropriate for transparent and epistemically
sustainable use of theoretical models.
The argument in Hong and Page (2004) has a two-pronged structure: The basic assumptions
of the ringworld model are used to derive an analytical proof intended to provide support for the
theorem. However, as argued by Thompson (2014), the implications of the proof are unclear:
even after technical corrections, the theorem only provides a highly abstract proof of possibility,
and its implications for a non-technical interpretation of diversity are difficult to judge. Although
we agree with Singer (2019) that the proof does rely on diversity and not merely on randomness
(see Thompson 2014), it still remains the case that as such, the proof tells us little about the
conditions under which the trade-off between diversity and ability can be expected to be
significant. Mere logical possibility is not enough for the far-reaching practical implications
suggested by Hong and Page. Their more persuasive evidence for DAB and its relevance for
real-world group problem solving are derived from their agent-based simulation of the ringworld
model. It is to this simulation that we now turn.
3. Problems in the Ringworld
The “computational experiment” used by Hong and Page to demonstrate DAB portrays a group of
agents collectively searching for optimal solutions in a one-dimensional landscape. The discrete
landscape consists of positions
1. . . 𝑛
on the number line, wrapped as a circle.
2
Value function
𝑉
defined over the set of positions assigns to each position a payoff value drawn from the uniform
2.
It turns out that the circular topology of the landscape does not make a difference to the results, as the distance
explored by the individual agents (and groups) typically does not exceed 20 steps along the 2000-step circle.
7
The diversity-ability trade-off in scientific problem solving
distribution [0,100]. The agents’ goal is to find the largest possible values on this landscape. To
do so, each agent employs a heuristic
𝜙
. A heuristic is defined as consisting of
𝑘
different jumps
of length 1. . . 𝑙 (e.g., [1,5,11] and [3,4,12] are two examples of heuristics with parameters
𝑘=3, 𝑙 =12
). Starting from its current position, an agent sequentially applies these jumps along
the landscape, and moves to a new position along the circle if the payoff associated with that
position is strictly larger than the current one. When no further improvement is possible, the
agent stops. The performance of an agent is defined as the expected payoff of the stopping points
over the different starting positions of the landscape, and over a set of landscapes.
Hong and Page implement group problem solving behavior as sequential, iterative search.
First, one agent initiates the search. As its local maximum is found, the second agent in the group
takes the baton, and applies the jumps included in its heuristic as long as they lead to
improvements. After all group members have taken their turn, a new round begins. The
collective search stops when no agent can make further progress. Group performance is defined
as the expected value of the position at which the group search stops.
In order to compare groups of high-ability problem solvers to more diverse ones, an
exhaustive set of agents (with respect to possible heuristics) is first ranked according to their
individual performance on a set of landscapes. A high-ability group of size
𝑔
is constructed from
the 𝑔highest performers in such a tournament, whereas the diverse group consists of 𝑔agents
sampled randomly from the population.
In their model analysis, Hong and Page (2004) report results for various sets of parameter
values. For example, for 𝑙=12, 𝑘 =3, 𝑛 =2000 they find that that the best individual agents
scored 87.3 whereas the worst agent’s score was 84.3. For groups of 10, the high-ability group
scored 92.56 and the random group 94.53. This difference in favor of the random group is the
diversity effect discovered in the simulation. Similar results were found by Grim and associates
8
The diversity-ability trade-off in scientific problem solving
(2019), and we were also able to replicate the findings.
Hong and Page suggest that there are reasons to believe that the random group scored higher
due to its diversity. An alternative way to express this finding is in terms of effective group size.
In our replication, we noticed that the difference in performance (’performance differential’)
between the random and the high-ability group was strongly correlated (.65) with the difference
in effective group size between the two groups, where effective group size was defined as the size
of the group heuristic from which overlapping elements had been removed. In other words, the
similarity between the members of a high-ability group results in the group being functionally
smaller (from the perspective of the problem-solving task). As the performance of a group
generally increases as its effective group size gets larger, it is not surprising that smaller effective
group size leads to worse performance.
