Ethicametrics: A New Interdisciplinary Science

Abstract

This paper characterises Ethicametrics (EM) as a new interdisciplinary scientific research area focusing on metrics of ethics (MOE) and ethics of metrics (EOM), by providing a comprehensive methodological framework. EM is scientific: it is based on behavioural mathematical modelling to be statistically validated and tested, with additional sensitivity analyses to favour immediate interpretations. EM is interdisciplinary: it spans from less to more traditional fields, with essential mutual improvements. EM is new: valid and invalid examples of EM (articles referring to an explicit and an implicit behavioural model, respectively) are scarce, recent, time-stable and discipline-focused, with 1 and 37 scientists, respectively. Thus, the core of EM (multi-level statistical analyses applied to behavioural mathematical models) is crucial to avoid biased MOE and EOM. Conversely, articles inside EM should study quantitatively any metrics or ethics, in any alternative context, at any analytical level, by using panel/longitudinal data. Behavioural models should be ethically explicit, possibly by evaluating ethics in terms of the consequences of actions. Ethical measures should be scientifically grounded by evaluating metrics in terms of ethical criteria coming from the relevant theological/philosophical literature. Note that behavioural models applied to science metrics can be used to deduce social consequences to be ethically evaluated.

1. Introduction

There are a few methodological papers on the ethics of metrics. For example, Zagonari [1] on science metrics; Islam & Greenwood [2] on business metrics; Nobles [3] on biodiversity metrics. There are a few empirical papers on the ethics of metrics. For example, Zagonari & Foschi [4] on science metrics.

There are some methodological papers on metrics of ethical behaviours. For example, Saltelli [5] and Di Fiore et al. [6] on public policy; Persad [7] and Tsan & Van Hook [8] on medicine; Jafino et al. [9] and Vecchione & Chalabi [10] on climate change; Gatto [11] and Ikerd [12] on business; Kuc-Czarnecka & Olczyk [13] and Lo Piano [14] on artificial intelligence. There are many empirical papers on metrics of ethical behaviours. For example, Bunce et al. [15] on the effects of workplace bullying and harassment on mental health conditions; Cheung & Yeung [16] on the consequences of parental nurturing on youth violence perpetration; Zagonari [17] on the impacts of foreign direct investment and cross-border trade on waste management, organic farming and energy conservation; Boţa-Avram et al. [18] on the influences of legal, political and country-level governance determinant factors on firms’ ethical behaviour; Bakas et al. [19] on the effects of control and work ethic environment on labour productivity; Abdelmoula et al. [20] on the consequences of business ethics on tax avoidance; Chen et al. [21] on the impacts of climate uncertainty on corporate fraud; Chouaibi et al. [22] and Landi & Sciarelli [23] on the influences of corporate social responsibility on financial performances; Marzouki & Ben Amar [24] and Nguyen [25] on the effects of corporate social responsibility on management earnings; Nugraheni et al. [26], Zagonari [27], Zagonari [28], and Zagonari [29] on the consequences of religious ethics on sustainability; Zagonari [30], Zagonari [31], and Zagonari [32] on the impacts of secular ethics on sustainability; Zagonari [33] and Zagonari [34] on the influences of both religious and secular ethics on sustainability; Zagonari [35] and Zagonari [36] on the implications of both religious and secular ethics on health and happiness.

There are no methodological papers on both ethics of metrics (EOM) and metrics of ethics (MOE), with empirical analyses on their potential over time and across disciplines. I will call Ethicametrics (EM) a new interdisciplinary scientific research area focusing on both EOM and MOE.

In other words, three main GAPS can be identified in the literature. First, the lack of a comprehensive methodological framework for both EOM and MOE (GAP 1): without this framework, it is not possible to appreciate EM as a single scientific research area (WHAT), with EOM and MOE simply characterised by different starting points, and it is not possible to provide a practical scientific justification for EM (WHY). Second, the absence of an inclusive methodological and empirical discussion for EOM and MOE (GAP 2): without this discussion, it is not possible to predict the potential of EM across disciplines (WHERE) and over time (WHEN). Third, the lack of a comprehensive set of good and bad scientific practices (GAP 3): without this set, it is not possible to appreciate EM as a single scientific research area, with EOM and MOE simply characterised by different external inputs (HOW), and it is not possible to help researchers spread EM (WHO).

The purpose of this paper is to bridge these three gaps by providing a comprehensive methodological framework (GOAL 1), by combining the methodological suggestions from the epistemological and empirical literature (GOAL 2), and by providing a comprehensive set of valid and invalid scientific practices (GOAL 3).

To achieve this, it depicts one diagram with coloured arrows, identifying crucial and negligible methodological linkages. It summarises the main points about WHY and the main points about WHAT from the epistemological literature by comparing them with the suggested methodological framework for EM. It shows two charts with coloured columns for different disciplines, highlighting a few articles inside EM and many articles outside EM. It provides two tables with perfect and imperfect examples of EM, by stressing that EM is not dependent on specific cultural contexts (e.g., Eastern or Western cultures) or analytical levels (e.g., individuals or countries).

