An Innovative Model Based on Carvalho Rodrigues's Entropy

to Assess Governance in Africa: A Guinea-Bissau Case Study

João Serras

, Paulo Morgado

and Jorge Malheiros

Centre of Geographic Studies, Institute of Geography and Spatial Planning, Associate Laboratory TERRA,

University of Lisbon, Lisbon, Portugal

Keywords: Governance Cohesion, Governance Modelling, Cohesion Phase Transition.

Abstract: Governance is an abstract, intersubjective, fluid concept, meaning that it is built upon shared beliefs, norms,

and practices that are collectively agreed upon by a society, community, or group. It means different things

to different cultural environments and scopes. Our current research addresses the challenge of obtaining in-

sight into Governance's underlying mechanisms by using the concept of Cohesion derived by Carvalho Ro-

drigues from applying Shannon's Entropy. Our study is based on empirical data obtained from field observa-

tions across Guinea-Bissau.

This paper presents our cohesion model and a first outlook for using it in the available data sets. It shows the

impact of several potential Governance Determinants over a set of specific Governance Dimensions, demon-

strating that Ethnicity Variation, local Community Morphology and the distance of Central Government fa-

cilities are the most impacting determinants for better cohesions.

1 INTRODUCTION

There’s no consensus about the meaning and scope of

of Governance, which may be related to organisation

sizes, from simple families to countries. Within the

specific context of our work, governance is under-

stood as the structuring of Governance, which is dis-

tinct from government, which refers to the act of gov-

erning. As defined by the Institute on Governance in

Canada, Governance refers to the way society or

groups within it organise themselves to make deci-

sions (Institute on Governance, 2022). Consequently,

in this study, the term Governance focus on social

Governance rather than narrower concepts such as

corporate Governance. Specifically, it pertains to how

public institutions and systems of authority operate to

manage public affairs and serve citizens' needs and in-

terests.

Governance is a complex intersubjective phenom-

enon influenced by various political, economic, so-

cial, and geographic factors. Significant and recurring

failures of international policies and institutions in ef-

fectively stabilising societies and promoting global

https://orcid.org/0000-0002-7619-509X

https://orcid.org/0000-0002-3220-4943

https://orcid.org/0000-0002-0976-044X

prosperity and well-being are of particular concern.

Examples include governance crises in regions such

as West Africa, e.g., Mali, Burkina Faso, Guinea-Co-

nakry, and Nigeria.

In recent years, there has been a growing interest

in understanding the drivers that impact Governance,

particularly in peripheral sphere of the European Un-

ion, such as West Africa as it is illustrated by the work

of many scholars such as (Abubakar et al., 2020;

Achanso, 2022; Krawczyk & Sweet-Cushman, 2016).

Guinea-Bissau, a small country in this region

characterised by its ethnic, religious, and social diver-

sity, irregular political trajectory—including a civil

war, political instability and economic underdevelop-

ment, in par with formal institutions, such as a consti-

tution derived from external concepts, presents a

compelling case for exploring this issue.

Our research seeks to obtain insight into how some

candidate Governance determinants influence govern-

ance outcomes in Guinea-Bissau, taken as a proxy of

West African societies. To achieve this, our group

used as a keystone the concept of Cohesion as pro-

posed by Carvalho Rodrigues (Carvalho Rodrigues,

Serras, J., Morgado, P. and Malheiros, J.

An Innovative Model Based on Carvalho Rodrigues’s Entropy to Assess Governance in Africa: A Guinea-Bissau Case Study.

DOI: 10.5220/0013360400003935

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 11th International Conference on Geographical Information Systems Theory, Applications and Management (GISTAM 2025), pages 187-194

ISBN: 978-989-758-741-2; ISSN: 2184-500X

187

1994; Carvalho Rodrigues & Peixoto, 1991). This was

used to assess several Governance dimensions and for

several possible drivers or Determinants.

2 CONCEPTUAL FRAMEWORK

2.1 Baseline Model

2.1.1 Complexity of Behaviour and

Information

In the book Systems, Entropy and Cohesion (Car-

valho Rodrigues & Peixoto, 1991, p. 213), the authors

introduce a fundamental distinction: the differentia-

tion between Complexity and Behavioural Complex-

ity, quoting, "[…] there are systems that contain or

encompass many elements, or parts, with very pre-

dictable behaviour, we would even say simple, and

there are very simple systems with few parts or ele-

ments with enormous behavioural complexity", a dis-

tinction that is considered fundamental for the re-

search we have set to carry out, which focuses pre-

cisely on the behavioural elements derived from Gov-

ernance. The authors add: "Complexity comes pri-

marily from the number of components, while behav-

ioural complexity is due to the type and degree of

links [between the components]".

