Design patterns of reward and punishment

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Design patterns of reward and

punishment

Charlotte S. Smoor 10786902 Bachelor thesis Credits: 18 EC

Bachelor Opleiding Kunstmatige Intelligentie University of Amsterdam Faculty of Science Science Park 904 1098 XH Amsterdam Supervisor dr. A. W. F. Boer

Leibniz Center for Law Faculty of Law University of Amsterdam

Vendelstraat 8 1012 XX Amsterdam

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Abstract

Laws and rules must be enforced in order for citizens to comply. This law enforcement can be executed by using a reward regime or a punishment regime. This thesis will investigate the use of a Petri Net model to determine which one of these enforcement regimes to apply in a situation, by providing an answer to the question how enforcement design patterns are superposed on representations of legal rules and how these can be expressed by a Petri Net. These design patterns consist of specific legal rules and jural relations. Different cases are simulated in the Petri Net model to determine what type of enforcement would be the most favorable in a specific case. The application of a punishment or reward regime in each situation is studied in terms of the probability of evidence and costs. The results show that given the specific conditions are provided, for a specific situation the Petri Net model is able to determine which enforcement should be applied.

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1 Introduction

The functioning of modern society is partially dependent on the existence of rules and laws which force people to behave in certain ways. Some of these rules are unspoken such as the social courtesy to let people disembark a vehicle before em-barking oneself. Other rules are written such as the law that one must not steal. The consequences related to compliance or noncompliance, rather than the rules itself, serve as a motivation for people to comply. As Austin purported: “law is the command of the sovereign backed by the threat of punishment”(Boer, 2014). The enforcement of rules can be conducted in two ways; by distributing rewards for compliance or punishments for violating rules. Traditionally, a punishment regime has been customary in law enforcement. This is broadly reflected in our society. For example, a police officer whose duty it is to enforce the law is equipped with a gun rather than candy to appear threateningly (De Geest & Dari-Mattiacci, 2013).

However, according to de Geest and Dari-Mattiaci (2013) there is an increas-ing tendency to use reward systems in different domains in society. For example, the recruitment of armies was formerly based on threats, but currently a reward-ing system is used to attract volunteers (De Geest & Dari-Mattiacci, 2013). Public authorities nowadays use subsidies and tax redemption to induce good behaviour. Furthermore, in criminal law information on crimes is stimulated by a money re-ward and good behaviour of prisoners could lead to a sentence reduction (De Geest & Dari-Mattiacci, 2013). Boer (2014) explains this trend by arguing that the most suited type of enforcement is almost entirely dependent on the situation. Based on the specific circumstances, the most suitable form of law enforcement can be de-termined. Furthermore, according to Boer (2014) evidence and the production of evidence play a major part in this enforcement process. He demonstrates that there is a clear distinction between the enforcement regimes if the probability of evidence available is less than one, which is usually the case. Unfortunately, the process of determining the most efficient regime in a specific situation can be very complex and time consuming, because all relevant factors have to be considered. This ex-plains the increasing interest in rationalization and automatization of enforcement regimes and the design principles to conceive enforcement arrangements (Boer, 2014).

In this study, the process of automatization will be investigated by representing design patterns of reward and punishment regimes in the form of a Petri Net and an attempt to answer the following questions will be provided: “How would enforce-ment design patterns be superposed on representations of specific legal rules, and can these be expressed by a Petri Net model? And is it possible to simulate these specific situations and to reproduce their results with a Petri Net model? ”

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This paper will be an extension of the research by Sileno (2016) in which the representation of legal rules in a Petri Net model is studied which was validated by processing specific situations of deontic paradoxes provided in literature. Both papers consider a knowledge representation problem and evaluate the model in terms of the adequacy of representing specific cases and their result. However, this paper will focus on the application of reward and punishment regime in specific situations, which are interesting boundary cases that explore important and often overlooked dimensions of the problem.

With the use of a Petri Net model, reward and punishment regimes are exam-ined which may yield a useful and obvious process-level difference between these regimes. By establishing this distinction, perhaps a satisfying model which con-siders all relevant factors of an enforcement process will be created which can be widely used as a facilitator in the field of law.

In order to provide an answer to the research question, all relevant factors of the enforcement process must be covered. A literature review will assist to clarify spe-cific definitions and concepts used in legal systems. Thereafter, applications of en-forcement regimes will be investigated by examination of different, already known cases to be able to comprehend the fundamental difference between a reward and punishment regime. As discussed above, every situation has specific circumstances which influence the choice for an enforcement regime. Together with legal rules, these circumstances will assist creating design patterns for reward and punishment by representing the rules and transitions in a Petri Net model. Each situation pro-vides certain probabilities, which will be assigned to the transitions in the Petri Net. When all relevant factors have been included in the Petri Net, stochastic sim-ulations can be conducted to try to reproduce the results of the specific cases as a validation of the representational adequacy of the proposed process-level descrip-tion in the form of a Petri Net. Lastly, these results will be compared to draw a conclusion and possibly, suggestions for further research will be provided.

2 Theoretical foundation

2.1 The role of evidence in law enforcement

This paper discusses concepts and definitions provided by the study Punishments, Rewards, and the Production of Evidence(2014) by dr. A. W. F. Boer. Boer (2014) addresses the open knowledge acquisition problem, of how to characterize the relationship between representations of legal duties and reward and punishment regimes. In the study, the importance of evidence in the process of distinction between enforcement regimes is emphasized. Boer (2014) introduces the evidence criterion: ”for a punishment regime to be applied, evidence of noncompliance is

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re-quired and for a reward regime to be applied, evidence of compliance is rere-quired.” It therefore follows that under a reward regime unmonitored compliance is treated as noncompliance, while under a punishment regime unmonitored noncompliance is treated as compliance (Boer, 2014). Both regimes create a different payoff and cost structure in situations. Moreover, the evidence criterion distinguishes enforce-ment process designs, as chosen by the regulator, rather than subjective experiences of payoffs (Boer, 2014).