In other words, the research questions can be summarised as follows: (1) What is EM, and why is it necessary? (2) Does EM have positive inner perspectives, and for which topics? (3) How should scientists implement EM and diffuse it?

The main methodological contribution of the present paper is twofold:

• EOM and MOE should be combined in EM as an inclusive interdisciplinary science (Section 2). Otherwise, cross-disciplinary improvements are not exploited.
• Insights from both the epistemological and empirical literature should be shared by using multi-level statistical analyses (Section 3.1). Otherwise, biased ethical assessments are obtained.

The main empirical contribution of the present paper is twofold:

• Too few articles inside EM, which produce unbiased estimations. EM should be depicted to a greater extent in an interdisciplinary book, by providing unbiased estimations by many scientists in many disciplines (Section 3.2).
• Too few scholars inside EM, which create good or bad examples. EM should be spread to a greater extent in a quantitative Special Issue, by providing good examples from many scientists in many disciplines (Section 4).

The structure of the present paper is as follows. Section 2 (WHAT and WHY) defines EM and details its necessity, by providing a diagram to depict a comprehensive methodological framework. Section 3 (WHERE and WHEN) summarises the main insights about WHAT and WHY from the epistemological literature, by presenting two charts to identify articles inside and outside EM. Section 4 (HOW and WHO) details the methodological features of the most recent articles inside EM, by providing two tables to show scientists producing good and bad examples of EM in different disciplines. Section 5 discusses the achievements with respect to the research questions, by highlighting strengths and weaknesses of EM. Section 6 discusses the achievements with respect to the research purposes, by highlighting the methodological successes of the present paper.

2. Methods: What (Definition) and Why (Necessity)

This section will provide the definition of EM (WHAT) and clarify the necessity of EM (WHY). This effort will also highlight which methodological steps are essential, unessential and complementary to the core methodological procedure, in order to distinguish articles inside EM from articles outside EM.

Ethics can be defined as a stock of values, beliefs, etc., which produce a flow of social/individual behaviours with beneficial/detrimental impacts at social/individual levels. Think of a specific type of physical capital (e.g., a sewing machine) used in a multiple production process (e.g., shirts and jackets) by some firms with their specific knowledge, where the (equilibrium) monetary value of a sewing machine (in the long-run) can be proved to be the discounted value of all shirts and jackets that include its production services. Note that the same values, beliefs, etc., can produce similar behaviours in alternative circumstances (e.g., a Christian behaves Christianly consistently through life) (e.g., think of the production of shirts and jackets). Moreover, the same stock of values, beliefs, etc., can produce similar behaviours many times (e.g., a Christian attends Mass weekly until it becomes a routine) (e.g., think of the production of shirts in subsequent times). Finally, a specific ethics (e.g., a belief in brotherhood of all human beings) can be evaluated by referring to the beneficial/detrimental consequences of actions arising from it (e.g., charities to poor people) (e.g., think of the average monetary value of a sewing machine used to produce a shirt, net of other production factors jointly used to produce it).

Consequently, a specific ethics can be properly evaluated if it is included in a behavioural model together with other factors affecting the same behaviour, where the behavioural model is estimated by referring to many observations of the same impact for some individuals in many contexts.

Thus, EM is a science (i.e., it assesses a phenomenon by referring to its repeated observations). Indeed, behaviours are observed many times across individuals, although each past behaviour cannot be repeated, since it happened in the past (WHAT). Moreover, researchers adopting a different approach miss crucial aspects of the ethical assessment (i.e., estimations are biased) (WHY). Finally, EM is an interdisciplinary science (WHAT). Indeed, ethics belongs to human sciences; statistics applied to observed human behaviours is a social science; topics and issues to be ethically evaluated refer to many different disciplines (e.g., computer science, medicine, decision science).

Figure 1 provides a comprehensive methodological framework. Note that mathematics is essential to represent a behavioural model. Moreover, statistics is crucial (i.e., central in Figure 1), because EM is a social science: a multi-level statistical analysis applied to panel/longitudinal data is required to avoid problems of under-specification. Finally, mathematics is crucial to measure ethical consequences.

In particular, Figure 1 shows the methodological core of EM (i.e., ethics included in a behavioural mathematical model to be estimated by multi-level statistical analyses) as the continuous black and blue lines. Note that behavioural models could be implicit (continuous blue line) (e.g., Min Ecological Footprint in [28]; Min inequality in access to health care in [15]; Max Gross Domestic Product in [37]; Max productivity in [19]; Max waste management, organic farming, and energy conservation in [17]; Max protection of minority shareholders interest in [18]), if goals and actions are well defined and tightly linked (i.e., a clear metrics). Similarly, an ethical metric could be implicit (continuous black line) (e.g., Min wastefulness of government spending in [18]; Min corporate fraud in [21]; Min tax avoidance in [20]), if beneficial/detrimental outcomes are ethically undisputable (i.e., a clear ethics).