Going back to the original DAB theorem, however, the explanation above seems to capture
only one side of the diversity–ability trade-off. Although the correlation between effective group
size and performance is an indication of the functioning of the "diversity mechanism," it is still
unclear why that effect is stronger than the influence of the "ability mechanism," i.e., the fact that
some heuristics should lead to higher performance than others, and that those high-performing
heuristics should be more common in high-ability groups. A closer inspection of the model
provides a solution to this puzzle.
Unlike Hong and Page, we regard the effect sizes from the simulation as remarkably small,
given that they originate from theoretical modeling where the modeler is free to explore a broad
range of hypothetical scenarios. One would expect a purely theoretical model, purpose-built to
examine and demonstrate a specific mechanism using heavy idealizations, to reveal relatively
unambiguous effects of the modeled mechanisms. As a matter of methodological principle, we
believe that conclusions drawn from agent-based modeling would be strengthened by showing
9
The diversity-ability trade-off in scientific problem solving
how the effect size can be manipulated by changing model parameters. In other words, being able
to "turn the dials" and observe how changes in model inputs result in systematic changes in the
modeled effect suggests that we have reached understanding about the dependencies between
model inputs and outputs (see Woodward 2003; Aydinonat, Reijula, and Ylikoski 2020).
Regarding the ringworld model, we argue there are two reasons to believe that the results reported
by Hong and Page do not provide genuine insight into the diversity-ability trade-off.
First, with the parameter values studied by Hong and Page, in nearly half of the cases, the
random group ends up with a full heuristic, that is, a heuristic consisting of all possible jumps
[1, . . . , 12]. Furthermore, only 13% of the random groups have an effective group size smaller
than 11. Hence, even if the agents in the high-ability group can make the jumps leading to high
performance, it is highly likely that the same jumps will also be included in the heuristic of the
random group – there is simply no way the high-ability group could systematically outperform
the random one.
Secondly, as Grim and his colleagues (2019) also noted, the purely random landscapes
studied by Hong and Page are simply not hospitable to anything that could be meaningfully
interpreted as “ability” or "expertise." For heuristic search to be applicable, the task needs to have
some structure or redundancy that the heuristic can exploit (Kahneman and Klein 2009;
Kauffman and Levin 1987). Hence, aggregated over several random landscapes, no significant
performance differences emerge between the different heuristics. This is seen in the very small
performance differences between the best and worst performing individual agents (see above) in
Hong and Page’s simulations: the "ability mechanism" does not get any traction on the
landscapes they studied. Therefore, we argue that the model does not appropriately capture the
trade-off between diversity and ability.
Grim and his coauthors (2019) propose to remedy this problem by partially smoothing out the
10
The diversity-ability trade-off in scientific problem solving
random landscape (by adding interpolated values between randomly generated values). They
argue that such a task representation can better capture ability, because on smoothed out
landscapes individual performance is more transportable to other landscapes of similar
smoothness. Yet a closer numerical examination of the results of this remedy again reveals only
small differences between diversity and ability. Even on smoothed random landscapes, the
expected performance difference between best performing and random individuals is minute.
This suggests that these landscapes simply do not represent a problem that is suitably complex for
exploring trade-offs between ability and diversity.
4. Modeling the diversity–ability trade-off on stairway land-
scapes
In order to better understand the tension between diversity and ability, we need to portray
scenarios where also ability plays a role. In our own simulations, we introduce a type of problem
where high ability – either at individual or group level – leads to noticeably increased
performance. In science, having the right methodology for the problem at hand often sharply
increases the epistemic payoff. Our stairway model differs from the Hong and Page ringworld
model only in problem structure. The specifications of agent and group behavior remain the same
as in the ringworld model. In generating problem landscapes, we start from the uniform noise
distribution employed by Hong and Page. On top of those landscapes, however, we superimpose
an increasing sequence of values, where the positions of the values are separated by intervals
drawn from a finite set of integers in 1. . . 𝑙 (see figure 2). We call this set the step set.
