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Decision-Making as a Social Choice Game
Gamifying an urban redevelopment process in search for consensus
Nan Bai1, Shervin Azadi2, Pirouz Nourian3, Ana Pereira Roders4
1,4Chair Heritage and Values, Department of Architecture Engineering and Tech-
nology, TU Delft 2,3Chair Design Informatics, Department of Architecture Engi-
neering and Technology, TU Delft
1,2,3,4{N.Bai|S.Azadi-1|P.Nourian|A.R.Pereira-Roders}@tudelft.nl
The paper reports the formulation, the design, and the results of a serious game
developed for structuring negotiations concerning the redevelopment of a
university campus with various stakeholders. The main aim of this research was
to formulate the redevelopment planning problem as an abstract and discrete
decision-making problem involving multiple actions, multiple actors with
preconceived gains and losses with respect to the comprising actions, and
decisions as combinations of actions. Using fictitious and yet realistic scenarios
and stakeholders as simulation, the results evidence how different levels of
democratic participation and different modes of moderation can affect reaching a
consensus and present in a mathematical characterisation of a consensus as a
state of equilibrium. The small set of actions and actors enabled a chance to
compute a theoretically optimal state of consensus, where the efficiency and the
effectiveness of different modes of moderation and participatory rights could be
observed and analysed.
Keywords: Serious Game, Consensus Building, Democratization, Game Theory,
Social Decision
INTRODUCTION
In this research, a playable serious game was de-
signed to simulate the further development of a uni-
versity campus in the following decades, taking into
account the cultural significance of the old cam-
pus buildings, even if not all buildings are listed as
cultural heritage, nor is the campus a conservation
area. The existence of cultural heritage challenges
the ideas of planning that are strongly influenced
by ordinary cost-benefit analyses. This paper shows
how the discretisation of a multi-actor decision mak-
ing problem can help structure a spatial planning
problem as a participatory/gamified planning pro-
cess, and pave the way for analysing such strategic
planning decisions using the conceptual frameworks
of graph theory and game theory.
The UNESCO 2011 Recommendation on the His-
toric Urban Landscape promotes greater inclusion
and democratization of heritage planning, and wher-
ever needed, make use of participatory tools to find
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555
consensus by the key stakeholders (Pereira Roders,
2019). However, stakeholders often perceive her-
itage differently, and they typically have different
kinds of stakes or concerns with respect to the re-
development of an urban area (e.g. an urban uni-
versity campus), thus conflicts can naturally arise be-
tween them in a planning process. As such, ne-
gotiation and finding consensus can be like a puz-
zle to find an optimal solution for (Bots & Hermans,
2003; Mayer et al., 2005). While such puzzles are
not necessarily insolvable, the stakeholders partici-
pating in the puzzle may need external help to real-
ize the existence of win-win solutions to avoid falling
into any dilemma(Cunningham & Hermans, 2018).
The conflicting opinions on various actions and their
consequences could be understood by stakehold-
ers by getting them involved in ‘simulation games’,
i.e. games simulating the decision-making processes,
especially construction and management [strategy]
games as defined in (Rollings & Adams, 2003). Such
games offer chances to experience other points of
views and thus potentially help reach consensus
more effectively (Werner, 2017).
GAME DESIGN AND SETTINGS
The main objective of this research is to frame a cam-
pus redevelopment planning process for TU Delft as
a multi-actor/multi-criteria decision-making process,
to be simulated as a social decision/strategy game
(Jackson, 2014). As this game seems to have the
potential to be generalized to other urban redevel-
opment planning cases, we formulate the problem
mathematically and computationally, in order to pro-
vide for further analysis with graph theory and game
theory (Easley & Kleinberg, 2010), as well as computa-
tional simulations with a larger number of iterations
using agent-based models.