In addition, Figure 1 shows the methodological steps which are not essential for EM (i.e., simplified procedures):

• (dotted blue line) Scientific measures of ethical concepts can be implicit if ethical assessments are obvious. For example, Healthy Life Expectancy at Birth can be assumed to better depict a beneficial impact than Life Expectancy at Birth.
• (dotted black line) Ethical measures of empirical consequences can be implicit if ethical grounds are obvious. For example, a larger increase in Life Expectancy at Birth on average can be assumed to be better than a smaller increase.

In addition, Figure 1 represents the methodological procedures excluded from EM (i.e., biased procedures):

• (green line) One observation (of a phenomenon) for many people can have beneficial social impacts (e.g., a tax on cigarettes reduces the quantity of smoke but not the number of smokers), but it is not possible to attach these observations to a specific ethics, since they could be linked to a behavioural flow rather than to an ethical stock (i.e., it amounts to the estimation of the marginal value of a sewing machine in terms of a shirt produced once by many firms in a specific context). Similarly, one observation (of a phenomenon) for one person can have detrimental social impacts (e.g., the arson of an illegal landfill of plastic materials), but it is not possible to attach this observation to a specific ethics, since it could be linked to an occasional behaviour rather than to a behavioural flow. In other words, a quick procedure based on “ethical policies, then ethical consequences” is biased, even if behavioural models and ethical measures are obvious, because it estimates flow rather than stock.
• (dotted red line up) Specific policies should not be starting points, unless they have affected behaviours for many periods in the past.
• (dotted red line down) Specific policies should not be ending points, unless they are expected to affect behaviours for many periods in the future.

Finally, Figure 1 shows the methodological steps that can be complementary to EM (i.e., additional procedures).

• (red line up) Specific institutions could be starting points, if they are included in the behavioural model.
• (red line down) Specific institutions could be ending points, if they are characterised by a specific ethics.

Some methodological remarks are worthy here:

• Some ethics of computer scientists in developing an artificial intelligence software does not need a behavioural model (e.g., the unethical goal could be to influence the opinion of students in favour of Nazism), since few people could behave unethically with unethical and detrimental social consequences (i.e., many observations for the implications of unethical behaviour by few individuals). In other words, computer scientists who alter their artificial intelligence software to increase consensus for a specific political party supporting Nazism could be evaluated in terms of its detrimental impacts on race equity, by relying on many observations in alternative contexts.
• The relative assessment of alternative ethics can be obtained by disregarding the periods of time they are expected to affect behaviours, under the assumption that alternative ethics will last for the same period of time.
• Some ethics of medical scientists in testing new drugs do not need a behavioural model (e.g., the unethical practice could be to test drugs without written acceptance by patients), since few people could behave unethically with ethical and beneficial social consequences (i.e., many observations of the consequences of unethical behaviour by few individuals). In other words, medical scientists who perform unauthorised experiments on people to implement a protocol for improving health conditions could be evaluated in terms of beneficial impacts on the health status of the general population by relying on many observations in alternative contexts.
• The use of ethics to achieve ethical goals (e.g., speeches by priests to increase recycling in [27]) might be an ethical strategy (i.e., the adoption of a specific ethics within a set of alternative ethics).
• Legislation could affect ethics in the long run (e.g., public smoking ban and the number of smokers in [38]).
• Ethics could have a negative monetary value (e.g., ethics as a socially responsible investment is not yet a reliable fundraising tool for Italian-listed companies in [23]) (i.e., ethics is an opportunity cost).
• Risks could have negative ethical consequences (e.g., fraud due to climate change in [21]).
• Metrics can be ranked in ethical terms (e.g., equity from alternative standardisations of the H-index in [4]), whereas ethics cannot be ranked in ethical terms (e.g., Islam better than Christianity in terms of equity), although alternative ethics can be ranked ethically in terms of outcomes (e.g., the observed gender inequity in alternative cultural contexts). In other words, consequentialism could be redundant if some statements about ethics are ethically undisputable (e.g., the sum of citations and articles over time in the original H-index favours old scholars).
• Rankings of ethics or metrics, even if based on continuous variables (e.g., monetary values in [37]; ecological footprint in [28]), should be used to identify static or dynamic suitable strategies rather than to prioritise specific aspects of detailed policies (i.e., rankings > evaluations).
• Time-invariant effects, either at an entity level (e.g., each country in [37]) or at a group level (e.g., developed vs. developing countries in [17]), should be used to depict specific unobserved or omitted features and to reduce variability across rather than within entities (i.e., fixed effects > random effects).

2.1. A Scientific Research Area

Figure 1 stressed both behavioural mathematical models and multi-level statistical analyses based on panel/longitudinal data as crucial methodological steps of EM (continuous blue line). In other words, EM is a scientific research area, because any EOM or MOE should be based on behavioural mathematical modelling to be statistically validated and tested (i.e., no validation is possible if the purpose of the model is not specified in advance in terms of problem addressed, orientation adopted, context analysed), with additional sensitivity analyses to favour immediate interpretations by avoiding vacuous rankings.

Next, ethical measures should be scientifically grounded (i.e., metric assumptions must be clearly stated) (e.g., Gini vs. Atkinson inequality indexes in [30]), by evaluating metrics in terms of ethical criteria coming from the relevant theological or philosophical literature (e.g., equity vs. efficiency of rankings based on H-index in [1]).