For an agent to climb the increasing subsequence, the stairway sequence, it must possess the
11
The diversity-ability trade-off in scientific problem solving
Figure 2: A stairway landscape with step set {5,12}, and, therefore, step set size 2.
heuristic jumps corresponding to the steps used to generate the sequence (e.g.,
[5,12]
in figure 2).
This strongly favors some heuristics over others: whereas an agent who does not possess the full
step set is bound to remain in the noise region of the landscape, a "high-ability" agent that has the
necessary heuristic can climb through the whole sequence (and even reach the maximum payoff
on the landscape, normalized to 1.0).
Figure 3 illustrates outcomes from our model with parameters values corresponding to those
studied by Hong and Page (2004) and by Grim an his colleagues (2019). The left panel presents
the difference between the performance of high-ability and random groups (positive values
standing for high-ability group advantage, and negative values, for random group advantage). The
results indicate that with these parameter values, stairway landscapes always favor high-ability
groups. Especially when the group size is small, because it is made up of high-performing
individuals (who typically possess valuable elements of the step set) the high-ability group
performs significantly better than the random group. The right panel presents the difference
between the redundancy of heuristics between the high-ability and random group (value 0 means
that the overlap of heuristics in both groups is the same). As suggested by findings by Hong and
12
The diversity-ability trade-off in scientific problem solving
Figure 3: High-ability vs. random groups on a stairway landscape, step size 3. (
𝑘=3, 𝑙 =12, 𝑛 =
2000; 100 repetitions over 100 landscapes)
Page (2004), random groups tend to have comparatively lower levels of overlap in their heuristics.
As group size increases, the redundancy in the high-ability group increases more than in the
random group. This suggests that when the group size is larger, random groups again begin to
approach the full heuristic, which obviously is sufficient for climbing the stairway sequence. For
this reason, at group sizes larger than 10, random groups catch up, and no significant
performance difference is observed between high-ability and random groups (left panel).
We argue that this tension between the "ability mechanism" and the "diversity mechanism"
captures the trade-off addressed by the DAB theorem. What happens, however, when the level of
ability or expertise required by the task changes? Different levels of task difficulty can be
represented by stairway landscapes with different step set sizes. For example, landscapes with
step set sizes up to three lie within the abilities of the individual agents studied in the simulation
(
𝑘=3
). Climbing the stairway for step sizes larger than 3 requires pooling heuristics from several
agents.
Figure 4 summarizes tentative findings from our studies with landscapes of varying difficulty.
In the figure, group size is represented on the horizontal axis, and step set size (complexity of the
13
The diversity-ability trade-off in scientific problem solving
Figure 4: High-ability-vs-random group performance differential on stairway landscapes (50
repetitions, each over 50 landscapes).
problem) on the vertical axis. The color represents the performance differential between the
high-ability group and the random group; lighter shades standing for high-ability group
advantage. A genuine trade-off between diversity and ability can be seen. Observe the contrast
between the upper-left quadrant, where ability dominates, and the lower-right, where random
groups have a slight advantage over the high-ability groups; ability dominates when group size
and step set size are small, whereas diversity leads to better performance when the group size and
step set size are larger.
Finally, our results suggest a conceptual distinction between the complexity and difficulty of a
problem: perhaps not surprisingly, ability dominates when the problem is simple in the specific
sense that multiple cognitive resources do not need to be combined to solve it. Note that if the
problem is simple in this sense, this does not necessarily mean that it is easy to solve. When the
problem becomes complex, requiring efficient division of cognitive labor, the diversity effect
begins to dominate over individual abilities. The results demonstrate how diversity and group
size begin to outdo individual ability only when the problem complexity exceeds the cognitive
resources of any single individual.
