SUPPLEMENTARY INFORMATION

Countering Protection Rackets using Legal and Social ApproachesAn Agent-Based Test

13

Table S.1. ODD+D Protocol for the Agent-Based Model of Protection Rackets

Here we include the ODD+D protocol for our agent-based model of protection rackets including guiding questions for those who may be unfamiliar with the structure (Müller et al., 2013). This information supplements the description of the model in the paper.

Outline ( template)

Guiding questions

Own ODD+D Model description

I) Overview

I.i Purpose

I.i.a What is the purpose of the study?

The purpose of the study is to test what are the independent and combined effects of legal and social approaches on the mafia and the rest of the population.

I.ii.b For whom is the model designed?

The model is designed to scientists and policy-makers interested in multi-disciplinary policing strategies to combat organized crime.

I.ii Entities, state variables, and scales

I.ii.a What kinds of entities are in the model?

· Mafia represents a mafia-type criminal organisation.

· State corresponds to all governmental institutions that are involved in combating the mafia, such as police and the judicial system. Its main purpose is to eliminate the mafia through direct actions such as the imprisonment of its members, the seizure of its properties, and the supporting of the victims of extortion.

· Entrepreneurs are producers, resellers, or providers of goods and services whose purpose is to make profit.

· Consumers represent the civil society and they may purchase goods and contract services from entrepreneurs.

· Non-Governmental Organisation (NGO) are civil society organisations, whose main goal is fighting mafia and promoting a “culture of legality” by publicising the negative effects that the Mafia has on the overall well-being of the society.

I.ii.b By what attributes (i.e. state variables and parameters) are these entities characterized?

· Mafia: number of Mafiosi, periodicity to request pizzo, extortion level, punishment severity, punishment probability, benefit, pentiti probability.

· State: number of police officers, duration of general investigations, duration of specific investigations, duration of bureaucratic activities, probability to capture a Mafiosi, probability of finding incriminating evidences, duration of custody, conviction probability, imprisonment duration, time to assist, periodicity of increasing Fondo di Solidarietà, probability of spreading normative information, proportion of Consumers and Entrepreneurs target of social norms.

· Entrepreneur: periodicity for receiving income, income, variation of income, product price, intrinsic risk inclination to report extortion, affiliation to NGO, individual and normative weights of social norms, salience of social norms, reputation Mafia as punisher, and reputation State as protector.

· Consumer: periodicity to buy product, number of Entrepreneurs to search product price, Entrepreneur’s reputation, individual and normative weights of social norms, and salience of social norms.

· NGO: probability of spreading of social norms, proportion of Consumers and Entrepreneurs target of social norms.

I.ii.c What are the exogenous factors / drivers of the model?

· Mafia: number of Mafiosi, periodicity to request pizzo, extortion level, punishment severity, punishment probability, benefit, pentiti probability.

· State: number of police officers, duration of general investigations, duration of specific investigations, duration of bureaucratic activities, probability to capture a Mafiosi, probability of finding incriminating evidences, duration of custody, conviction probability, imprisonment duration, time to assist, periodicity of increasing Fondo di Solidarietà, probability of spreading normative information, proportion of Consumers and Entrepreneurs target of social norms.

· Entrepreneur: periodicity for receiving income, income, variation of income, product price, intrinsic risk inclination to report extortion, and individual and normative weights of social norms.

· Consumer: periodicity to buy product, number of Entrepreneurs to search product price, and individual and normative weights of social norms.

· NGO: probability of spreading of social norms, proportion of Consumers and Entrepreneurs target of social norms.

I.ii.d If applicable, how is space included in the model?

The model does not represent space explicitly. Consumers and Entrepreneurs, however, are nodes in a scale-free network that defines their range of perception regarding actions of others.

I.ii.e What are the temporal and spatial resolutions and extents of the model?

Temporal resolution: the time units of the model do not have correspondence to a real time.

Spatial resolution: the model does not have space representation.

I.iii Process overview and scheduling

I.iii.a What entity does what, and in what order?

See Section 2.1 Model overview of the main text for a description about the actions and their ordering. Follow a summarised list of the agents’ actions unordered.

Mafia: Request pizzo, Benefit Entrepreneur, Punish Entrepreneur, Collaborate with the State

State: General Investigation, Specific Investigation, Imprison Mafioso, Assist Entrepreneur, and Social Norm Spread

Entrepreneur: Receive Income, Pay pizzo, Report pizzo, Collaborate with the State, Join NGO, Social Norm Spread, and Reputation Spread

Consumer: Shopping (e.g., purchase products), Social Norm Spread, and Reputation Spread

NGO: Social Norm Spread

Some actions are triggered based on an exogenous periodicity defined using probability distribution functions and others are reactions to some other action.