Note that ethical rankings aiming at identifying feasible strategies (i.e., with realistic parameter values such that a strategy can achieve its goal) and reliable strategies (i.e., with a tight statistical relationship between a strategy and its goal) provide meaningful support to EM. Moreover, these methodological suggestions should be applied differently in different disciplines (e.g., at a country level in social sciences vs. at an individual level in health sciences). Finally, EM is a social science, since ethics is assumed to be shared by some people (i.e., few or many).

2.2. An Interdisciplinary Research Area

Figure 1 stressed the ethical source as a crucial methodological step of EM (continuous black line). In other words, EM is an interdisciplinary research area because EM articles should refer to EOM or MOE in more traditional fields (e.g., Environmental Science, Computer Science, Research Policy, Public Policy) or less traditional fields (e.g., business, health), with essential mutual improvements (i.e., it favours cross-disciplinary enrichment, by avoiding intra-disciplinary discussions).

Next, behavioural models should be ethically explicit (i.e., ethical assumptions must be clearly stated, mutually consistent and tightly consistent with applied metrics) (e.g., the CBA instrumental value of nature vs. the MCA intrinsic value of nature in [39]) by evaluating ethics in terms of the actions’ consequences (e.g., Ecological Footprint in [28] measures sustainability as an ethical goal to be achieved by religious and secular ethics, whereas Life Satisfaction and Healthy Life Expectancy at Birth in [36] measure Happiness and Health as non-ethical goals to be achieved by religious and secular ethics).

Note that EM speaks to scholars and teachers (i.e., responsible for the metrics development and the socially acceptable ethical criteria), as well as to policy makers and administrators (i.e., responsible for the metrics adoption and the possibly consequential unethical behaviours). Moreover, the degree of interdisciplinarity of a scholar’s CV can be properly evaluated [40]. Finally, ethics could be used as a tool to check for knowledge and participation of stakeholders in relatively small samples [41].

2.3. Summary

EM is needed as an interdisciplinary science, including EOM and MOE.

3. Results: Where (Disciplines) and When (Dynamics)

The previous section provided the definition of (WHAT) and many reasons for (WHY) EM as an interdisciplinary science. In this section, I will compare these insights with the main outcomes in the literature about WHAT and WHY of MOE and EOM in order to highlight possible differences and complementarities. This effort will also show the relative numbers, dynamics, and concerns of articles inside and outside EM, in order to evaluate its potential development.

3.1. Epistemology Without Applications

Although it is advocated by methodological scholars (e.g., [42] in climate change, [43] in public policy, [44] in artificial intelligence, [45] in corporate responsibility) and is required by urgent issues (e.g., artificial intelligence, climate change), there is no interdisciplinary literature on WHY MOE and EOM should focus on which topics. Nonetheless, the following FIVE aspects are highlighted as crucial for WHY. In particular, EM should:

• Make a stringent relationship between quantification and associated contexts or purposes, while avoiding the symbiotic relationship between quantification and trust.
• Be a defence against statistical abuses perpetrated by public or private actors, possibly using consequentialism in ethical quantification.
• Assign responsibilities to social actors when metrics produce unintended or undesirable effects, stressing that techniques are never neutral.
• Bridge scholarship with society by joining scholars from different disciplines within the same methodological framework.
• Bridge social actors with society by using ethical quantification to explain strategically legitimated decisions.

Next, although it is advocated by methodological scholars (e.g., [46,47,48]) and it is required by urgent issues (e.g., artificial intelligence, climate change), there is no interdisciplinary literature on WHAT MOE and EOM should be in which topic. Nonetheless, the following TEN aspects are highlighted as crucial for WHAT. In particular, EM should:

• Specify the purpose of the mathematical model to be statistically validated and tested by reflecting on the ambiguity, indeterminacy, and complexity of the problem under consideration.
• Clarify the ethical assumptions by distinguishing evidence from values to encourage social learning about unfolding possible stakes, biases, interests, blind spots, overlooked narratives, and worldviews of the developers.
• Choose analytical tools that are consistent with the purpose of the model by stressing their inner assumptions.
• Consider the relationship between error and complexity in choosing models and variables by performing sensitivity analyses to favour immediate interpretations.
• Avoid under-specification problems by applying adequate statistical units and methods to properly communicate uncertainty.
• Clarify all ethical implications by highlighting the relationship between power and knowledge.
• Use mathematically grounded metrics to evaluate empirical consequences.
• Use theologically and philosophically grounded ethics to evaluate empirical consequences.
• Check for consistency of ethical assumptions built into mathematical models and ethical principles used in empirical evaluations by performing sensitivity auditing.
• Specify all policy implications by highlighting people or institutions responsible for policy implementations.

Note that ethics or metrics should not be necessarily evaluated in terms of the actions’ consequences.

Thus, the crucial differences between these points and the insights from Figure 1 are that both behavioural mathematical models and multi-level statistical analyses based on panel/longitudinal data are crucial methodological steps (continuous blue line).