14
The diversity-ability trade-off in scientific problem solving
One could object to our stairway model on seemingly similar grounds to the ones on which
we based our criticism of the original ringworld model. We questioned the DAB results on the
basis that the model was built to favor diversity over ability. Why would our model fare any
better, as it was clearly built to favor ability over diversity? This objection misses our point,
however. Our argument is that the original model cannot be used to model the trade-off between
diversity and ability, because it cannot be used to represent the gains from ability. Of course, we
fully admit that the stairway landscape is built to favor ability, but the model nevertheless also
retains the gains from diversity. Stairway landscapes give both ability and diversity their due, and,
therefore, can illuminate the trade-off between them. This, we argue, was the original and
interesting interpretation of the DAB results to begin with.
5. Conclusions
The original results by Hong and Page do not provide reliable evidence for the
diversity-beats-ability theorem because the ringworld model, especially its task implementation,
does not allow for ability to adequately influence individual or group performance. This
one-sidedness implies that their model cannot be used to explore the possible trade-offs between
diversity and ability in problem-solving groups. Our exploration of stairway landscapes illustrates
how the results by Hong and Page (2004) rely on a problematic task structure to get their results.
Stairway landscapes provide a better model for "medium-hard" problems which require
specialized abilities and true division of cognitive labor. Such landscapes can be used to model
the interplay between diversity and ability relevant, and its effects on the division of cognitive
labor in science.
Our tentative modeling results suggest a trade-off between diversity and ability. Ability is
15
The diversity-ability trade-off in scientific problem solving
favored when the problem is moderately difficult, requiring only a few different expert heuristics,
and when groups are small. Diversity is favored when the problem is complex, requiring multiple
component solutions, and when the groups are large. A further qualitative effect can be observed
at the point where problem complexity increases beyond the capacity of a single agent and
necessitates division of cognitive labor: simple problems solvable by individuals favor ability
regardless of group size.
Acknowledgments
We thank Kristina Rolin, Inkeri Koskinen, Renne Pesonen, and the other members of the TINT
group (University of Helsinki), as well as the participants of Diversity in Science workshop
(Tampere University, 5 May 2019) and the poster sessions at EPSA 2019 (University of Geneva)
for their helpful comments. Thanks to Kate Sotejeff-Wilson for editing the manuscript. This
research was carried out as a part of the project "Social and Cognitive Diversity in Science"
funded by the Academy of Finland.
16
The diversity-ability trade-off in scientific problem solving
References
Aydinonat, N. E., S. Reijula, and P. K. Ylikoski. 2020. “Argumentative landscapes: the function
of models in social epistemology.” Synthese, forthcoming.
Darden, L. 1997. “Recent work in computational scientific discovery.” In Proceedings of the
Nineteenth Annual Conference of the Cognitive Science Society, 161–166. Mahwah, New
Jersey: Lawrence Erlbaum.
Grim, P., D. J. Singer, A. Bramson, B. Holman, S. McGeehan, and W. J. Berger. 2019. “Diversity,
ability, and expertise in epistemic communities.” Philosophy of Science 86 (1): 98–123.
Holman, B., W. J. Berger, D. J. Singer, P. Grim, and A. Bramson. 2018. “Diversity and
democracy: Agent-based modeling in political philosophy” [in en]. Historical Social
Research 43 (1): 259–284.
Hong, L., and S. E. Page. 2004. “Groups of diverse problem solvers can outperform groups of
high-ability problem solvers” [in en]. Proceedings of the National Academy of Sciences of
the United States of America 101 (46): 16385–16389.
. 2001. “Problem solving by heterogeneous agents.” Journal of economic theory 97 (1):
123–163.
Jeppesen, L. B., and K. R. Lakhani. 2010. “Marginality and problem-solving effectiveness in
broadcast search.” Organization science 21 (5): 1016–1033.
17
The diversity-ability trade-off in scientific problem solving
Kahneman, D., and G. Klein. 2009. “Conditions for intuitive expertise: A failure to disagree.”
American Psychologist 64 (6): 515–526.
Kauffman, S., and S. Levin. 1987. “Towards a general theory of adaptive walks on rugged
landscapes.” Journal of Theoretical Biology 128 (1): 11–45.