Periodic actions:

· Mafia: Request pizzo

· State: General Investigation, Social Norm Spread

· Entrepreneur: Receive Income

· Consumer: Shopping

· NGO: Social Norm Spread

Reactive actions:

· Mafia: Benefit Entrepreneur, Punish Entrepreneur, Collaborate with the State

· State: Specific Investigation, Imprison Mafioso, Assist Entrepreneur

· Entrepreneur: Pay pizzo, Report pizzo, Collaborate with the State. Join NGO, Social Norm Spread, and Reputation Spread

· Consumer: Social Norm Spread and Reputation Spread

· NGO:

II) Design Concepts

II.i Theoretical and Empirical Background

II.i.a Which general concepts, theories or hypotheses are underlying the model’s design at the system level or at the level(s) of the submodel(s) (apart from the decision model)? What is the link to complexity and the purpose of the model?

Social Norms (Conte, Andrighetto, & Campennì, 2013), rational choice theory (Gambetta, 1988, 1993; Schelling, 1971), and a cultural approach to understanding mafias (Arlacchi, 1988; Blok, 1974; Hess, 1973; Paoli, 2003; Schneider & Schneider, 1976, 2005).

II.i.b On what assumptions is/are the agents’ decision model(s) based?

Agents can be separated into two groups based on their decision-making complexity. The State, the Mafia, and the NGO are represented as agents whose decisions are based on fixed probabilities initialised at the start of the simulation. In contrast, Entrepreneurs and Consumers use more sophisticated reasoning abilities. They base their choices on a combination of instrumental and social considerations as reported in (Nardin et al., 2016, pp. 1125–1134).

II.i.c Why is a/are certain decision model(s) chosen?

The complexity of the State, the Mafia, and the NGO presents itself as a challenge to model in detail each of their decision-making processes. Several studies show that individuals are not driven only by economic motives, but in large part by social influences.

Additionally, we are interested in understanding how the combination of instrumental (i.e., coercive and economic) and social (i.e., social norms) policies influence human behaviours and how this impacts on protection rackets operation.

Thus, we define that Consumers and Entrepreneurs are central entities in the model whose decision-processes require further detailing.

II.i.d If the model / a submodel (e.g. the decision model) is based on empirical data, where does the data come from?

The decision model is based on a cognitive architecture that includes economic and social aspects (Andrighetto et al., 2013; Conte et al., 2013; Realpe-Gómez, Andrighetto, Nardin, & Montoya, 2018). No empirical data are used in the modelling phase.

We, however, extract some input parameter from empirical data:

1. the weights of the individual and normative drive was calibrated using data reported in different European Values Surveys (see Section 6 Interfacing Data and Simulation Model in Sartor (2015, pp. 29–55)).

2. a database of more than 600 cases of extortion in Sicily and Calabria during the past decade (https://datorium.gesis.org/xmlui/handle/10.7802/1116)

II.i.e At which level of aggregation were the data available?

The data were not aggregated. The European Values Surveys provided information about individual survey answers and the database of cases in Sicily contains information about each individual case reported.

II.ii Individual Decision Making

II.ii.a What are the subjects and objects of decision-making? On which level of aggregation is decision-making modeled? Are multiple levels of decision making included?

Please see item I.iii

II.ii.b What is the basic rationality behind agents’ decision-making in the model? Do agents pursue an explicit objective or have other success criteria?

Entrepreneurs decide to pay pizzo if they have an economic incentive (i.e., benefits + possible punishment) that surpasses the amount requested and the salience of the norm ‘Pay pizzo request’ is greater than the ‘Do not pay pizzo request’. Otherwise, Entrepreneurs decide not to pay pizzo.

Entrepreneurs report the pizzo request to the State if they decided not to pay pizzo and the chance of being protected by the State (i.e., reputation of the State as protector) exceeds the risk of being punished by the Mafia (i.e., reputation of the Mafia as punisher).

Consumers purchase products of Entrepreneurs who offer the lowest price, but also has a high reputation as a non pizzo payer.

II.ii.c How do agents make their decisions?

Please see (Nardin et al., 2016, pp. 1125–1134) for a detailed description of how agents make their decisions.

II.ii.d Do the agents adapt their behaviour to changing endogenous and exogenous state variables? And if yes, how?

Yes.

Entrepreneurs adapt their behaviour by adjusting their belief on the State protectiveness, Mafia punitiveness, and the salience of the norms.

Consumers adapt their behaviours by adjusting their belief on the Entrepreneurs reputation as pizzo payer and the salience of the norms.