According to the evidence criterion, which serves as a relatively clear rule of thumb to decide which regime to apply in a specific case, the following examples are con-sidered.

1. A contract extension, bonus or promotion automatically given to all employ-ees unless there is evidence of bad performance is a punishment regime.

2. Not extending a residence permit because of evidence of criminal behaviour is a punishment regime.

3. Tax exemptions based on evidence are reward regimes.

4. Enforceability of formal sales agreements is a reward regime.

Lastly, Boer (2014) concludes that the primary function of a reward regime is the production of evidence, which would otherwise not exist. Therefore, a reward structure is far more common than expected in a system that uses punishment as a threat, because one cannot be punished for not producing evidence of compliance. Thus, the use of a enforcement regime is almost entirely dependent on evidence and the production of evidence. The study provides a model in the form of a Petri Net in which the role of evidence is included in the enforcement process. The next section presents a short introduction to Petri Nets.

2.2 Petri Nets

As discussed, this paper serves as a continuation of the work of Sileno (2016), in which Sileno defends his choice for the use of Petri Nets in legal systems by em-phasizing the necessity for more transparency which the visual power of the Petri Net notation offers. Petri Nets were introduced by Carl Adam Petri in 1962 as a useful graphical tool for the representation of complex logical interactions among physical components or activities in a system (Bobbio, 1990). Petri Nets permit an explicit representation of the concurrent, interconnected activity of the system’s components (Meldman & Holt, 1971). This makes them applicable to all systems, not only computer systems. Petri aimed to demonstrate that asynchronous systems

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are more powerful than synchronous systems (Sileno, 2016). It was Petri’s inten-tion to give up the ficinten-tion of global states (Brauer & Reisig, 2009). Discrete acinten-tions occurring in physical systems only affect a part of the system’s components. Thus, actions cannot be defined as relations between two global states. For that reason, Petri thought of a notation that is based on the partial orderings induced by causal relations (Sileno, 2016). This makes it possible to trace the effects that one part of the system has on any other part, which increases the ability to analyze and un-derstand complex systems such as legal systems. Also, it aids in the detection and clarification of ambiguities and inconsistencies in the natural-language descriptions of systems, and it also permits straightforward computer simulation (Meldman & Holt, 1971). Hence, this makes the Petri Nets particularly suitable for this paper’s purposes.

2.3 Hohfeld’s Principles

The Petri Net models proposed in Sileno’s thesis (2016), as will the models pro-posed in this paper, are constructed according fundamental legal rules defined by Hohfeld in Some Fundamental Legal Conceptions as Applied in Judical Reasoning (1913). With this article, Hohfeld aimed to increase understanding of basic con-ceptions of the law, such as legal elements that enter into all types of jural interests. Instead of conventionally taking the legislator’s perspective, Hohfeld investigated the basic conceptions of the law, and decided to proceed by analyzing the insti-tutional matter as it is concretely used in the actual activity in the courts (Sileno, 2016). In his study, Hohfeld found that one of the greatest obstacles to under-standing the solution of legal problems often arises from the assumption that all legal relations may be reduced to ”rights” and ”duties,” and that these categories are therefore adequate for the purpose of analyzing even the most complex legal interests (Hohfeld, 1913). In an attempt to clear up this misconception, Hohfeld introduced eight fundamental jural relations which are shown in figure 1. Accord-ing to Hohfeld, these jural relations divided into opposites and correlatives were sufficient to represent all legal configurations (Sileno, 2016). In their essence, the two Hohfeldian tables reflect two distinct dimensions of the legal relations holding between two correlated parties, such as two social actors that are bound by legal provisions (Sileno, 2016). For example, a right is the jural correlative to a duty, and power is the opposite of disability. Hohfeld argued that in each situation a legal relation involves two parties which have a correlative relation to each other.

To illustrate with a contemporary example involving a traffic situation, suppose someone runs a red light and collides into another person. In this situation these two persons share a legal correlative relation. The second person had the right to drive, while the first person had the duty to stop before the red light. After the

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collision, the second person has power over the first person who is liable for rein-forcement because of noncompliance to the rule of stopping for a red light. Since according to Hohfeld all legal configurations can be reduced to and described with these jural relations, Sileno (2016) also uses these rules in his Petri Nets to model deontic paradoxes as a validation of the model’s representational adequacy. Using a similar approach, this paper examines the representation of different sce-narios in which either a reward or a punishment regime is applied.

Figure 1: Hohfeld’s jural relations

2.4 Carrots and sticks

In this paper, the definitions discussed in the article The Rise of Carrots and the Decline of Sticksby de Geest and Dari-Mattiacci are used to explore the funda-mental distinction of reward and punishment regimes by studying their examples of various situations in which either a reward or a punishment regime is used. In the article, rewards and punishment are referred to as carrots and sticks. A carrot is a payment to the citizen from the lawmaker that is made if he or she has been monitored and found complying, and a stick is a payment by the citizen that is made if he or she has been monitored and found violating.

De Geest and Dari-Mattiacci argue that in situations with simple settings sticks are superior to carrots. These simple settings apply when all citizens have the same effort costs, which are costs made in order to comply and the lawmaker is aware of these costs and asks for equal efforts from all the citizens. Regarding these cases, sticks are preferred because the lawmaker can easily set the punishment so high that all citizens are forced to comply.