They go on to say that there is a relationship be-

tween these two concepts, which, in the authors' in-

terpretation, is achieved through the "amount of infor-

mation needed to describe or interpret the behaviour

of the system", which does not depend on the number

of constituent elements, but instead on the type and

diversity of their connections.

An example of this situation, in terms of urban or-

ganisation figure below shows two communities with

roughly the same population: Gendo and Sansanto, in

the Oio region, north of Bissau. Gendo is a type of

agglomeration with no orientation and Sansanto is a

street type Community, with a clear orientation and

organisation around the road.

Figure 1: Spatial organisation of two typical communities

in Guinea-Bissau in the Oio region. Gendo (left) and San-

santo (right).

Thus, Gendo exhibits a higher complexity in

household distribution with a similar number of con-

stituents; however, it requires more information to

properly describe as it exhibits greater entropy.

2.1.2 Information, Entropy and Cohesion

It is possible to determine the degree of Cohesion of

a structure maintained by information, as is the case

in social structures, based on the quantity of infor-

mation in that structure, which in human society can

translate into a sense of well-being or degradation

(Carvalho Rodrigues & Peixoto, 1991, pp. 217–223).

To determine this, they use the results of Fisher as

mentioned by Frieden (Frieden, 1998), Shannon

(Shannon, 1948) and the equation derived by F Car-

valho Rodrigues for the quantity of information (Car-

valho Rodrigues, 1994, p. 22):

(1)

Where σ is the number of occurrences of an event

and N the number of possible events. Estimating H

for of the communities and for each of the Govern-

ance dimensions and determinants is the keystone

constituent of our work.

2.1.3 The Cohesion Curves

Carvalho Rodrigues (Carvalho Rodrigues, 1994, pp.

42–43), established the behaviour of a system cohe-

sion as it depends on a relevant factor. The figures

below, illustrate the situation.

Figure 2: Justice Dimension Cohesion function extracted

from the actual Guinea-Bissau dataset. The maximum Co-

hesion was obtained at 0.368.

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Figure 3 : Justice Dimension Cohesion function. This plot

illustrates that, for Justice, the larger portion of the commu-

nities have a slope greater than -1, or 45º, which can inter-

pret as this being strongly cohesive and export entropy to a

relatively small number of communities – the ones having

slope greater than1. In social terms it may mean that people

are comfortable with Justice, a natural outcome, since most

of the Justice is practices by Big Men and Good Men repre-

sentants. A compound slope greater than -1, actually, -0.806

may be interpreted as an overall positive cohesion, in this

case, for the Justice Governance Dimension.

2.1.4 Governance and Cohesion

Vergolini (Vergolini, 2011, pp. 198–199), quoting

Canadian Heritage, defines Social Cohesion as "a

process that contributes to building a common sense

of belonging to the same community" and Lafaye

(Lafaye, 2011) refuses a clear definition, preferring to

describe and discuss various types of interpretation of

social Cohesion, including societal, individualistic

and mixed models, and thus finding multiple defini-

tions.

It is important to clarify that in our study, the con-

cept of Cohesion does not directly correspond to so-

cial Cohesion, but to the more abstract concept of Co-

hesion of a System, regardless of its specific type.

It is also assumed that governing a society consists

of introducing mechanisms to organise it. In other

words, governing consists on reducing the Entropy of

the society system, which, by direct implication, cor-

responds to increasing the Cohesion of that system.

To explain the behaviour of the constituents of an

anarchic society with maximum Entropy requires a

vast amount of information describing all the individ-

ual behaviours; to describe the behaviour of a com-

pletely organised society with recognised, shared and

obeyed laws, you need to know the rules that shape

the personal behaviours, which are necessarily far

fewer in number. Thus, it is essential to distinguish

HDI: Human Development Index

between two broad classes of concepts: the dimen-

sions of Governance, i.e. the elements that allow us to

gauge how Governance is practised, and the determi-

nants of Governance, i.e. the elements that can poten-

tially impact the sense of Governance, a sure sense

and coherence, concepts that we intend to clarify and

characterise below.