II.ii.e Do social norms or cultural values play a role in the decision-making process?

Yes, social norms play an important role in the decision-making process. Please see Section 5.4 in (Nardin et al., 2016).

II.ii.f Do spatial aspects play a role in the decision process?

No

II.ii.g Do temporal aspects play a role in the decision process?

None

II.ii.h To which extent and how is uncertainty included in the agents’ decision rules?

The decision of some agents are already probabilistic like the State, the Mafia and the NGO.

Consumers and Entrepreneurs decision utility functions aggregate multiple factors and generate a value between 0 and 1, which is used as a threshold (i.e., probability) to compare against a randomly generate value and decide which action to perform.

For instance, an Entrepreneur calculates the probability of paying a pizzo request equals to 0.66. To decide whether to pay or not, the Entrepreneur draws a random number; if the number is less than 0.66 the Entrepreneur pays extortion, otherwise the Entrepreneur does not pay.

This decision structure, first, allows to account for uncertainty, but also eliminates the need for the designer to define fixed thresholds to each decision-making process.

II.iii Learning

II.iii.a Is individual learning included in the decision process? How do individuals change their decision rules over time as consequence of their experience?

The individuals change their behaviour depending on the beliefs about the State, Mafia and social environment, they learn by experience. However, there is not a change on the decision rules of the individual over time.

II.iii.b Is collective learning implemented in the model?

None

II.iv Individual Sensing

II.iv.a What endogenous and exogenous state variables are individuals assumed to sense and consider in their decisions? Is the sensing process erroneous?

Individuals do not sense variables, they sense actions performed by or affecting their immediate neighbours in the network. The actions’ information is propagated by the environment that considers some uncertainty on action propagation.

The affected variables are:

· Consumers: Entrepreneur’s reputation, and salience of social norms.

· Entrepreneurs: salience of social norms, reputation Mafia as punisher, and reputation State as protector.

II.iv.b What state variables of which other individuals can an individual perceive? Is the sensing process erroneous?

None

II.iv.c What is the spatial scale of sensing?

Immediate neighbours in a free-scale network.

II.iv.d Are the mechanisms by which agents obtain information modeled explicitly, or are individuals simply assumed to know these variables?

Sensing is local only. However, Consumers and Entrepreneurs can receive communication messages from the State, the NGO, and other Consumers and Entrepreneurs (i.e., their neighbours in the network). These messages also lead to the update of the variables indicated in item II.iv.a.

II.iv.e Are costs for cognition and costs for gathering information included in the model?

None

II.v Individual Prediction

II.v.a Which data uses the agent to predict future conditions?

None

II.v.b What internal models are agents assumed to use to estimate future conditions or consequences of their decisions?

None

II.v.c Might agents be erroneous in the prediction process, and how is it implemented?

None

II.vi Interaction

II.vi.a Are interactions among agents and entities assumed as direct or indirect?

Both, direct and Indirect

II.vi.b On what do the interactions depend?

Interactions depend on sensing and communication.

II.vi.c If the interactions involve communication, how are such communications represented?

These communications are represented as pre-defined messages exchanged among agents.

II.vi.d If a coordination network exists, how does it affect the agent behaviour? Is the structure of the network imposed or emergent?

The structure of the network is imposed and static. The network used is a scale-free network that interconnects Consumers and Entrepreneurs. The network defines the range of perception of the agents, but not directly their behaviour.

II.vii Collectives

II.vii.a Do the individuals form or belong to aggregations that affect, and are affected by, the individuals? Are these aggregations imposed by the modeller or do they emerge during the simulation?

No

II.vii.b How are collectives represented?

No

II.viii Heterogeneity

II.viii.a Are the agents heterogeneous? If yes, which state variables and/or processes differ between the agents?

No

II.viii.b Are the agents heterogeneous in their decision-making? If yes, which decision models or decision objects differ between the agents?

No, the decision-making structure is the same to all agents of the same type.

II.ix Stochasticity

II.ix.a What processes (including initialization) are modeled by assuming they are random or partly random?

The processes that are random or partly random are:

Mafia

· Decision to the next pizzo request and whom to request from

· Decision to punish non-pizzo payer Entrepreneurs

· Decision to collaborate with the State (i.e., become pentito)

State

· Duration of general investigation

· Initiate a specific investigation

· Duration of specific investigation

· Duration of bureaucratic activities

· Capture a Mafioso

· Duration of custody

· Decision to convict a Mafioso

· Duration of imprisonment

· Decision to assist a punished Entrepreneur

· Time between recharge of the Fondo di Solidarietà

Entrepreneur

· Decision to pay pizzo

· Decision to report pizzo request

· Decision to report punishment

· Time between receiving wage

· Decide collaborate to the State

· Decision to join NGO

Consumer

· Decision whom to buy a product from

· Time between purchases

NGO

· Time to accept the affiliation of an Entrepreneur

· Decision to spread social norms

II.x Observation

II.x.a What data are collected from the ABM for testing, understanding, and analyzing it, and how and when are they collected?