However, in some situations punishment is not the most efficient option. For instance, studies investigating long prison sentences found that there is no reliable evidence available of an effect which is sufficiently large enough to justify the costs of long prison sentences (Durlauf & Nagin, 2011). In some of these complex cases, it may be more cost beneficial to use a different type of reinforcement. The study of de Geest and Dari-Mattiacci support this finding by arguing that the use of carrots

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are more efficient in complex societies in which simple settings do not apply. Two examples of this are the specification problem and the singling out danger. The specification problem describes the situation in which it is unclear to the lawmaker what to expect from each individual citizen. This may lead to the lawmaker setting norms to which not every citizen is able to comply. For instance, if citizens are obliged to report suspicious financial transactions or to help people in need, then the lawmaker generally has the problem that it is unknown who was specifically in the circumstances of having that duty. The use of a punishment regime in this case would result in punishing the innocent, because often the citizens cannot help that they are not in the circumstances to comply which leads to a distortion in the dis-tribution of wealth. The singling-out danger is a problem in which the lawmakers require significantly higher efforts from specific citizens and less from others. For example, when it is required to send members of families to serve in the army. A punishment regime would cause all families to send a member, which is unneces-sary, and would create an undesirable change of wealth if families simply cannot comply. Thus, a punishment regime should not be used when the law requires a significantly higher burden from certain citizens than from others. Under a reward regime, people are required to comply but in return they receive a compensation for their effort (De Geest & Dari-Mattiacci, 2013)

The article concludes that although the use of sticks has become a popular ap-proach, it may be not the best solution in all situations. Deciding between the use of reward or punishment regime in a specific situation is a difficult process and it is necessary to consider all available information and circumstances of a specific situ-ation. The effects of the enforcement regimes on the specific cases are examined in terms of transaction costs in which the inevitable monitoring costs to increase the likelihood of evidence play a major role, risk costs and the distributional distortion of wealth which will also be considered in this study.

In the next section the important role of evidence in legal processes, the principles of fundamental legal concepts defined by Hohfeld and the specific situations such as the examples provided by Boer (2014), specification problem and the singling out problem will be considered to create an enforcement design pattern.

3 Research method

In order to create an enforcement design pattern, all relevant factors of an enforce-ment process such as the functioning of a legal system and in particular, the design and fundamental difference of a reward and punishment regime must be consid-ered. The distinction between the two regimes will be made based on the prob-ability of evidence and the costs related to an enforcement regime in a particular

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situation. Thereafter, all factors of the process will be translated into one Petri Net for stochastic simulation that adequately covers the identified evaluation cases by varying the probabilities that take place in the transitions.

3.1 Petri Net

A Petri Net is capable of creating a clear visual representation of a complex sys-tem, because it is a directed graph with two types of nodes, the places and the transitions. A place, in which one or more tokens can reside and a transition, a normal transition or a XOR transition can only be connected to each other by a certain relation. For each transition, if all input places contain at least one token, the transition is enabled to fire. If a transition fires, tokens are moved from input places to output places (Sileno, 2016).

During a simulation, an emitter starts firing a certain number of tokens which flow through the model according to the given probability of the transitions. In case of a normal transition, the same amount of tokens can be fired to all connected places. In case of a XOR transition, a token is only fired to one state according to the assigned probability. When a token is fired successfully through the Petri Net, it reaches a collector which marks the end point of the flow. After the simula-tion the collector indicates how many tokens have reached that particular collector. The Petri Nets created in this study will be modelled in Petri net markup language (PNML) with Yasper, a modelling tool developed in collaboration between TU Eindhoven and Deloitte (TU/Eindhoven & Deloitte, 2005a). In Yasper, a case sen-sitive place is depicted as a yellow circle, a normal transition as a green square, and a XOR transition as an orange diamond. The relation between a state and a transi-tion is represented as a normal arc, which is a black arrow indicating the directransi-tion of the flow or as an inhibitor arc which is a black line with a dot (TU/Eindhoven & Deloitte, 2005b).

To create a Petri Net which can be used to simulate different situations, a sim-ple model is considered in figure 2 to illustrate the specifics involved in a model. The model represents an action scheme which will aid in comprehending the basic functioning of a Petri Net. Suppose a medical emergency occurs on an airplane, and there is only one licensed doctor on board. The doctor feels professionally responsible and obligated to save his fellow passenger (his motive to do A). Before the doctor intervenes, he has to be certain that the emergency does not fall beyond the reach of his professional domain. For instance, if the passenger has a heart attack and the doctor is a dentist. If he is not likely to save the passenger, he might be sued. To avoid this, he makes an estimation of the probability of successfully completing the action, which can be considered as his affordance. Yet, when he decides to take action but however does not have the disposition (e.g. the

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situa-tion was already to critical), he will not succeed to save the passenger. All these states are represented in the model and in order to successfully succeed the action resulting in an outcome, all conditions must be valid.

Figure 2: Basic action scheme (Sileno, n.d.)

3.2 Distinction between punishment and reward regime

A punishment and reward regime have certain similarities. First, they share the same purpose: to get citizens to comply to a rule. Secondly, in both regimes spe-cific costs are involved. A punishment regime can even be redefined into a reward regime. For example, a mother asks her son to walk the dog before nightfall and as a reward he will receivee 10. When he does not succeed to walk the dog be-fore the indicated time, he has to pay backe 5. This scenario can be reformulated to the scenario that the son will receivee 5 for walking the dog, but if he does so before nightfall he receives ae 5 bonus. The former would be a punishment regime and the latter a reward regime, but both scenarios have the same outcome. However, this argument only holds if monitoring occurs with a probability equal to 1 (De Geest & Dari-Mattiacci, 2013) or if the boy is able to provide evidence of compliance.

The difference between the regimes relies on the fact, as previously discussed, that in a reward regime, a payment is made to the citizen from the lawmaker if he or she has been monitored and found complying, and in a punishment regime a payment is required from the citizen if he or she has been monitored and found violating (De Geest & Dari-Mattiacci, 2013). As defined by Boer (2014) punishment and reward regimes can roughly be distinguished as follows:

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• There is a rule A defined by the lawmaker, established in advance of appli-cation of a regime, and in awareness of involved citizens, which states that the citizens ought to do A, upon certain circumstances C.

• In a reward regime, the regulator attaches a reinforcement with positive util-ity (r) to performance of A, while it reacts neutrally to nonperformance of A.

• In a punishment regime, the regulator attaches a reinforcement with neg-ative utility (¬ r) to performance of A, while it reacts neutrally to non-performance of A.