The essential assumption here is that Governance

contributes to structuring a society, which globally

corresponds to lowering its Entropy, which will be re-

flected in the fact that cohesion indicators indicate a

change of phase at higher values on the scale of loss

of Cohesion.

2.2 Governance Dimensions

Various groups of Governance Indicators have been

proposed by various organisations.

To move forward with the identification of indi-

cators, we have taken the following indicators com-

monly accepted as universal as a basis for governance

indicators: Education, Health, Justice, Food Security

and Infrastructure. This selection is based on a com-

bination of perspectives from three public sources:

the World Bank indicators (World Bank, 2023) , the

UNDP indicators to make up the HDI

, and the United

Nations SDGs

(United Nations Department of Eco-

nomic and Social Affairs, 2015, 2023). From these,

the below Governance Dimensions were structured to

obtain an understanding of the possible impact.

Table 1: The studied Governance Dimensions.

ACRONYM DESCRIPTION

Education

Health

Justice

Food Securit

Famil

Wealth

Infrastructure e

ment

Culture

Community Assets

Happiness

2.3 Possible Impacting Governance

Determinants

The authors found no significant body of research

work linked to empirical data regarding drivers of

governance at a Community level, leaning to the con-

clusion that its scope and granularity are not main-

stream investigations. In fact, mainstream work is

much related to abstract concepts such as some key

SDG: Sustainable Development Goals

An Innovative Model Based on Carvalho Rodrigues’s Entropy to Assess Governance in Africa: A Guinea-Bissau Case Study

189

determinants reported in the African Governance Re-

port (Africa Governance Report, 2023) and by the

World Bank (World Bank, 2023), to not only account

for actual livelihoods but also carry a pure top-down

perspective on Governance. Two simple examples il-

lustrate the situation in rural West-Africa: on Rule-of-

Law villagers find, regularly, that the Koran along

with their social norms, provides any requirable rule

to be obeyed, thus the ultimate State Law, the Consti-

tution, written somewhere by non-related (normally

dead) people, is not really to be considered, and Con-

trol-of-Corruption, villagers find that this concept

somehow contradicts what is, for them, considered

normal business procedures.

Nevertheless, the work of scholars such as Rot-

berg (Rotberg, 2009), Alence (Alence, 2004), and

Chabal (Chabal, 2009), should be noted as they ad-

dress relevant elements of livelihoods and their link-

age to forms of governing.

Nevertheless, the African Union published its

own Development Agenda for 2063, linked to the

SDGs, containing 7 major aspirations from which po-

tential drivers for Governance could be drawn and

would constitute the foundation of our set of Deter-

minants.

In fact, the determinants of Governance will be

the elements that contribute to Governance taking

place in the society under analysis, in this case

Guinea-Bissau, taken as a proxy for West Africa,

which implies, that in terms of the basic principles of

information theory which are directly related to the

concept of Entropy in the 2

principle of thermody-

namics: the lower the Entropy, the more organised

the system is and likely to attain the ultimate goal of

Governance: organise.

The final list of potential Determinants to evaluate

is listed in the below table

Table 2: The suggested Governance Determinants.

ACRONYM DESCRIPTION

Communit

Mor

holo

dst Distance to Government Service.

etn Ethnical Variation

ss Chabal Rules

nds Needs and Wants Satisfaction

env Environment Stress

iv Public Investment

sec Secularity Bias

soc Social Organisation and relations with

nei

hbour communities

Naturally, this situation must be taken with extreme cau-

tion as there is no distinction from democracy to dicta-

torship which may carry similar cohesion values but

may also have wildly different outcomes in respect to

2.4 Modelling Determinants' Impact

The next step in the work is to propose a method to

evaluate the impact on Governance, of the several De-

terminants under analysis. To assess this, the follow-

ing set of axioms was accepted:

 Governance intimately implies the structuring

of a society; this means that the higher the cohe-

sion value of an indicator, the best Governance

is in that specific indicator

 The impact of a specific Determinant, can be

measured by identifying the Communities for

which the cohesion value (H) is higher than the

median, doing the same for the Communities

with H lower than the median, and computing

for the specific Dimension analysis, the values

of H on the Dimension for both sets and the pic-

ture below illustrates this strategy.

Figure 4: The impact of the Determinant Environment

Stress on Community Wealth. It may be noticed that both

curves are pretty much aligned, which suggests that there is

no real noticed impact of the Environment on local wealth

conditions.