In the game design, agents (stakeholders) A, ob-
jects (sites) o, choices available for those objects c,
and decisions dconsisted of choices per each ob-
ject in our game. The notation of these items and
their relations are mentioned in Table 1 and Table
2. All the agents are directly or indirectly related to
the campus redevelopment issue, thus having their
own preference and judging criteria. The decisions
will change over different rounds during the game,
meaning some of the decisions from the set Dwill
be eventually discovered over time, which we denote
with a time superscript d(t)as customary in the study
of Markov Chains. For example, the starting situation
d(0) is also considered to be a decision (which entails
doing nothing, but also keeping all states the same as
they are).
A preference type function Θis defined for
agents, describing their preference, objection, or in-
difference regarding the choices applicable to ob-
jects. The preference type of each specific agent
on possible scenarios of campus development is de-
duced from their online-accessible profiling and re-
ports. For any decision d∈D, we can define a
utility mapping function u(ai,d)for each agent ai
that checks the corresponding value in θifor all the
choices indexed with respect to objects in d, and re-
turns the sum of the preference type values. This util-
ity value is used to determine the corresponding vote
decision φiof an agent aibased on the voting func-
tion φ(ai,d)(cf. Table 3).
By adjusting the values of λi−and λi+, different
voting strategies of agents can be described, which
may allow for compromising, bargaining, trading-off
and/or paying-back as an entity. However, for the
sake of simplicity, a high value was assigned for the
ratio of the two parameters for all the agents, where
Table 1
The nomenclature
about agents in the
game
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Table 2
The nomenclature
of objects, choices
and decisions in the
game
λi−
λi+
≥min this case, thus giving the objections
much higher importance than the preferences. This
also means that the an agent will not agree to a deci-
sion deven if there is only one objected choice for a
particular object.
Considering the individual votes ϕiof all the
agents involved, a voting configuration ϕ(t)can be
formed. Further, a transformationrule can be defined
for transforming the vote to φ(t)to give “YES” votes
and “NO” votes different weights, namely 1for YES
and −αfor NO. In this case, a relatively large value α
was assigned to make sure that a complete consen-
sus must be met for the decision d.
A vector of voting weights w=
[w1, w2, . . . , wn]T∈Rnis also assigned for all
the agents, which is an unknown parameter for the
agents initially. The final voting result for decision
d(t)is thus:
υ(t)=υd(t)=wTϕ(t)(1)
For each round of voting, υ(t)>0when a consensus
is met, in other words, when the voting process is suc-
cessful, and vice versa. The individual voting weight
wireflects multiple layers of information, which can
be the social status, the decision power, the repre-
sentative pool size, and the social inclusion of agents
in the decision-making process. For an extreme sce-
nario, wican be equal to 0, which indicates that even
though the agent is invited to vote, their opinion is
not taken into account for reaching consensus and
making final decisions, which is a cruel truth often
happening in the real world.
Four different configurations of the voting
weights w[r], r ∈ {1,2,3,4}were designed, which
reflect the different levels of democratisation (Bo-
gaards, 2010). To be more specific, w[1] and w[2] are
all in a high level of democratization, where every-
one can vote, and everyone’s vote counts. In w[1]
all the agents’ weight equally, while in w[2], there
are hierarchies for voting weights. In practice, the
agents with higher weights (importance/relevance)
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Table 3
The nomenclature
of the preference
type, utility, and
vote functions
also get more chances to propose new ideas to the
decision-making, this process is also mimicked in this
game simulation. In contrast, w[3] and w[4] are all in
a low level of democratization, where even though
everyone is invited in the discussion and everyone
can vote, not everyone’s vote counts. In w[3], only
experts are given a non-zero weight, thus leading to
an expert-based decision-making scenario, while in
w[4] only the ones with either power or capital in-
cluding the municipality and the big companies are
given a non-zero weight, thus resulting as in a capi-
talist scenario. All the four democratization levels are
quite common in the real world.