Based on weighing off the payoff of reinforcement against the costs of performance of A, a citizen can determine whether to comply or to violate.

3.2.1 Evidence

As we have seen in the previous example, when the probability of monitoring is equal to 1, it is easy to check for compliance or non-compliance. However, the probability of monitoring is generally more likely to be less than 1. Suppose the following example: the lawmaker demands citizens to switch to sun-powered en-ergy, but only 10 percent can be monitored. In a penalty regime, the base price (b) ise 100 and the penalty for violating the rule is e 90, because there is evidence of only 10 percent of noncompliers. In a reward regime, the base price is alsoe 100, but the reward ise 90 (because it is paid to only 10 percent of the compliers). This means that compliers will receive at moste 100 under a penalty regime while un-der a bonus regime, they will receive either e 100 (the base price, in case of no monitoring) ore 190 (the base price plus the e 90 reward, in case of monitoring). Under a penalty regime, violators will receive eithere 100 (the base price, in case of no monitoring) ore 10 (the base price minus the e 90 penalty, in case of moni-toring), while they will always receivee 100 under a reward regime. This example shows that the probability of evidence (E) plays an important role in the distinction between a reward regime and a punishment regime. This is also illustrated by table 1 in which the probability is less than 1. This table shows, as already discussed, that in a reward regime monitored complying citizens will be treated as non-complying citizens, while in a punishment regime non-monitored, nonnon-complying citizens will be treated as complying citizens.

Another example which shows the importance of evidence is when one buys a product, one generally receives a receipt as evidence for the purchase. This receipt can also be used to return the product, because it functions as proof that the product was purchased in that particular store. However, when a product is stolen from the

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Regime Compliance Non-compliance

E ¬ E E ¬ E

Punishment b b b - r b

Reward b + r b b b

Table 1: Payoff reinforcement

store and there is no evidence, the thief will not be punished. The probability of evidence of compliance or the probability of evidence of non-compliance can have a major impact concerning the decision of what type of enforcement regime will be applied. Therefore, in each situation the probability of evidence is considered.

3.2.2 Costs

Another important factor in the choice for a reward or punishment regime in a spe-cific situation are the costs related to the type of enforcement. On the one hand, this includes the costs citizens put in for law compliance (the effort costs). On the other hand, these are the costs of the lawmaker which are tried to minimize while attempting to achieve rule compliance. For instance, it is more cost efficient for the lawmaker to penalize thieves, rather than rewarding non-thieves, because theft occurs less often than non-theft (De Geest & Dari-Mattiacci, 2013). In another article, De Geest and Dari-Mattiaci (2009) define a formal model on how to es-tablish the value of a reward or punishment in terms with the effort costs and the monitoring probability. The following notations are used:

• e = effort cost of a citizen to comply

• r = reward

• p = punishment

• Pr= monitoring probability of reward

• Pp= monitoring probability of penalty

Under a reward regime, citizens will comply if the payoff of compliance is higher than the payoff of noncompliance considering the probability of being monitored. This is represented in the following formula (De Geest & Dari-Mattiacci, 2009).

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Under a punishment regime, citizens will comply if:

e≤ Pp× p (2)

The lawmaker sets the values of the reward or punishment and the monitoring probabilities high enough, that all citizens will comply if:

e= Pr× r = Pp× p (3)

The costs that the lawmaker attempts to minimize entail transaction costs, risk costs and distributional distortion costs (De Geest & Dari-Mattiacci, 2013). Trans-action costs include monitoring costs and processing costs. Monitoring costs are the ex ante costs made before a particular regime is applied, to be able to monitor a citizen for compliance or noncompliance. These costs are inevitable in the process of obtaining evidence and therefore, rise as the probability of monitoring increases. Processing costs are the ex post costs of actually paying a reward or collecting a punishment. Processing costs are dependent on the amount of citizens on whom the law is enforced (De Geest & Dari-Mattiacci, 2013). For example, the costs of installing a speed monitor camera are monitoring costs, but processing costs in-clude the costs of taking actual photographs and collecting information about the violator’s address. Risk costs involve the assumption that citizens are equally risk averse, but due to the inability to monitor all citizens some bear the risk of receiv-ing no recognition for their effort. Compliers are subject to risk under a reward regime, and under a punishment regime violators are subject to risk. De Geest and Dari-Mattiacci (2013) use the amount of citizens subject to risk and the magni-tude of the sanctions used as proxies for the risk costs. At last, to understand the distributional distortion costs it is important to bear in mind that the purpose of a penalty or reward is to motivate citizens to comply with a rule, not to change the distribution of wealth in society. However, a penalty or reward may result in citi-zens becoming poorer or wealthier than others (De Geest & Dari-Mattiacci, 2013). To illustrate the latter, consider a punishment regime that demands one thousand village citizens to help building a dam to prevent the city from getting flooded. This corresponds to an effort cost ofe 50, but every visitor receives a compensa-tion ofe 75 that consists of not getting flooded. However, each citizen is a typical free-rider: if he does not help, the dam will still get built because others would still cooperate. In this case, a punishment regime would not create a great distributional distortion between all the citizens. However, when one citizen is required to build the whole dam (an effort ofe 1,000) while all others do nothing, and the full-time worker is incentivized through a penalty, he would be substantially impoverished

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by the rule. But the purpose was to build a dam, not to change the existing wealth distribution. The solution to prevent the distributional distortion would be by using a reward regime, motivating the worker with a reward ofe 1000.

3.3 Design Pattern

3.3.1 Hohfeldian jural relations

The enforcement Petri Net model is based on the work of Hohfeld in Some Fun-damental Legal Conceptions as Applied in Judicial Reasoning(1913), in which he introduced eight fundamental jural relations (recall from section 2). The Petri Net model in figure 3 makes use of the legal relations of a right and a duty as shown in figure 1, which involves two opposing parties sharing a legal relation. One party makes a certain claim to the opposing party which is accompanied by a duty to do A which is shown in the Petri Net model. When one person fails his duty to do A, the person will be liable to be punished for noncompliance. By extending this model, based on the simulation of a specific situation the model is capable of con-sidering the positive and negative payoffs of a reward and a punishment regimes which leads to the decision which enforcement regime is the most efficient. This particular model is provided by Boer (2014) which is shown in the appendix (fig-ure 6). In this paper, we will use this model as a foundation for further research. The difference between this model and the Petri Net created in this paper will be discussed in the following section.