3 ASSESSING AND COMBINING

DATA

3.1 Strategy to Address Core Concerns

3.1.1 Key Concerns

The strategy to address data quality and completeness

of the available data sets is bound to two sets of core

their sustainability and/or development and happiness,

so best must be framed under the limited concept of de-

taining better cohesion.

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concerns: first, there exist no surveys that directly

question the adopted Governance Dimensions or De-

terminants, so a means of converting the available in-

formation into observed variables had to be estab-

lished and, secondly, the available data, itself, needed

to be assessed for its quality, namely in what regards

the explanation of the variations, i.e., the independ-

ency of the available 1,400 data points per each of the

208 communities, which conducted to a separated

study whose results are summarised below.

3.1.2 Raw Data Analysis Outlook

Raw Data Analysis, consisted in obtaining prelimi-

nary insight into the data collected, and checking

some of their key parameters, such as the likeliness of

its consistency, namely for explaining the variation,

identification of correlations, etc...

3.1.3 Correlation Analysis

Correlation analysis was carried using both Pearson

and Spearman methods.

Figure 5: The figure suggests an overall comprehensive set

of data points, with 90% of them having correlation factors

less than 0.3. The negative correlation, the % is much

higher, suggesting that the Data Set displays a significant

orthogonality.

3.1.4 Principal Component Analysis

The goal of carrying out this analysis was to identify

the most relevant questions as measured by their con-

tribution to the most relevant Factors. For this, the fol-

lowing SPREE plot was obtained.

3.1.5 Combining Raw Data into Dimensions

and Determinants

To achieve this all the data elements were analysed

and classified into one of the Dimensions or one of

the Determinants, avoiding any overlap to ensure or-

thogonality.

Figure 6: The plot displays the relative relevance of the PC

and, Kaiser Criterion, in red in the figure. Principal Com-

ponent with an eigenvalue less than 1 explains less variance

than one of the original variables in standardised data. How-

ever, a quick observation hints that, with roughly 20 com-

ponents, we could explain most of the variation.

4 COHESION ANALYSIS

4.1 Cohesion Assessment Highlights

A thorough analysis is out of the scope of the current

communication, so we present its current outcome as

per the estimated impact of Determinants on Govern-

ance.

The next table presents a quick outlook of the

overall Cohesion analysis.

Table 3: Cohesion Highlights.

DESCRIPTION

p @

max H

global

slope

DIMENSIONS

Education 0.370 0.368 1.394

Health 0.414 0.365 1.078

Justice 0.368 0.368 0.806

Food Security 0.367 0.368 0.705

Family Wealth 0.365 0.368 1.357

Infrastructure equipment 0.368 0.375 1.118

Culture 0.368 0.368 0.499

Community Assets 0.368 0.378 1.447

Happiness 0.368 0.361 0.724

DETERMINANTS

Community Morphology 0.368 0.378 1.507

Distance to Government Service. 0.369 0.368 1.083

Ethnical Variation 0.374 0.368 1.225

Chabal Rules 0.353 0.368 0.778

Needs and Wants Satisfaction 0.358 0.368 0.600

Environment Stress 0.003 0.016 1.541

Public Investment 0.080 0.201 2.728

Secularity Bias 0.368 0.368 0.385

Social Organisation and relations

with neighbour communities

0.367 0.368 0.716

The interpretation is that the lower the max H

and/or the p@max H, the less cohesive the structure.

Subsequently, the outline values shown in Table 3,

An Innovative Model Based on Carvalho Rodrigues’s Entropy to Assess Governance in Africa: A Guinea-Bissau Case Study

191

suggest that the Health Dimension is more cohesive

than any other Dimensions or Determinants, as it

peaks at 0.414 for the p@max H parameter. However,

its global scope of 1.078 hints that the number of com-

munities with low entropy levels is less than Justice,

Food Security or Culture. A likely interpretation is

that, for instance, Culture and Justice are more homo-

geneous than Health across the country. A special note

is the value of the slope found for Happiness, which is

consistent with Culture, Food Security and Justice,

which is likely to suggest that they are interrelated, po-

tentially due to the type of West-African communities.

Finally, we should mention two outliers, Environ-

ment Stress and Public Investment that clearly require

a close inspection of the source data, as they present

slope values very high, accompanied by p-axis values

very low.