A set of output data files are generated as the result of their execution of the model, please refer to Section 4.1.7 (Nardin, Andrighetto, Székely, & Troitzsch, 2015) for a complete list of output data collected.

II.x.b What key results, outputs or characteristics of the model are emerging from the individuals? (Emergence)

The keys results emerging from the model are reported in the Results section of the main text, which consider the following outcomes:

· the imprisonment of Mafiosi,

· the efficiency of the State at imprisoning Mafiosi,

· pizzo requests and punishments meted out by the Mafia,

· pizzo paying and reporting by Entrepreneurs, and

· the social norms’ saliences of Entrepreneurs.

III) Details

II.i Implementation Details

III.i.a How has the model been implemented?

The model is implemented using Java

IV)

III.i.b Is the model accessible and if so where?

Yes, the model implementation is available at https://github.com/LABSS/gloderss

III.ii Initialization

III.ii.a What is the initial state of the model world, i.e. at time t=0 of a simulation run?

The initial values of the model’s parameters to each treatment reported in the main text is available in Table S.2.

III.ii.b Is initialization always the same, or is it allowed to vary among simulations?

See Table A1 in the main text. The values vary among treatments, but they are the same when running replications of the same treatment in which only the random seed changes.

III.ii.c Are the initial values chosen arbitrarily or based on data?

Some initial values like Mafia’s extortion level, and Consumers’ and Entrepreneurs’ Individual and Normative weights were chosen based on empirical data, while the other values were chosen arbitrarily. However, we show that the chosen values reproduces macro-patterns observed in Sicily in the last decade (see Figure 2 in the main text).

III.iii Input Data

III.iii.a Does the model use input from external sources such as data files or other models to represent processes that change over time?

No external data are used in the model.

III.iv Submodels

III.iv.a What, in detail, are the submodels that represent the processes listed in ‘Process overview and scheduling’?

None

III.iv.b What are the model parameters, their dimensions and reference values?

None

III.iv.c How were submodels designed or chosen, and how were they parameterized and then tested?

None

Table S.2. Initial value of the parameters of each agent type for each treatment. Yellow rows indicate that the value changes among treatments.

AGENT PARAMETERS

TREATMENT

B

LA

SA

CA

CONSUMER

 

 

 

 

Number of Consumers

200

200

200

200

Time between Purchase

NORMAL(30,10)

NORMAL(30,10)

NORMAL(30,10)

NORMAL(30,10)

Number of Entrepreneurs to Research

5

5

5

5

Initial Entrepreneurs Reputation as Not Payer

0.00

0.00

0.00

0.00

Entrepreneurs Threshold to consider as Not Payer

0.00

0.00

0.00

0.00

Sanction Threshold

0.90

0.90

0.90

0.90

Sanction Discernibility

0.10

0.10

0.10

0.10

Individual Weight

0.50

0.50

0.50

0.50

Normative Weight

0.50

0.50

0.50

0.50

Norm Pay Extortion

0.93

0.93

0.93

0.93

Norm Not Pay Extortion

0.07

0.07

0.07

0.07

Norm Denounce

0.07

0.07

0.07

0.07

Norm Not Denounce

0.93

0.93

0.93

0.93

Norm Buy from Paying Entrepreneur

0.50

0.50

0.50

0.50

Norm Buy from Not Paying Entrepreneur

0.50

0.50

0.50

0.50

 

 

 

 

 

ENTREPRENEUR

 

 

 

 

Number of Entrepreneurs

100

100

100

100

Wage Periodicity

NORMAL(30,2)

NORMAL(30,2)

NORMAL(30,2)

NORMAL(30,2)

Minimum Wage

500

500

500

500

Maximum Wage

1000

1000

1000

1000

Wage Variation

0.50

0.50

0.50

0.50

Minimum Price

50

50

50

50

Maximum Price

100

100

100

100

Denounce Alpha

0.50

0.50

0.50

0.50

Collaboration Probability

0.10

0.10

0.10

0.10

Affiliate Threshold

1

1

1

1

Affiliated Entrepreneurs

0.00

0.00

0.00

0.00

Reputation State Protector

0.10

0.10

0.10

0.10

Reputation State Punisher

0.10

0.10

0.10

0.10

Reputation Mafia Punisher

0.90

0.90

0.90

0.90

Individual Weight

0.50

0.50

0.50

0.50

Normative Weight

0.50

0.50

0.50

0.50

Norm Pay Extortion

0.93

0.93

0.93

0.93

Norm Not Pay Extortion

0.07

0.07

0.07

0.07

Norm Denounce

0.07

0.07

0.07

0.07

Norm Not Denounce

0.93

0.93

0.93

0.93

 