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3.3.2 Updated model

In order to simulate different situations with specific circumstances, certain prob-abilities must be assigned to the transitions. In the initial model, the transitions allow tokens to flow to multiple states. After updating the model, some of these transitions are changed into a XOR transition. A XOR transition consumes a to-ken from one of its input places, if any, and produces a toto-ken in one of its output places, if any according to the assigned probability. Thus, in simulation the XOR transition serves as a probability mass function over the possible transitions. By varying these probabilities in the XOR transitions, the conditions of situations with different circumstances can be simulated. The updated model can be seen in figure 7 in the appendix. Furthermore, the model is modified according to the specific conditions in order to properly represent the situations and to create the design patterns.

4 Results

This paper considers a number of interesting situations with specific circumstances provided by De Geest and Dari-Mattiaci (2013) and Boer (2014) and the use of different enforcement regimes, punishment or reward, in each situation is studied in terms of the probability of evidence and costs. For each case, the influence of evidence is considered and thereafter simulations are executed using the model cor-responding with the specific conditions of the situations. For each case, different collectors are relevant for analysis and obtaining results. Furthermore, every simu-lation done in Yasper has different outcomes which explains the difficulty of exact reproduction.

4.1 Evidence based examples

The examples provided by Boer in Punishments, Rewards, and the Production of Evidence(2014), discussed in section 2.1, highly rely on the production of evi-dence. In each example a regime can only be enforced based on the production of evidence of compliance or noncompliance. Each of these probabilities of providing evidence is separate, and are often diverse. This means that absence of evidence of noncompliance is no evidence of compliance and vice versa. When the probability of evidence of compliance or evidence of noncompliance increases, the monitor-ing probability can be reduced which lowers the monitormonitor-ing costs in each situation. Furthermore, it is assumed that the citizens prefer earning money rather than earn-ing nothearn-ing or losearn-ing money, which will lead to the citizens weighearn-ing off the payoff

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of the reinforcement in their decision for compliance or noncompliance. The law-maker will pursue the highest probability of compliance by determining the most efficient regime within reach.

Figure 4: Simplified enforcement model

4.1.1 Simulations

Each example is considered in four situations; total compliance under a reward and punishment regime and total noncompliance under a reward and punishment regime in order to show which regime is more favorable. Figure 4 illustrates the simplified version of the whole enforcement model (figure 7) with the states and XOR transitions which are of importance for obtaining the results. As the costs related to a regime are highly dependent on the monitoring probability, simulations with varying monitoring probabilities have been executed by adjusting the prob-ability in the XOR nodes recognize A and recognize failure to A. The monitoring

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probability of 0.3 is used in the simulations of these example, because it provided a good indication of the effect evidence has on both regimes. Furthermore, each situation is simulated with a total of 100 tokens which represent the number of cit-izens.

The simulation of the first situation from the examples provided by Boer (2014) is considered, in which a contract extension, bonus or promotion is automatically given to all employees unless there is evidence of bad performance. This situation when all citizens comply is considered in table 2 and when all citizens violate in table 3 under both a reward (upper table) and punishment regime (lower table). The effort costs of a citizen for good performance ise 75. A bonus in this case is worthe 100.

Collected Costs per citizen (e ) Processing costs (e )

Monitored 37 75 3700

Non-monitored 63 75 0

Monitored 37 75 0

Table 2: Example 1: Reward and Punishment regime in compliance

Monitored 33 0 0

Table 3: Example 1: Reward and Punishment regime in noncompliance

Secondly, a case is considered in which a residence permit is not extended when there is evidence of criminal behaviour. Suppose that extending a residence permit is equal toe 500, and the effort costs for one citizen for not committing a crime ise 100. In table 4, this situation is considered when all citizens comply and in table 5 when all citizens violate under both a reward (upper table) and punishment regime (lower table).

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Monitored 37 100 18,500

Monitored 37 100 0

Monitored 33 0 0

Non-monitored 67 0 34,500

Monitored 33 0 0

In the first two examples, there is evidence of 33 noncomplying citizens and 67 citizens who do not get monitored. As can be seen in the tables, the processing cost under a reward regime are high for the non-monitored noncompliers because they receive a reward, while there are no costs involved under a punishment regime. In both situations, when a reward regime is used the probability of evidence of compliance would most likely be high resulting in high reward costs.

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Thirdly, the situation is represented in which tax exemptions based on evidence are provided. Suppose the tax is equal toe 1000, but with evidence it is e 800. The simulation is shown in table 6 and 7.

Monitored 37 800 0

Monitored 37 1000 0

Monitored 33 1000 0

Monitored 33 0 0

And finally, in table 8 and 9 the situation in which enforceability of formal sales agreements is considered. When enforceability of formal sales agreement is pro-vided, there is evidence (e.g. a contract) of an official amount which is agreed upon from both parties. Both parties are legally bound, which avoids situations where suddenly the buyer must pay more than the amount which was agreed upon. Sup-pose drawing up a formal sales agreement costse 100, and these are compensated by the lawmaker. Simplified, the compensation from the lawmaker ofe 150 stands for the certainty that when there is evidence of someone breaching the contract, he will get prosecuted by the lawmaker.

In the final cases, by rewarding to provide evidence the probability of evidence of compliance would increase which leads to rewarding compliers for good behav-ior. When a punishment regime is used, the monitoring probability must be high to collect evidence of noncompliance which leads to high monitor costs.