Mannix, E., and M. A. Neale. 2005. “What differences make a difference? The promise and reality
of diverse teams in organizations.” Psychological science in the public interest 6 (2): 31–55.
March, J. G. 1991. “Exploration and exploitation in organizational learning.” Organization
science 2 (1): 71–87.
Newell, A., and H. A. Simon. 1972. Human problem solving. Vol. 104. 9. Prentice-Hall
Englewood Cliffs, NJ.
Page, S. E. 2008. The difference: how the power of diversity creates better groups, firms, schools,
and societies. Paperback. Princeton, N.J. ;Woodstock: Princeton University Press,
. 1996. “Two measures of difficulty.” Economic Theory 8 (2): 321–346.
Reagans, R., and E. W. Zuckerman. 2001. “Networks, diversity, and productivity: The social
capital of corporate R&D teams.” Organization science 12 (4): 502–517.
Simon, H. A. 1989. “The scientist as problem solver.” Complex information processing: The
impact of Herbert A. Simon, 375–398.
Singer, D. J. 2019. “Diversity, not randomness, trumps ability.” Philosophy of Science 86 (1):
178–191.
18
The diversity-ability trade-off in scientific problem solving
Steel, D., S. Fazelpour, B. Crewe, and K. Gillette. 2019. “Information elaboration and epistemic
effects of diversity.” Synthese, forthcoming.
Thompson, A. 2014. “Does diversity trump ability?” Notices of the AMS 61 (9): 1–024.
Woodward, J. 2003. Making things happen : A theory of causal explanation. Oxford studies in
philosophy of science. New York: Oxford University Press.
19
... As the authors note, a collection of agents is effectively a single problem solver armed with the abilities of several agents. Their simulation has been criticized on conceptual, formal, and methodological grounds (Thompson, 2014;Reijula & Kuorikoski, 2021), but from an empirical perspective we can also add that the group interaction of cognitively diverse agents has the capacity to result in mutually corrective processing that transcends the cognitive repertoire of the participants individually. How highly skilled individuals actually perform in groups in comparison to more cognitively diverse but less competent ones depends obviously on the group but also on the task (Hill, 1982) and arguably also on how the feedback mechanism psychologically activates and operates. ...
Article
Full-text available
The social epistemology of science would benefit from paying more attention to the nature of argumentative exchanges. Argumentation is not only a cognitive activity but a collaborative social activity whose functioning needs to be understood from a psychological and communicative perspective. Thus far, social and organizational psychology has been used to discuss how social diversity affects group deliberation by changing the mindset of the participants. Argumentative exchanges have comparable effects, but they depend on cognitive diversity and emerge through critical interaction. An example of a cognitive psychological theory is discussed that explains how mutual reasoning affects how we think, make decisions, and solve problems, as well as how cognitive biases may facilitate an efficient division of cognitive labor. These observations are compared with the existing results in the social epistemology of science. Moreover, I explicate the conceptual differences between the distributed and social processing of information. While argumentative exchanges belong to the latter domain, most existing simulations model modular distributed processing, which may compromise their real-world relevance and proper conceptual interpretation. However, I aim not to criticize the existing simulation methods but to promote an approach from the cognitive psychology of reasoning that complements the current use of organizational psychology and computer simulations by investigating a different set of mechanisms relating to similar phenomena of interest in the social epistemology of science.
Article
Full-text available
We argue that the appraisal of models in social epistemology requires conceiving of them as argumentative devices, taking into account the argumentative context and adopting a family-of-models perspective. We draw up such an account and show how it makes it easier to see the value and limits of the use of models in social epistemology. To illustrate our points, we document and explicate the argumentative role of epistemic landscape models in social epistemology and highlight their limitations. We also claim that our account could be fruitfully used in appraising other models in philosophy and science.