3.2. Applications Without Epistemology

The application of the methodological points suggested in the previous section will allow me to distinguish articles inside and outside EM. In particular, Figure 2 depicts the articles from Scopus in the last 20 years identified by ethics, panel/longitudinal data, behaviour as keywords (i.e., left side of Figure 1). Next, Figure 3 depicts the articles from Scopus in the last 20 years identified by ethics, measure, data, and EQUITY as keywords (i.e., right side of Figure 1).

Figure 2 shows that articles inside EM (continuous blue line) are few (i.e., a maximum of 3 articles per year), relatively recent (i.e., mainly in the last 10 years), stable over time (i.e., increasing trends are not observed), and relatively focused (i.e., mainly on business and environmental sciences, as well as on economics and social sciences). Figure 3 shows that articles outside EM (i.e., dotted blue line) on MOE, apart from medicine, are also few, relatively recent, not increasing over time, and relatively focused. Note that figures like Figure 3 could be obtained by using Efficiency, Diversity/Inequality, Inclusion/Accessibility, and Justice as keywords. Indeed, the total number of articles obtained for equity (i.e., 101) is comparable to the total number of articles obtained for Efficiency (i.e., 133), Diversity (i.e., 81), Inequality (i.e., 60), Inclusion (i.e., 372), Accessibility (i.e., 106), and Justice (i.e., 96).

Thus, there are too many biased estimations from articles outside EM (e.g., inadequate approaches in Medicine).

3.3. Summary

Both epistemology and applications are needed to improve and develop EM.

4. Results: How (Applications) and Who (Researchers)

The previous section showed that articles inside EM in the last 20 years are few, stable over time, and focused on a few disciplines (Figure 2). In this section, I will detail the most recent articles (i.e., last 5 years) in terms of the methodological features specified in Section 1 (Figure 1). This effort will also show the relative numbers, dynamics, and disciplines of scholars inside EM, in order to identify some research strategies.

4.1. Perfect Examples

Table 1. Recent (2019–2025) perfect examples of Ethicametrics. Abbreviations: DIS = scientific discipline, UNI = observation unit, N = number of authors, EXP = explicit, FE = fixed effects, COU = at a country level, IND = at an individual level, REL/SEC = religious/secular ethics, LS = life satisfaction, HLEB = Healthy Life Expectancy at Birth, EF = Ecological Footprint, GDP = Gross Domestic Product, OM = Olympic medals, NPE = National pride and efficiency, SCE = Social cohesion and ethics.

Reference	Outside Ethics	Behavioural Model (Maths)	Measure Consequence (Stats)	Ethical Assessment (Maths)	Outside Ethics	Policy Institution	DIS	UNI	N
	Continuous Black	Ethics or Metrics	Impacts	Metrics	Dotted Black	Dotted Red
Zagonari [30]	NO	EXP	FE	EF	Many	NO	ES	COU	1
Zagonari [27]	REL	EXP	FE	EF	NO	NO	ES	COU	1
Zagonari [31]	NO	EXP	FE	EF	Efficiency	NO	ES	COU	1
Zagonari [33]	NO	EXP	FE	EF	NO	NO	ES	COU	1
Zagonari [29]	REL	EXP	FE	EF	NO	NO	ES	COU	1
Zagonari [35]	REL/SEC	EXP	FE	LS	EXP	NO	AH	COU	1
Zagonari [36]	REL/SEC	EXP	FE	LS, HLEB	NO	REL/SEC	AH	COU	1
Zagonari [37]	REL/SEC	EXP	FE	GDP	Efficiency	REL/SEC	EFE	COU	1
Zagonari [49]	REL/SEC	EXP	RE	OM	NPE, SCE	NO	AH	COU	1
Zagonari [50]	REL/SEC	EXP	FE	LS, HLEB	NO	REL/SEC	AH	COU	1
Zagonari [1]	Outside Metrics	EXP	FE	H-index	Ranking	Improved H-index	DC	IND	1

details the recent (2019–2025) articles from Figure 2, which could be taken as valid examples based on the methodological steps identified in Section 1, since they explicitly provide a behavioural mathematical model.

Thus, a set of 11 articles could be an adequate starting point to be shared by scholars as a reference scientific guideline.

4.2. Imperfect Examples

Table 2. Recent (2019–2025) imperfect examples of Ethicametrics. Abbreviations: DIS = scientific discipline, UNI = observation unit, N = number of authors, IMP = implicit, FE = fixed effects, RE = random effects, REL/SEC = religious/secular ethics, COU = at a country level, IND = at an individual level, MH = mental health, EF = ecological footprint, WM = waste management, OF = organic food, EC = electricity consumption, FDI = foreign direct investment, CBT = cross-border trade, VP = violence perpetration, CIG = compliance with Islamic governance, PMS = protection of minority shareholders, WGS = wasteful of governmental spending, LP = labour productivity, TA = tax avoidance, SRI = socially responsible investment, COE = cost of equity, FC = fraud commission, ME = management earnings.