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Monitored 37 100 5550

Monitored 37 100 0

Monitored 33 0 0

4.2 Case 1: Homogeneous Society with a Fully Informed Lawmaker

The first and most simple case provided by de Geest and Dari-Mattiaci (2013) in-volves a homogeneous society with a fully informed lawmaker. This means that all citizens have equal effort costs for compliance and the lawmaker is completely aware of these costs. Because of this full awareness, the lawmaker is able to set the values of a reward and punishment high enough that every citizen must comply, according to equation 3 considered in section 3.2.2. The threat of punishment is enough to achieve complete compliance, which leads to the fact that no penalties have to be distributed. However, the rewards do have to be paid if evidence of com-pliance is demonstrated. This case has the following consequences on transaction costs, risk and distributional distortion costs.

• Transaction costs:

The use of a reward regime or a punishment regime will cost an equal amount in terms of monitoring. Punishment will generate no processing costs, since punishment is never executed. Under a reward regime, all monitored com-plying citizens must be rewarded which generates immense processing costs. In conclusion, a reward regime generates more transaction costs than a

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pun-ishment regime. • Risks:

A punishment regime creates no risk, even if monitoring occurs with a prob-ability less than 1. Because all citizens comply and those who are monitored are never punished, and treated the same as unmonitored citizens. Instead, under a reward regime, all complying citizens are subject to the risk of either being monitored and rewarded or not being monitored but still bearing the effort cost.

• Distributional distortion costs:

Because all citizens comply and all individuals bear the same effort cost and no one is punished, there are no distributional distortion costs involved in a punishment regime. However in a reward regime, only the citizens who are monitored will receive a reward. According to De Geest and Dari-Mattiaccia, this is the lottery effect in which compliers are forced to par-ticipate in a virtual lottery (De Geest & Dari-Mattiacci, 2013).

4.2.1 Probability of evidence

Since all citizens comply, only evidence of compliance is considered. The proba-bility of evidence of compliance will most likely be high, because it can be used to proof compliance or not to be punished for noncompliance. This way the citizens are less dependent on the lottery effect and the monitoring probability which leads to the ability of reducing the monitoring probability. As a result, the monitoring costs for both a reward and a punishment regime may be reduced. In this situation, all citizens comply causing the nonexistence of monitoring costs in a punishment regime, which means only the costs of a reward regime will be decreased. The costs of a reward regime is now entirely dependent on the number of citizens which produce evidence of compliance. Therefore, when the probability of evidence is higher than the monitoring probability, a reward regime will be costly causing a punishment regime to be superior.

4.2.2 Simulations

In order to illustrate, consider the following situation. The effort costs of each citizens aree 20, and the probability of being monitored is 0.5 and the reward is e 50 under a reward regime. The monitored compliers become e 30 richer and the others receive no compensation for their effort costs. In a punishment regime, the penalty for monitored violators ise 50. The results are obtained using the model illustrated in figure 4, and are shown in table 10 and 11.

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Monitored 57 +30 1710

Non-monitored 43 -20 0

Table 10: Reward regime

Monitored 33 -20 0

Non-monitored 67 -20 0

Table 11: Punishment regime

As the table 10 and 11 show, the processing costs of a reward regime are high compared to the processing cost of a punishment regime since all citizens comply making a punishment regime superior to a reward regime, if equation 2 holds.

4.3 Case 2: Citizens Have Different Effort Costs

The second case has previously been referred to as the singling out problem. It involves a society in which the citizens do not all have the same effort costs, but the lawmaker is nevertheless fully informed about these individual effort costs and is able to set the values of reward and punishment high enough that all citizens will comply. For example, the lawmaker demands all citizens to give up some land for the construction of a new highway, but some owners are only required to give up a small front yard while others must sacrifice a wide pasture. This singling out problem has the following effects on transaction costs, risks and distributional distortion costs.

• Transaction costs:

Since all citizens comply, the transaction costs in this case are the same as in the first case. The monitoring costs are dependent on the monitoring prob-ability; a higher monitoring probability leads to a higher monitoring costs. Furthermore, a punishment regime still generates less transaction costs than a reward regime, because every citizens complies. A reward regime gener-ates costs which are dependent on the individual rewards and the amount of evidence available of complying citizens.

• Risks: A punishment regime generates no risk because all citizens comply and therefore face no risk of punishment. Under a reward regime, all citizens

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bear some risk in case the monitoring probability is less than 1. Thus, a reward regime generates more risk.

• Distributional distortion costs: Under a punishment regime, citizens with higher effort costs may be more impoverished and thus have a major dis-advantage compared to citizens with lower effort costs. Therefore, a pun-ishment system involves distributional distortion costs. These costs increase when there is a larger distribution between the effort costs. A regime which provides a general reward also causes a distributional distortion. General re-wards both enrich monitored citizens, who receive a compensation for their effort, while also potentially impoverish non-monitored citizens, who do not receive a compensation for their effort. Furthermore, a general reward may overcompensate citizens with a lower effort cost, since they receive a reward that is higher than their effort costs.

This can be illustrated with a numerical example, consider ninety citizens who have ae 200 effort cost while ten citizens have an effort cost of e 50. If a general reward or punishment will be applied, they must be set ate 200 in order for all citizens to comply. In this case, a reward regime will overpay ten citizense 150, which results in a total overpayment ofe 1500. A punishment regime will underpay ten citizens bye 150, but more importantly it will underpay the other ninety by e 200 each. Thus, the total underpayment in this regime is e 19500. In conclusion, in this case a punishment regime will distort more. However, in another case in which for example there are more citizens with lower effort costs, it is possible that a punishment regime will distort less.

However, a reward as opposed to a punishment can be individualized in terms of their amount. Individualized rewards can remove the unequal effort effect by rewarding each citizen according to his effort costs. This reward regime creates a smaller distributional distortion than punishment regime. Individualized penalties will not accomplish the same, because punishment is applied in case of noncompli-ance. Therefore, by individualizing punishment, differences among violators are created but not among compliers. Overall, a reward regime is superior to a punish-ment regime if the distributional distortions are significant, which is the case in the example we will simulate.