Parallel to the voting process considering the
preference type of agents, two functions γ(dj)and
κ(dj)are defined that check choices per objects
in the explored decision d(t)and return the [non-
monetary] gain and the [monetary] cost of making
a choice for a specific object for the whole society,
regardless of the individual preference or the voting
result. In this game, these functions are evaluated
from a look-up table with precomputed values. But
in practice, they can be replaced by some environ-
mental assessment modules. The total social benefit
ρ(t)for the society by making the decision d(t)can
be defined as a gain-cost ratio (cf. Table 4):
ρ(t)=ρd(t)=m
j=1γ(dj)
m
j=1κ(dj)|dj∈d(t)(2)
A social decision game could also be regarded as an
optimization problem. However, it is also argued by
some scholars (Jackson, 2014) that finding a mech-
anism to optimize all the valued features of a so-
cial decision game can be very hard, if not impos-
sible. For brevity, this research focuses on search-
ing for the best-fitting decision d(t), satisfying υ(t)
(a constraint) and maximising ρ(t)(an objective)
of the social decision system given a game setting
(A, o,c,Θ,u, φ, w, γ, κ).
The value of υ(t)represents how happy each
agent would be in the end about the decision d(t).
This can reflect the feature of “Individual Rationality”,
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Table 4
The nomenclature
of the social
benefits in the
game
which is “a requirement that each individual would
weakly prefer participation in the mechanism to not
participating” (ibid).
The value of ρ(t)represents how much bene-
fit the whole society gets from the decision d(t).
This can reflect the feature of “Efficiency”, which is
“a requirement that a social decision maximises the
sum of utilities of the individuals in society” (ibid).
However, ideally the efficiency of a decision must be
checked against the preferences of all agents in the
sense of Pareto Efficiency.
REAL-WORLD SIMULATION
Serious Gaming Workshop
After building the social decision game setting
shown in section 2, it was first implemented it in a
real-world simulation. Thirty participants took part
in the game during an international workshop on
‘democratisation’ hosted at TU Delft, within the ITN
HERILAND program. Initially, four democratisation
levels have been designed as described above. How-
ever, due to the limited number of participants, only
three of them (without the 3rd group setting) were
successfully implemented as a real-world simulation.
The three groups faced differentlevels of democ-
ratization in terms of the weights and rights during
the vote for the agents, thus having a different w[r],
and ceteris paribus.
The background information, the rules, the dy-
namic, and the settings of the game were explained
to the participants before the game started in the
workshop. The preference types of all the agents
were written on a profile card given to the partici-
pant confidentially (see an example in Figure 1). They
needed to read their assigned profiles and make sure
they understood the game rules before starting. All
participants could choose to reveal, hide, or misrep-
resent as much information written on their profile
card as long as they obey the ONLY rule of being loyal
to their mandated preference types when they voted
for decisions. As is discussed in section 2, the agents’
voting decision in relation to their utilities was sim-
plified into a non-compromising non-payback strat-
egy, i.e., do not vote ”YES” for any decision d(t)that
consists of any object-choice pair djthat they are
Figure 1
Example of the
game interface
during the
workshop. Left: the
sites to decide on.
Right: The
stakeholder profile
declaring the
preference type of
each agent.
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Figure 2
The decision made
by each group
within each group
are shown as
polygons, whose
vertices are the
chosen choices per
each object
(coloured groups).
The height of the
coloured bars
indicates the
potential social
benefit of each
choice per object.
Hexagons are
slightly offset
inwards and
coloured differently
so as to distinguish
different rounds of
the games.
mandated to oppose to, no matter how many other
object-choice pairs in the same decision are in their
preference, even though that decision may lead to a
higher overall social benefit.
During the workshop, a ‘game master’ was as-
signed to each group, who observes, coordinates,
records, and monitors the gaming process. They
made sure that all participants (agents) followed their
mandated strategy and voting rules. Each group
started from the same initial decision d(0), which
triggered a “NO” vote for at least one agent. They
had four rounds to discuss, negotiate, and propose
a new decision d(t), t ∈[1,4] to be voted at the end
of each round.