Reference	Outside Ethics	Behavioural Model (maths)	Measure Consequence (Stats)	Ethical Assessment (Maths)	Outside Ethics	Policy Institution	DIS	UNI	N
	Continuous Black	Ethics or Metrics	Impacts	Metrics	Dotted Black	Dotted Red
Landi & Sciarelli [23]	NO	IMP	RE	SRI	NO	NO	SS	IND	2
Bakas et al. [19]	NO	IMP	RE	LP	NO	NO	EEF	COU	3
Zagonari [17]	REL/SEC	IMP	FE	WM, OF, EC	IMP	FDI, CBT	ES	COU	1
Boţa-Avram et al. [18]	NO	IMP	RE	PMS, WGS	NO	NO	SS	IND	3
Zagonari [28]	REL/SEC	IMP	FE	EF	Equity	REL/SEC	ES	COU	1
Abdelmoula et al. [20]	NO	IMP	RE	TA	NO	NO	BMA	IND	3
Nugraheni et al. [26]	REL	IMP	RE	CIG	NO	NO	BMA	IND	3
Bunce et al. [15]	NO	IMP	RE	MH	NO	NO	MED	IND	6
Cheung & Yeung [16]	NO	IMP	RE	VP	NO	NO	MED	IND	2
Zagonari [32]	NO	EXP	NO	EF	Many	NO	ES	COU	1
Marzouki & Ben Amar [24]	NO	IMP	RE	SRI	Equity	NO	BMA	IND	2
Chen et al. [21]	NO	IMP	RE	FC	NO	NO	BMA	IND	4
Chouaibi et al. [22]	NO	IMP	RE	COE	NO	NO	BMA	IND	4
Nguyen [25]	NO	IMP	RE	ME	NO	NO	BMA	IND	4
Zagonari & Foschi [4]	Outside Metrics	IMP	FE	H-index	Ranking	Improved H-index	DC	IND	2

details the recent (2019–2025) articles from Figure 2, which could be taken as invalid examples based on the methodological steps identified in Section 1, as they implicitly provide a behavioural mathematical model.

Thus, a set of 37 scholars could be a reasonable starting point to develop EM as a science applied to different topics in different disciplines.

4.3. Perfect Applications in Alternative Contexts

The previous sections detailed the methodological features of valid and invalid examples for articles inside EM by referring to the methodological framework suggested in Section 1. This section will compare four main methodological features of two articles applying EM in different contexts to highlight the large flexibility of EM in terms of mathematical models, statistical models, estimation methods and validation procedures. In particular, I will summarise topics and compare methodologies of a paper on Olympic ethics [49] entitled “The requiem of Olympic ethics and sports’ independence” (let me call it the OLY paper) and a paper on body ethics [50] entitled “Having a body vs. being a body to achieve happiness and health” (let me call it the BOD paper).

As for topics, the OLY paper suggests two interrelated theoretical models to empirically summarise the literature on the relationships between sports and both religious and secular ethics and to empirically evaluate to what extent religious and secular ethics, as well as sport policies, affect achievements in sports. I identified two national ethics (national pride/efficiency) and two social ethics (social cohesion/ethics) by measuring achievements in terms of alternative indices based on Olympic medals. I introduced two sport policies (a quantitative policy aimed at social cohesion, a qualitative policy aimed at national pride) by distinguishing sports in terms of four possibly different ethics to be used for both the eight summer and eight winter Olympic Games from 1994 to 2024. I applied income level, health status, and income inequality to depict alternative social contexts. I used five main religions and three educational levels to depict alternative ethical contexts. Next, the BOD paper suggests a theoretical framework to conceptually schematise the literature on the main religious and secular approaches to body (i.e., “HAVING a body” vs. “BEING a body”) in sports disciplines and physical activities, and it develops an interrelated theoretical model to empirically evaluate the extent to which these religious and secular approaches affect the long-run equilibrium in happiness and health. I identified three secular BEING approaches (i.e., Aristotle, Husserl & Merleau-Ponty, Deleuze). I identified one secular HAVING approach (i.e., Descartes). I identified five religious HAVING approaches (i.e., Buddhism, Christianity, Hinduism, Islam, Judaism).

As for methodologies, decision units are governments in the OLY paper and individuals in the BOD paper, whereas goal variables are Olympic medals in the OLY paper and happiness and health levels in the BOD paper. In particular, as for mathematical models, governments in the OLY paper choose alternative sport policies to maximise alternative goals (i.e., national pride, social cohesion, social ethics, national efficiency), which could possibly depend on the prevailing religious and secular ethics. I depicted each alternative goal by a single equation: a Poisson stochastic process possibly dependent on some factors; a stochastic production function dependent on production factors and possibly dependent on other factors; and a deterministic production function dependent on production factors and possibly dependent on other factors. Next, individuals in the BOD paper choose alternative religious or secular ethics to achieve a long-run equilibrium in happiness and health, which is affected by the prevailing economic and social contexts. I depicted this equilibrium by a two-equation dynamic system based on interrelated happiness and health, possibly dependent on other factors. As for statistical models, the OLY paper applies linear regressions with random effects in Poisson Analysis, log-linear regressions with fixed effects in Stochastic Frontier Analysis, and linear estimations in Data Envelopment Analysis, whereas the BOD paper applies linear regressions with lags and fixed effects. As for estimation methods, the OLY paper applies Maximum Likelihood for Poisson and Stochastic Frontier Analyses and Minimum Distance from Production Frontiers for Data Envelopment Analysis, whereas the BOD paper applies Three Stage Least Squares. As for validation procedures, the OLY paper checks for the consistency of specific results obtained by applying alternative analyses (i.e., Poisson, Stochastic Frontier and Data Envelopment Analyses), whereas the BOD paper refers to the consistency of expected results for joint and disjoint dependent and independent variables.