Similarly to the first case, only evidence of compliance is considered since all citi-zens comply. Once again, the increase of the probability of evidence of compliance leads to the monitoring probability to be reduced which leads to lower monitoring costs. However, in this case the individualized effort costs must be considered.

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Providing evidence of individualized effort costs, a distinction between citizens with high effort costs and low effort costs can be made which leads to a lower distributional distortion in both regimes.

4.3.2 Simulations

The example which was discussed above is simulated and the results are shown in table 12-15. Two simulations were conducted in the model illustrated in figure 4. In the first simulation, 90 % of the total of 100 citizens had a high effort costs of e 200 and in the second simulation 10 % had a low effort cost of e 50. The size of these populations can be adjusted according to the conditions of the situation. The monitoring probability is set by varying the probability in the XOR nodes recognize Aand recognize failure to A (see figure 4). In table 12 and 13, the simulation is shown with a monitoring probability of 0.3 and in table 14 and 15 the monitoring probability is 0.6 in order to show the effect of evidence on both regimes in this situation.

High effort Low effort Processing costs (e ) Distortion

Monitored 33 3 7200 +450

Non-monitored 57 7 0 -11,750

Monitored 33 3 0 -6750

Non-monitored 57 7 0 -11,750

In table 12, it is shown that the transaction costs of a reward regime aree 7200. Only the citizens with a low effort cost are overpaid, thus the overpayment ise 450. Table 13 shows that the processing costs of a punishment regime are equal to 0. However, every citizen is underpaid because both the monitored citizens as the non-monitored citizens do not receive a compensation for their effort costs.

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Monitored 50 7 11400 +1050

Non-monitored 40 3 0 -8150

Monitored 50 7 0 -10,350

Non-monitored 40 3 0 -8150

By comparing the situation with different monitoring probabilities, it is shown that in this situation a higher monitoring probability results in a higher distortion when monitored and lower when not monitored. Overall, a punishment regime cre-ates a greater distributional distortion making a reward regime superior. However, the outcome of the simulation is dependent on the percentage of citizens with high effort costs and low effort costs in terms of the distributional distortion costs.

4.4 Case 3: The Lawmaker Has No Information on the Citizens’ In-dividual Effort Costs

This case, previously referred to as the specification problem involves a lawmaker which does not know the individual effort costs of citizens, and thus also may also not know which citizens are able to comply with a norm at reasonable costs. This may lead to the punishment of citizens who are simply unable to comply. For instance, when a punishment regime is used to motivate citizens to play the piano, citizens who lack a musical talent may be punished. Suppose that only one citizen who lives in a street with 100 neighbors has information about a crime which took place in this street. The law enforcer however, does not know who this is. The effort costs are e 1000 to come forward with the information. A reward can be provided by offering ae 1000 reward to the complier or by giving all 100 neighbors ae 1000 fine, except for the one who offers the information. In this situation, punishment will generate high transaction costs and distributional distortion by impoverishing 100 citizens who live in one street compared to the rest of the village. Another example which involves an opposite situation that some citizens are unable to violate the rule created by the lawmaker because they lack the ability or the opportunity to do so. Suppose that violation of the rules

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requires a specific skill, such as hacking into a government system. Most people do not have the ability to do this. Thus, inability to comply weakens the case for a punishment regime, and inability to violate weakens the case for a reward regime because rewards may be distributed to the wrong citizens. This specification case has the following consequences on transaction costs, risk and distributional distortion costs.

• Transaction costs: It is assumed that the lawmaker sets the values of the reward and punishment at a level that all who are able to comply do so and all who are unable to comply violate. A punishment regime will be used more often than a reward regime if there are more violators than compliers. Thus, if the majority of the citizens is unable to comply a punishment regime loses their intrinsic transaction costs advantage.

• Risk: Also, a punishment regime starts generating more risks if there are more violators than compliers. For instance, all citizens who are unable to compose a song would live in fear that they might be singled out for moni-toring and receive a penalty.

• Distributional distortion costs: In this case, some individuals have larger effort costs than others and some effort will not be monitored. This automat-ically leads to a distortion. A punishment regime will also generate a lottery effect because some individuals who are unable to comply will be punished. The lottery effect of a reward regime will also increase to the extent that the rule is applied to citizens who are unable to violate. These distortion how-ever cannot be corrected by individualizing the reward or the penalty when the lawmaker is not aware of the precise amount of the individuals’ effort costs.

In this case, the probability of evidence of either compliance or noncompliance is considered, because it provides an increasing probability of determining the most efficient regime. The increase of probability of evidence of both, will result in re-ducing the monitoring probability and the related costs. When citizens provide ev-idence of noncompliance, the lawmaker is still not informed because it is unknown if citizens are willingly violating the rules or simply are not under the circum-stances to comply. In contrast, when citizens provide evidence for compliance the lawmaker become mores informed. Unfortunately, the probability of evidence of noncompliance is more likely to be higher than the probability of evidence of com-pliance due to the majority of noncomplying citizens (unwillingly or not). In a situ-ation in which most citizens comply, the probability of evidence of non-compliance

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will be very low. The use of a punishment regime in this case will most likely lead to non-complying citizens not providing evidence of non-compliance.

Figure 5: Enforcement model

4.4.2 Simulations

The example which was discussed above is simulated in the model illustrated in figure 5 and the results are shown in table 16-19. Other than the previous cases, the lawmaker does not know whether a citizen is under the circumstances to comply. This is why the node Recognize C is of importance in this case. Once again, the monitoring probability is set by varying the probability in the XOR nodes recognize Aand recognize failure to A. In this situation, only one person of the total of 100 citizens is under the correct circumstances and therefore has a high effort cost and the rest has a low effort. In table 16 and 17, the monitoring probability is 0.3 and in table 18 and 19 the monitoring probability is 0.6 in order to show the effect of evidence on both regimes in this situation. Table 16 shows that in a reward regime the transaction costs aree 1000. In this case, there is no distributional distortion

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Monitored 1 29 1000 0

Non-monitored 0 70 0 0

Monitored 1 29 0 -29,000

because the effort costs is equal to the reward. In table 17, it appears that there are no transaction costs in a punishment regime. However, a non-complying and monitored citizens will be penalized and there are costs attached to distributing and collecting the penalty. This costs however are negligible in contrast with the costs of the noncomplying citizens.