It was stressed to all the participants and the
game masters that this game had twofold goals: 1)
that the primary goal for the game was to find a
decision that gets a “YES” from all participants, i.e.
proposing a good-enough social decision that could
fulfil the requirement of “Individual Rationality”, char-
acterized as a consensus that minimally satisfied ev-
eryone involved; and 2) that the secondary goal was
to seek to maximize the total gain-cost ratio of the
final decision provided the consensus was already
met, thus proposing a better social decision that ful-
filled the requirement of “Efficiency”.
Since in one of the three groups, the votes of
some of the agents were ‘secretly’ dumped (with a
wi= 0), there was a special outcome, where the pri-
mary goal was reached while some agents were vot-
ing “NO”. In this case, the ‘excluded’ agents could join
forces and use a special card “FIGHT” to start a strike,
which could force the others to invalidate the ‘suc-
cessful’ outcome and resume further discussion con-
sidering their opinions. For each group r∈ {1,2,4}
and for each round t∈ {0,1,2,3,4}, the decision
d(t)[r]∈Dand the voting configuration φ(t)[r]∈
{−1,1}nwere recorded for each round of the game
for all the three groups to be used in the analysis.
Simulation Outcomes
The three groups played the game under the instruc-
tion of the game masters. Almost all the participants
expect for (a8)the citizen in group 1 obeyed their
mandated preference types. Within the 4 rounds of
game, two of the three groups (group 2 & 4) managed
to reach consensus and came up with an individual
rational decision d that was not opposed by any par-
ticipant. The other group (group 1) also claimed to
have reached consensus while a8(the citizen) dis-
obeyed the rules and voted YES even though the de-
cision did not completely match his mandate. Mean-
while, one of the groups (group 2) managed to reach
the only feasible & efficient decision that maximized
the social benefit ρ(d). As shown later, this was very
unlikely to happen if left only to chances, since only a
rather small portion of the decision set Dwould sat-
isfy the primary goal of individual rationality (0.36%
for group 1 and 2, and 3.6% for group 4, considering
their different voting weights w[r]). The decisions
for each of the groups are plotted in Figure 2.
Interestingly, group 4 reached their “incomplete”
consensus regardless of the “NO” votes from some of
the participants who had a voting weight wiof 0 in
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the second round already. The fact that those partici-
pants were ignored triggered three of them to initiate
a “FIGHT” striking against the outcome. The group
resumed the discussion and approached a complete
consensus that eventually satisfied everyone.
ANALYSIS
Analytic Methods
Here, the proposed mathematical framework in Sec-
tion 2 would be extended with a set of analytical
methods for studying: 1) the difference of the ex-
plored decisions in each round, 2) the effectiveness
of the game dynamics, and also 3) the effectiveness
of the different democratisation set-ups in different
groups.
Figure 3
The embedding of
the decision graph
in the polar
coordinate system.
To create this
embedding, we
map the index of
each decision to
angular coordinates
and we map the
reversed social
benefit of the
decision to radial
distance. This
means that as closer
the decisions get to
the center of the
graph, the higher
their gain-cost ratio
is for the society.
The first step is to enumerate the decision space and
model the relations of the decisions together. Here,
the decision space is modelled with as a graph Γ.
Within this graph, each node represents a decision d,
and each edge indicates that the nodes at the end of
it differ in one and only one of their object-choices dj.
Consequently, the graph Γrepresents the similarities
of the decisions since it is essentially connecting sim-
ilar node-decisions. In Γ, each node has a degree of
m×(l−1). This is because the choice of any one
of the objects can be differed(mpossibilities) and
that choice can be differed to any choice except the
one already existing in the decision (l−1possibili-
ties). Considering the setup of the gaming workshop,
each node in Γhas a degree of 6×(5 −1) = 24.
Moreover, Γhas a diameter of m, since traversing
each edge is equivalent to changing a choice about
a certain object, and it is obvious that by changing
the choice of all objects, one at a time (in total m
times), any node-decision d(t)can be reached from
any other node-decision d(s).