Note that both papers use the STATA software (version 18.0), but any other statistical package could be fine. Next, both papers provide the relevant statistics to test for the assumptions on fixed vs. random effects (e.g., Hausman specification test), stationarity of variables (e.g., Levin–Lin–Chu unit root test), and causality between variables (e.g., Dumitrescu–Hurlin Granger non-causality test).

4.4. Summary

EM, as a new journal, is needed to spread a conscious application of its scientific methodologies.

5. Discussion

In the present paper, I applied one diagram, two charts, and two tables to answer the research questions specified in Section 1. The diagram showed that both behavioural mathematical models and multi-level statistical analyses based on panel/longitudinal data are crucial methodological steps of EM in order to avoid biased estimations of marginal impacts. The two charts showed that EM has no positive inner perspective in any discipline, since increasing trends in articles inside EM are not observed. The two tables showed that there are many bad examples of EM produced by some scholars and some good examples of EM produced by one scholar. In other words, these approaches enabled me to answer all research questions.

The main weaknesses of EM can be summarised as follows:

Ethics is assumed to be exogenously given, although ethics could be constructed ex-post to justify actions, and actions could become habits or ethics in the long run (i.e., ethics as a given stock is estimated by measuring its impacts on observed flows). However, ethics can be assumed to be fixed in the short run, since it takes years or decades or centuries for ethics to change. For example, Catholic ethics on gender equity in Mulieris Dignitatem by John Paul II (1988) (www.vatican.va) differ from gender equity in De Rerum Novarum by Leo XIII (1891) (www.vatican.va).

Variables used in statistical analyses (e.g., believers in Christianity in terms of percentages) could affect the obtained results. However, the adequacy of these variables could be tested by using instrumental variables (e.g., [36]).

Definitions used in mathematical models (e.g., ethics measured by its consequences) could affect the obtained decisions. However, the suitability of a given approach (e.g., consequentialism) can be tested by comparing results with alternative variables. For example, consequentialist assessments of gender inequality obtained by statistical analysis could be compared with the male/female relative earnings (%) in all Christian countries or with the relative importance of male/female witnesses in front of a court (%) in some Muslim countries.

The main strengths of EM can be summarised as follows:

• Ethics as a stock (of social values) in a behavioural model can be used to evaluate its dynamics over time (e.g., a decrease in religiosity in Western countries) (e.g., [35]) and to compare its cost across entities (e.g., religiosity across countries in terms of GDP) (e.g., [37]).
• Ethics as (a stock of) social values in a behavioural model can be used to assess interactions across groups between alternative social ethics (e.g., Western values in developing countries) and to assess interactions between social behaviours and social institutions over time (e.g., divorce rates in Western countries).
• The logical chain from ethics to institutions through social impacts of social behaviours can be used to evaluate ethically consistent changes in institutions to achieve specified ethical goals (e.g., [49,50]).

Note that EM is close to post-normal sciences, as ethical assessment is justified by the urgency of decision-making for some specific issues where uncertainty and conflicts between values and interests prevail [51]. Consequently, its positive and normative claims rely on transparency of values, robustness to disagreement about values, and openness to debate about values [52], although normative claims are based on positive claims, by measuring and ranking ethics.

Moreover, I used “statistics and mathematics” instead of “econometrics and economic modelling” because EM is not focused on economic issues. However, EM is similar to Neoclassical Economics, since:

• EM refers to a universal context (i.e., ethics are general rules), although the realism of assumptions in specific cultural contexts leads to more causal models [53]. In other words, EM is closer to socialised habits from Evolutionary Behavioural Economics than to utility maximisation from Neoclassical Economics or to specific cognitive biases from Behavioural Economics (e.g., [54,55]).
• EM is focused on targeted decisions depicted by behavioural models (i.e., ethics are beneficial or detrimental constraints to individual decisions), although ethics represent a social structure with a restrictive or enabling effect on opportunity and flourishing of individuals [56]. In other words, EM is closer to reciprocal transactions from parental bent in Evolutionary Behavioural Economics than to market transactions from self-interest purposes in Neoclassical Economics or to specific cooperative attitudes from Behavioural Economics (e.g., [57,58]).
• EM is deductive (i.e., general models to be tested are based on general rules) by applying an engineering approach (i.e., it is based on mathematics and statistics) to measure and rank ethics [59], but it is also abductive (i.e., explanatory hypotheses are tentative and require verification).
• EM aims at model estimation rather than at model selection, assuming that a correctly specified model enables the achievement of closures of causal sequences, although models are provided by moral philosophy and theology [60]. This requires detailed justifications of simplifying assumptions (LIMIT 1).
• EM aims at causal inference rather than causal discovery [61], where the average impacts (to depict possible interactions at an individual level) at a social level (e.g., to depict share ethics at a country level) obtained from large datasets with fixed effects should be preferred to small datasets with random effects (to account for structural differences in relative importance of ethics). This requires huge efforts in constructing panel/longitudinal datasets (LIMIT 2).
• EM can use instrumental variables [62], although these variables need interpretations and they must satisfy some theoretical conditions, which can be hardly tested in practice (LIMIT 3). Actually, the same instrumental variables could be used as regressors.
• EM can use both frequentist or classical inference as well as Bayesian, likelihood, or Akaikean inferences [63], although these latter inferences (all referring to the Likelihood Principle) require a priori information, a statistical model, and a posteriori criteria (LIMIT 4). Actually, frequentist tools could be used to compare two models at once.