Article
Full-text available
We suggest that philosophical accounts of epistemic effects of diversity have given insufficient attention to the relationship between demographic diversity and information elaboration (IE), the process whereby knowledge dispersed in a group is elicited and examined. We propose an analysis of IE that clarifies hypotheses proposed in the empirical literature and their relationship to philosophical accounts of diversity effects. Philosophical accounts have largely overlooked the possibility that demographic diversity may improve group performance by enhancing IE, and sometimes fail to explore the relationship between diversity and IE altogether. We claim these omissions are significant from both a practical and theoretical perspective. Moreover, we explain how the overlooked explanations suggest that epistemic benefits of diversity can depend on epistemically unjust social dynamics.
Article
Full-text available
The Hong and Page ‘diversity trumps ability’ result has been used to argue for the more general claim that a diverse set of agents is epistemically superior to a comparable group of experts. Here we extend Hong and Page’s model to landscapes of different degrees of randomness and demonstrate the sensitivity of the ‘diversity trumps ability’ result. This analysis offers a more nuanced picture of how diversity, ability, and expertise may relate. Although models of this sort can indeed be suggestive for diversity policies, we advise against interpreting such results overly broadly. © 2019 by the Philosophy of Science Association. All rights reserved.
Article
A number of formal models, including a highly influential model from Hong and Page, purport to show that functionally diverse groups often beat groups of individually high-performing agents in solving problems. Thompson argues that in Hong and Page’smodel, that the diverse groups are created by a random process explains their success, not the diversity. Here, I defend the diversity interpretation of the Hong and Page result. The failure of Thompson’s argument shows that to understand the value of functional diversity, we should be clearer about how we conceive of and measure that diversity. © 2019 by the Philosophy of Science Association. All rights reserved.
Article
Diversität und Demokratie: Agent-Based Modelling in der politischen Philosophie: Agent-based models have played a prominent role in recent debates about the merits of democracy. In particular, the formal model of Lu Hong and Scott Page and the associated "diversity trumps ability" result has typically been seen to support the epistemic virtues of democracy over epistocra-cy (i.e., governance by experts). In this paper we first identify the modeling choices embodied in the original formal model and then critique the application of the Hong-Page results to philosophical debates on the relative merits of democracy. In particular we argue that the "best-performing agents" in the Hong-Page model should not be interpreted as experts. We next explore a closely related model in which best-performing agents are more plausibly seen as experts and show that the diversity trumps ability result fails to hold. However, with changes in other parameters (such as the deliberation dynamic) the diversity trumps ability result is restored. The sensitivity of this result to parameter choices illustrates the complexity of the link between formal modeling and more general philosophical claims; we use this debate as a platform for a more general discussion of when and how agent-based models can contribute to philosophical discussions. © 2018 GESIS - Leibniz Institute for the Social Sciences. All rights reserved.
SUMMARY—As the workplace has become increasingly diverse, there has been a tension between the promise and the reality of diversity in team process and performance. The optimistic view holds that diversity will lead to an increase in the variety of perspectives and approaches brought to a problem and to opportunities for knowledge sharing, and hence lead to greater creativity and quality of team performance. However, the preponderance of the evidence favors a more pessimistic view: that diversity creates social divisions, which in turn create negative performance outcomes for the group.
Article
This book develops a manipulationist theory of causation and explanation: causal and explanatory relationships are relationships that are potentially exploitable for purposes of manipulation and control. The resulting theory is a species of counterfactual theory that (I claim) avoids the difficulties and counterexamples that have infected alternative accounts of causation and explanation, from the Deductive-Nomological model onwards. One of the key concepts in this theory is the notion of an intervention, which is an idealization of the notion of an experimental manipulation that is stripped of its anthropocentric elements. This notion is used to provide a characterization of causal relationships that is non-reductive but also not viciously circular. Relationships that correctly tell us how the value of one variable Y would change under interventions on a second variable Y are invariant. The notion of an invariant relationship is more helpful than the notion of a law of nature (the notion on which philosophers have traditionally relied) in understanding how explanation and causal attribution work in the special sciences.