 

 

 

 

STATE

 

 

 

 

Number of Police Officers

20

20

20

20

General Investigation Duration

NORMAL(10,5)

NORMAL(100,10)

NORMAL(10,5)

NORMAL(100,10)

Bureaucratic Activities Duration

NORMAL(100,5)

NORMAL(50,10)

NORMAL(100,5)

NORMAL(50,10)

Specific Investigation Duration

NORMAL(10,5)

NORMAL(300,10)

NORMAL(10,5)

NORMAL(300,10)

Specific Investigation Probability

0.20

0.80

0.20

0.80

Capture Probability

0.20

0.80

0.20

0.80

Evidence Probability

0.01

0.20

0.01

0.20

Custody Duration

CONSTANT(10)

CONSTANT(150)

CONSTANT(10)

CONSTANT(150)

Conviction Probability

0.10

0.60

0.10

0.60

Imprisonment Duration

NORMAL(100,5)

NORMAL(500,100)

NORMAL(100,5)

NORMAL(500,100)

No Collaboration Punishment Probability

0.10

0.30

0.10

0.30

No Collaboration Punishment

0.10

0.50

0.10

0.50

Time to Compensation

CONSTANT(50)

CONSTANT(50)

CONSTANT(50)

CONSTANT(50)

Fondo di Solidarieta

0

4000

0

4000

Recharge Fondo di Solidarieta

NORMAL(500,100)

NORMAL(500,100)

NORMAL(500,100)

NORMAL(500,100)

Proportion Transfer Mafia Resources to Fondo

0.00

0.50

0.00

0.50

Spread Information Function

CONSTANT(200)

CONSTANT(200)

CONSTANT(200)

CONSTANT(200)

Proportion of Consumers

0.00

0.00

0.00

0.05

Proportion of Entrepreneurs

0.00

0.00

0.00

0.05

 

 

 

 

 

MAFIA

 

 

 

 

Number of Mafiosi

20

20

20

20

Demand Periodicity

NORMAL(10,2)

NORMAL(10,2)

NORMAL(10,2)

NORMAL(10,2)

Demand Affiliated Probability

1.00

1.00

1.00

1.00

Extortion Level

0.10

0.10

0.10

0.10

Punishment Severity

0.75

0.75

0.75

0.75

Punishment Probability

0.90

0.90

0.90

0.90

Minimum Benefit

0.00

0.00

0.00

0.00

Maximum Benefit

0.10

0.10

0.10

0.10

Pentiti Probability

0.00

0.00

0.00

0.00

 

 

 

 

 

NON-GOVERNMENTAL ORGANIZATION

 

 

 

 

Time to Affiliate

NORMAL(200,5)

NORMAL(200,5)

NORMAL(200,5)

NORMAL(200,5)

Spread Information Function

tanh(#{NUMBER_ACTIONS},0.1)

tanh(#{NUMBER_ACTIONS},0.1)

tanh(#{NUMBER_ACTIONS},0.1)

tanh(#{NUMBER_ACTIONS},0.1)

Proportion of Consumers

0.00

0.00

0.10

0.10

Proportion of Entrepreneurs

0.00

0.00

0.10

0.10

Figure S.1. Mafia imprisonment. Means plotted and error bars indicate ±1 standard deviation. (A) The number of Mafiosi (out of 20) imprisoned in each treatment and (B) proportion of investigations that are specific investigations. The dashed line indicates the change to baseline parameters

Figure S.2. Actions of the Mafia. Means plotted and error bars indicate ±1 standard deviation. The number of (A) pizzo requests made by Mafiosi and (B) punishments inflicted upon Entrepreneurs. The dashed line indicates the change to baseline parameters.

Figure S.3. Entrepreneurs’ actions. Means plotted and error bars indicate ±1 standard deviation. The (A) proportion of pizzo requests paid and (B) reported in each treatment. The dashed line indicates the change to baseline parameters.

Figure S.4. Social norm importance in the population. Means plotted and error bars indicate ±1 standard deviation. Saliences of the social norm (A) pay pizzo, (B) do not pay pizzo, (C) report pizzo, and (D) do not report pizzo. The dashed line indicates the change to baseline parameters.

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