Monitored 1 56 1000 0

Monitored 1 56 0 -56,000

By comparing the situation with different monitoring probability, it is shown that an increase of the monitoring probability leads to more evidence of noncompli-ance which results in a higher distortion in a punishment regime making a reward regime superior.

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5 Conclusion

The purpose of this study was to establish design patterns for reward and punish-ment which have an effect on the determination of the most efficient reinforcepunish-ment regime in a specific situation. These specific situations were provided by Boer (2014) and De Geest and Dari-Mattiaci (2013) in which the impact of a punish-ment and reward regime are examined in terms of the probability of evidence and costs. The design patterns are created in a Petri Net model in which legal rules and jural relations represent the rules. Each situation has characteristic circumstances which are expressed in the Petri Net to conduct a stochastic simulation that ade-quately covers the identified evaluation cases by varying the probabilities assigned to the transitions. Each situation was simulated by modifying the Petri Net model according to the specific conditions, which led to the representation of each case and the establishment of design patterns for reward and punishment.

The obtained results appear to be according the known outcome of the cases provided in the literature. Overall, the importance of the production of evidence is shown from the results. Without evidence, compliance and violation cannot be monitored and no regime can be enforced. According to the results of the first two examples provided by Boer (2014) in which two distinct situations are con-sidered involving the granting of a contract extension, bonus or promotion to all employees unless there is evidence of bad performance and not extending a resi-dence permit when there is eviresi-dence of criminal behaviour, a punishment regime is favorable. In these examples, the transaction costs under a reward regime are high because rewards have to distributed. This is however unfavorable, because non-monitored noncompliers get rewarded which motivates people to violate the rules. Good behaviour should be the norm and therefore disobedience will most likely, depending on the monitoring probability, result in a punishment. By using a punishment regime, good behaviour is stimulated by extending a bonus or resi-dence permit and by showing bad behaviour a citizen receives nothing. The results of the other two examples show that the provision of tax exemptions and formal sales agreements is based on a reward regime. In both regime, no processing costs are involved. However, the costs per citizen are relatively lower in a reward regime which makes this regime more favorable to motivate citizens to behave in certain ways.

The results obtained from the first case with a homogeneous society with a fully informed lawmaker show that a punishment regime is more suitable, because the costs related to a reward regime are significantly higher that the costs related to a punishment regime. In this case, the threat of punishment leads to total compli-ance. Therefore, the transaction costs under a punishment regime only consist of monitoring costs which are the same for both regimes and no processing costs are

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involved, while under a reward regime rewards have to distributed. Furthermore, increasing the monitoring probability results in higher transaction costs under a reward regime. From the case in which citizens have different effort costs, the singling out problem, it can be concluded that a reward regime is preferred above a punishment regime. Comparing the obtained result, a punishment regime cre-ates higher distributional distortion costs because citizens generally do not receive a compensation for their effort. This distortion, especially under a punishment regime, is augmented when a higher monitoring probability is used. This advo-cates for the use of a reward regime. In the case of the specification problem, the lawmaker is not aware from which citizen a higher effort is required. This makes it difficult to monitor violation, because some citizens might not be under the cir-cumstances to comply which makes the use of a punishment regime inferior. The results also show that a punishment regime creates a high distributional distortion while a reward regime creates no distortion.

In conclusion, it is possible to express enforcement design patterns by a Petri Net model and by varying the probabilities in the transitions this model can be used to simulate specific situations and the most efficient enforcement regime for that particular situation can be determined. For each situation all specific factors and correlating probabilities were known before conducting the stochastic simulation which enabled the acquisition of the expected results. However, in other situations the specific circumstances may not be known beforehand. This lack of information will result in the requirement of more simulations to generate a plausible outcome. Even then, it is not certain that the obtained outcome is the most efficient regime for that situation. Thus, the use of the Petri Net model to determine the most ef-ficient regime for a specific case is only recommended when all conditions of a situation are available. In a future research, the possibility of creating a system which is able to decide which regime is best to apply in any given situation could be investigated. In the present study, the application of enforcement regimes are compared in terms of costs and probability of evidence. However, when more components of the enforcement process are considered the model may be able to determine the most efficient regime for more situations. In order to analyze the results and finding possible correlations between available evidence in a given sit-uation and the enforcement process, machine learning could be used. When after simulating a great deal of situations with specific conditions a strong correlation between certain factors is found, it may be possible to get a proper result based on less available evidence which will make the enforcement process more efficient and less time consuming.

A different important aspect of reinforcement, although not discussed in this paper, is the ethical issue. The choice for an enforcement regime will have victim-ization as a inevitable consequence, unless the society is completely homogeneous.

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In a reward regime, there will be victimized complying citizens who do not receive a reward while others do and in a punishment regime, some might get punished for noncomplying while others do not. A future research could investigate to include the minimization of injustice and victimization in the framework for determining the most efficient enforcement regime.

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De Geest, G., & Dari-Mattiacci, G. (2009). Carrots versus sticks. Amsterdam Center for Law Economics Working Paper No. 2009-13.

De Geest, G., & Dari-Mattiacci, G. (2013). The rise of carrots and the decline of sticks. The University of Chicago Law Review, 80(1), 341–393.

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Hohfeld, W. N. (1913). Some fundamental legal conceptions as applied in judicial reasoning. The Yale Law Journal, 23(1), 16–59.

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processes via petri nets. Retrieved 2017-05-22, from

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Figure 6: Enforcement model (Boer, 2014)

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Figure

7:

Updated

enforcement

Design patterns of reward and punishment