On the decision graph Γthe graph-theoretical
distance (path-length) between every two decisions
can be used to measure the difference of those de-
cisions distd(s),d(t)(see Figure 3). Comparing
the distance between the decisions of each round, it
can be used to compare the extent to which a group
explores the whole range of possible decisions in a
game-round (cf. section 4.2 for exemplary results).
This particular definition of distance makes it pos-
sible to eventually relativize the progress made in
decision-making in each round of the game. To indi-
cate such relative progress, the leap difference func-
tion ζis defined as dividing the change in the gain-
cost ratio by the distance of two decisions (cf. Table
5 for details):
ζd(s),d(t)=ρd(t)−ρd(s)
distd(s),d(t)(3)
Analyses of Simulation Outcomes
Firstly, the decision graph (Γ) for the game setup is
formed given the objects (o) and choices (c). The
preference type of voters specify which decision-
nodes are consensual and which are not. Since the
voters are different in each group, the set of consen-
sual decision-nodes differ per group; and as reaching
consensus is the primary condition of this game, the
percentage of consensual nodes gives a rough esti-
mate of how hard it would be to reach a consensus
in this game. During the gaming workshop, group 1
and 2 had 12 consensual decision nodes, while the
limited number of voters in group 4 had made a con-
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Table 5
The nomenclature
of analytic methods
Figure 4
Green nodes are
consensual
decisions, and Red
nodes are
non-consensual
decisions. Blue
trajectory and the
numbers indicates
the progression of
decision making
through playing
rounds for each
group. Black circles
highlight the
bounds of gain-cost
ratio for the
consensual
decisions.
sensus more-easily reachable and raised the number
of consensual nodes to 120 (see Figure 4).
The distance function relativizes the change in
rounds compared with each other, and in the whole
game compared between groups. This relativization
reveals the amount of exploration that has happened
in rounds and groups. In Figure 5, group 1 and 2
have explored more of the decision graph compared
to group 4. In addition, by comparing the gain-cost
ratio of the decision of each round against the tra-
versed distance on the graph, it shows that although
all the group have started from ρd0= 10, only
group 2 has finished the game with the same gain-
cost ratio.
DISCUSSIONS
It is remarkable that that all three groups with dif-
ferent levels of democratisation have finally reached
consensus (or claimed to have reached consensus) in
the limited rounds of discussions and negotiations
for this game design, as it is almost impossible to
reach consensus purely searching and discovering
the arena randomly, according to a brute-force com-
putation. There must have been some strategies to
learn from the human participants about how they
manage to transform the information and learn from
the past scenarios. However, it is arguable that the
setting is only hard if the preference types of the in-
dividuals are not a common knowledge to the society
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Figure 5
Blue line: gain-cost
ratio plotted
against the
traversed distance,
Orange Line: leap
difference function
against traversed
path lengths per
each round. After
the “FIGHT” in the
round 2 for group 4,
the leap difference
function becomes
negative. It is also
presented that the
initial round of all
groups has a
negative value,
which is due to the
fact that they have
started from a
non-consensual
node with 10,
therefore their first
step has been
toward consensus,
rather than
maintaining the
gain-cost ratio.
Moreover, in the
last round of all
groups the leap
function has a
positive value.
throughout the game process. The initial state of this
game satisfies such a requirement, where the prefer-
ence profile is claimed to be confidential (as shown
in Figure 1). However, any specific behavioural strat-
egy of the participants was allowed during the dis-
cussions. If they come into a point where everyone
agrees to collaborate and unveil their secret prefer-
ence types, then the game is no longer a dilemma
(as is also the case for the repeated form of the Pris-
oner’s Dilemma), rather a simple puzzle to observe
and solve. This also mimics the reality and implies the
value of such participatory social decision game for
the real-world competition and collaboration.