4.2 Impact Evaluation Highlights

4.2.1 Impact on Dimensions

To estimate the overall impact of the studied Determi-

nants, our project obtained the sum of the lags between

the High Cohesion and Low Cohesion curves as illus-

trated above in Figure 4 for each specific Dimension.

The open source meethere app, developed within

our project provides a detailed output of this analysis

and it is not in the scope of the current communica-

tions to analyse the full set of outcomes. Neverthe-

less, we show the result for the Education Dimension

in the below figure to illustrate our analysis.

Figure 7: The impact of the Determinants on the Education

Dimension.

The Chabal Principles represent the local societal norms

Several scholars, such as (Fox, 2015), incorporate the con-

cept of Secularity within Liberalism they consider it a

The above figure shows that the different Deter-

minants have different impacts and, out of the nine

Determinants, only four, Ethnicity Variation, Com-

munity Morphology, Public Investment and Govern-

mental Distance carry better results. These findings

suggest that if the Government wants to focus its mea-

gre resources on improving Education, it will benefit

by addressing its policies, investment, and budget

spending, specifically in those factors.

4.2.2 Overall Impact on Governance

To obtain the Overall impact on Governance for each

Determinant, the project added all individual contri-

butions to each dimension:

Figure 8: The figure show that the most relevant drivers of

Governance.

The above figure shows that Public Investment,

Chabal Principles

(Chabal, 2009), Ethnic Variation,

Government Services availability, and Community

Morphology, have an edge over Secularity

, Societal

Organisation, Environment Stress and Satisfaction of

immediate Needs.

This can be interpreted as, being drivers of Gov-

ernance, namely the availability of Government Ser-

vices at community level, expenditure in them will

likely potentially bring the best outcomes. A good ex-

ample, when we look at the detailed inputs for this list

Determinant, is the benefit of replacing the process of

Citizen card, which currently is at the Region

level,

to at a Sector

level, which would come at almost

zero spending.

vital element within liberalism, acting as a safeguard for

individual freedoms, equality, and pluralism

Region: Admin 1

Sector: Admin 2

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192

4.3 Applicability Outside

Guinea-Bissau

Societies across West Africa, such as in Senegal,

Mali, Guinea and Guinea-Bissau do have similitudes,

both Cultural, Linguistic and Norms as it is proposed

by Ameka et alia (Ameka & Breedveld, 2004), when

studying local norms and do not consider the specific

country level separation, but West-Africa as a whole,

which concurs with scholars such as Herskovitz in

several publications such as (Melville & Herskovits,

1924), Conton (Conton W.F., 1961), (Achebe, 2022)

and (Bohas et al., 2018). All these authors stress com-

monality either due either to similitude of local norms

and mores or the impact of roughly 1,400 years of Is-

lam governing framework. Illustrating this situation,

the two below Figures evidence the similitude of the

Social Norms, Mores and Religion.

Figure 9: Map produced by Herskovits evidencing areas of

cultural similitude.

Figure 10: Map sourced from Wikipedia (Wegomakity-Tri-

noyesi, 2024), showing the current impact of Islam in West-

Africa.

5 CONCLUSIONS AND

FURTHER WORK

The present communication highlights the use of Co-

hesion as a means to uncover and substantiate politi-

cal drivers and subsequent options for Governance.

Its first findings are positive and provide clues for de-

tailed modelling, namely enabling machine learning

geographic prediction algorithms, which is the next

step in our work.

In addition, the authors are keen to, after comple-

tion of the current work, obtain insight into how the

memes related to the Dimensions and Determinants

propagate within the geographical space, testing their

propagation through several methods.

ACKNOWLEDGEMENTS

We would like to express our profound gratitude to

Prof. Fernando Carvalho Rodrigues for his insightful

introduction to cohesion modelling and for his pa-

tience in detailing interpretations, which greatly en-

hanced the depth of this study. We also extend our

heartfelt thanks to Eng. Inussa Baldé, General Secre-

tary of the Guinea-Bissau/Senegal Cooperation

Agency, for his invaluable advice and guidance in in-

terpreting the outcomes of this research. Our sincere

appreciation goes to the Government of the Republic

of Guinea-Bissau for authorising the use of official

data, which was essential for this work. Finally, we

are deeply thankful to Dr. Muminatu Jaló for her in-

valuable hints and expertise regarding local cultural

elements, which provided important contextual in-

sights for this study.

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