In contrast, EM is different from Neoclassical Economics, since:

8.

EM is not limited to rational decisions based on the internal consistency criterion and the self-interest pursuit approach by interpreting the rationality of choices as a reason for choices (i.e., free scrutiny of objectives and motivations) [64].

9.

EM does not aim at predicting actual behaviours by avoiding the assumptions of stable and complete preferences, interactions in markets tending to reach an equilibrium, fixed societies, and absence of uncertainty [65].

10.

EM is an evolutionary science referring to an open system (i.e., some outcomes are caused by something that went before them, with cumulative causation and without predetermined purpose) rather than a taxonomic science referring to a closed system (i.e., EM provides empirical generalisations of historical phenomena, where exceptions are interpreted as disturbing factors) [66] by applying a quantitative approach to human motivations and social achievements with an explanatory rather than descriptive perspective.

In other words, EM is close to heterodox economics (i.e., critiques of the hard core of economics) by studying the interaction of human agency and social institutions or structures [67], although it does not apply methodological pluralism [68].

Finally, EM is close to New Institutional Social Sciences (i.e., critiques of the protective belt of economics), since EM refers to average individuals rather than to a whole society (i.e., EM is individualistic rather than holistic) [69], although decisions by individuals are conditioned by historical contexts [70] and social interactions [71]. Next, EM aims at measuring ethics (i.e., ethics, as a stock of socially shared values, positively or negatively affects individual decisions aiming at pursuing, rationally or not rationally, specified goals) [72] rather than at identifying its origin (i.e., EM does not reduce social norms and structures to the atomistic interaction of optimising individuals) [73]. Consequently, EM is an observational rather than an experimental science, sometimes using populations rather than samples at a national level for a specified period.

6. Conclusions

The purpose of this paper was to provide a comprehensive methodological framework (GOAL 1), combine the methodological suggestions from the epistemological and empirical literature (GOAL 2), and provide a comprehensive set of good and bad scientific practices (GOAL 3). The previous sections showed that I succeeded methodologically. In particular, EOM and MOE should both be included in EM as a single interdisciplinary science, where EOM and MOE represent different methodological starting points. Insights from both the epistemological and empirical literature should be combined by using behavioural mathematical models and multi-level statistical analyses based on panel/longitudinal data. Next, I provided some empirical insights. In particular, a set of 11 valid examples of EM could be an adequate starting point to be shared by scholars as a reference scientific guideline for EM. A set of 37 scholars committed to EM could be a reasonable starting point to develop EM as a science applied to different topics in different disciplines.

In summary, EM has two main empirical implications and two main practical implications. As for empirical implications, EM measures moral actions by disregarding ethical systems. Indeed, the same moral action could be supported by different and incompatible ethical systems (e.g., waste recycling is a moral action, but Christianity supports this action as a duty towards future generations based on the expected beneficial consequences for future generations, whereas Buddhism suggests this action as a duty towards nature regardless of possibly beneficial consequences for future generations). Note that ethics is a consistent system of values (i.e., cultural values, religious values), whereas morality is a set of ethically suggested and unsuggested actions (i.e., desirable and undesirable actions). Next, EM allows comparisons of ethics in terms of objective criteria by measuring the consequences of moral actions. Indeed, moral actions within an ethical system cannot be theoretically evaluated within another ethical system.

As for practical implications, EM favours intercultural and interreligious dialogues among managers or leaders on specific goals or policies. Indeed, measuring ethics in terms of the actions’ consequences allows them to focus on the possibly compatible moral actions (e.g., waste recycling, energy conservation) rather than on the likely incompatible ethical systems. Next, EM allows agents or stakeholders to compare moral actions in terms of relative effectiveness to achieve shared goals (e.g., environmental sustainability). Indeed, compliance with policies based on alternative ethics (e.g., waste recycling requires and energy conservation does not require the solution of collective action problems to be efficient, respectively) could be different in alternative cultural or religious contexts (e.g., Christianity and Buddhism, as more and less communitarian religions, might be relatively effective in waste recycling and energy conservation, respectively).

Future applications of EM could refer to old topics to be analysed transparently and scientifically. For example, demographic policies. Next, future applications of EM could refer to new sensitive topics to be discussed transparently and scientifically. For example, war decisions.