Future research is expected to construct an
Agent-Based Simulation Model using the same game
settings as described in this paper. The performance
of different strategy models and voting mechanisms
will be tested, including a benchmark performance
with random walks. Agents can be devised to follow
the strategies that is learnt from the real-world sim-
ulation from human participants and related state-
of-art research. It is also promising to study the
effect of changes in the proposed parameters and
functions to allow more complicated social settings,
which may include scenarios in which: trade-offs
or compromises of certain individuals are allowed;
learning and diffusion of preference types could oc-
cur; each agent represents a different number of peo-
ple and thus have different weights; or majority con-
sensus, rather than complete consensus is expected.
Later the games with different settings can be tested
with humans again, comparing with our computa-
tional simulation results, and teaching them to per-
form even better.
The eventual purpose of this research is to in-
tegrate democratization and participation into the
decision-making process for heritage redevelopment
and spatial planning, as is one of the essential goals of
the HUL recommendation. I t is also interesting to see
that in our real-world simulation outcome, the group
2, where all agents could vote but only part of them
could propose new ideas, reached the optimal solu-
tion most easily; while the group 4, where some of
the agents are invited to the discussions but were not
given the right to vote, triggered the “FIGHT” branch
and started a strike in their society; and in the group
1, where the highest level of democratization was
assigned and each agent could change the decision
evenly, there was a great chaos during the discussion
and one of the agent even had to play up to deceive
the game master that the consensus was met. This
is also consistent with the idea that the democracy is
necessary, but among the different forms of democ-
racy the informed consent would contribute to the
most efficient democratization (McGee, 2009).
CONCLUSIONS
The objective of the research was to frame an ur-
ban development problem as a gamified multi-
actor/multi-objective social decision-making process
and accordingly formulate the problem mathemati-
cally so that it can be further analyzed by means of
graph theory and game theory.
The biggest question in the background of the
research was whether such problems can be solved
computationally (at least from a mathematical point
of view), and if yes, why should they be framed as
games? The answer to this question is partially de-
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563
pendent on the scale (level of detail) and thus the
complexity of the problem and to some extent on
the social aspects of the problem. Our formulation
shows that the order of complexity of such problems
is exponential with respect to the number of objects
raised to the power of a maximum number of choices
available per each object. This could be a justifica-
tion to apply [meta] heuristics to search for optimal
outcomes. However, there may still be two reasons
why both gaming and artificial intelligents methods
(meta-heuristics) could be relevant at the same time:
on the one hand, in case of large problems, they
could be NP-hard, i.e. mathematical problems with
no known algorithms for solving them systematically
in polynomial time, whose solutions can only be ‘ap-
proximated’; and on the other hand, even if the so-
lution is approximated by means of algorithms and
machines, humans must be involved in formulating,
understanding, and attempting to solve the problem
so that they can ‘accept’ and ‘abide by’ the solution
(the final decisions). In other words, the didactic use
of the game and its necessity for enabling participa-
tion cannot be overruled by the use of AI methods.
On the contrary, the two approaches need to be com-
bined to make the most out of such decision-making
processes, socially and scientifically.
The main contribution of the paper is propos-
ing a formal (mathematical/computational) formula-
tion of a ‘wicked-problem’. The analyses performed
on the proceedings of the games show that design-
ing such games and playing them can help diverse
groups reach consensus more efficiently.
ACKNOWLEDGEMENT
Authors Nan Bai and Ana Pereira Roders were sup-
ported by of the HERILAND project funding (Marie
Sklodowska-Curie grant agreement No 813883). Au-
thors Shervin Azadi and Pirouz Nourian were sup-
ported by the GoDesign project funding (Ontwerp
en Overheid, grant agreement number AUT03G).
The suggestions of anonymous reviewers are grate-
fully appreciated. The authors thank Maria Valese,
Francesca Noardo, Azadeh Arjomand Kermani,
Roberto Rocco, and Franklin van der Hoeven, for
their suggestions and/or contributions for/in organ-
ising the serious gaming workshop.
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