Adapting Islamic Law Disputes to Fair Division in Microeconomics: An Axiomatic Analysis of Three Problems
Burak Doğan, Sinan ErtemelThis study explores the intersection of microeconomic theory and Islamic jurisprudence. We analyze three legal disputes from Islamic history that can be conceived as fair division problems in microeconomics. The solutions proposed by jurists of that time are scrutinized and compared with answers posited by classical division rules. The effected comparisons highlight the similarities and differences between Islamic and conventional economic resolutions. We use the axiomatic approach to define generalizable rules based on the solutions offered by eminent Islamic jurists Abu Hanifa and Abu Yusuf. Our analysis reveals that Abu Hanifa’s methodology and the concede-and-divide rule are identical. Moreover, Abu Yusuf’s approach mirrors the constrained Ibn Ezra rule. We examine the principles characterizing the concede-and-divide and Ibn Ezra rules and find these doctrines compatible with Islamic tenets. In conclusion, our study connects Islamic law with microeconomic theory through its unique exploration of legal disputes perceived through the lens of fair division problems. Our findings contribute to the scholarly understanding of how established division rules can be adapted to align with Islamic values and how Islamic allocation methods can be illustrated using an axiomatic approach.
İslam Hukuku’ndan Paylaşım Meselelerinin Mikroiktisatın Adil Paylaşım Alanına Uyarlanması: Üç Problemin Aksiyomatik Analizi
Burak Doğan, Sinan ErtemelBu çalışmada İslam tarihinden alınan üç mesele mikroiktisatın işbirlikçi oyun teorisi bağlamında adil paylaşım problemi olarak modellenmektedir. Meselelere dönemin hukukçularının sundukları çözümler ile klasik paylaşım kuralları aksiyomatik karakterizasyon yöntemiyle kıyaslanmıştır. Bu kıyaslamayla beraber adil paylaşım aksiyomlarının İslamiliği incelenmiştir. Aksiyomatik yaklaşımla, ünlü İslam hukukçuları Ebu Hanife’nin ve Ebu Yusuf’un belirli bir mesele için önerdikleri çözümler genelleştirilerek kural haline getirilmiştir. Ebu Hanife’nin Münazaa Yöntemi adını verdiğimiz dağıtım yöntemi ile Talmud’ta bahsi geçen Vazgeçileni-ver-kalanı-böl Kuralı’nın; Ebu Yusuf Kuralı diye adlandırdığımız dağıtım yöntemi ile Sınırlandırılmış İbn Ezra Kuralı’nın aksiyomatik olarak eş oldukları tespit edilmiştir. Sonuç olarak bu makale, ilgili mikroiktisat literatürüne İslam hukuku meselelerini ve dağıtım yöntemlerini tanıtır, literatürde yerleşik kural haline gelmiş kurallar için İslami temeller gösterir, dönemin fakihlerinin sunduğu çözümlerin adilliğini aksiyomlar vasıtasıyla ölçmeye çalışır.
Cooperative game theory in microeconomics examines fair division in the sharing of resources among individuals with conflicting claims to them. The extant literature generally addresses this issue in relation to the total material values of claims vis-à-vis the material value of the relevant resources. A claims problem (or bankruptcy problem) occurs when the resource is relatively scarce; a surplus sharing problem arises when the resource is relatively abundant.
Disputes suited to the context of fair division problems are as old as human history. In fact, the first and subsequently oft-referenced disagreements studied in this context in the extant literature are presented in the Talmud, one of the most central Judaic texts. For example, the contested garment problem in the Talmud concerns two people holding the ends of a garment: one lays claim to the entire apparel while the other claims half the garment. The allocation method is deemed the solution to this problem from the Talmud. This approach was generalized and transfigured into the concede-and-divide rule, according to which the dispute may be resolved by assigning three quarters and one quarter of the garment to the respective claimants. Similarly, the dispute can be resolved by allotting two-thirds and one-third of the garment to the respective claimants by using the proportional rule, which satisfies the concept of distributive justice postulated in Aristotle’s Nicomachean Ethics (V).
The disputes scrutinized in the existing literature include ancient problems compiled from the Talmud as well as more recent disputes modeled as exemplars of fair division problems. Some modern conflicts discussed in the literature include disputes relating to revenue distribution for museum pass programs, allocation of university resources among faculties, distribution of broadcasting revenues obtained from broadcasting sports events, the ventilator distribution problem encountered during the COVID-19 pandemic, and the aircraft landing. The rules applied to such problems examined in the literature, whether ancient or modern are not limited to the concede-and-divide or proportional rules. Extant research defines numerous rules for distribution such as constrained equal awards, constrained equal losses, Piniles’ rule, the Talmud rule, minimum overlap, the Ibn Ezra rule, Rabad’s proposal, the random arrival rule, and the sequential priority rule. Researchers frequently use the methodology of modeling a previously unexamined dispute notwithstanding its relevance in the context of a fair division problem and to utilize the defined rules to resolve the problem. Scholars have also defined established allocation methods and presented them along with certain problems as distribution rules. The axiomatic characterization approach is adopted in such cases to define an allocation method as a distinctive rule. The axiomatic approach adopted in the present study requires a rule to be defined through the features that characterize it. Each rule applied to resolve the problem is unique. Thus, each defined distribution rule proposes a unique solution to the considered problem. Hence, every rule applied to a problem yields a distinct solution to it. Using the axiomatic approach, the motives underlying the distribution rationale can be distinguished to some extent by investigating the properties of the rule if the solution posited for a problem is obtained by applying a specific rule that can be generalized to the problem. For instance, the proportional rule is characterized in the literature by the properties of composition up and self-duality. Therefore, the proportional rule can be said to embody the concepts conveyed by these two attributes. Similarly, the term axiomatic characterization defines a distribution method as a unique rule distinguished by its features. Specifically, the axiomatic characterization of distributions is explained as a more tangible comparison of the understanding of justice of practitioners.
Islamic history is extremely rich in describing cases that can be defined as fair division problems and in defining allocation methods that can be generalized and characterized as distribution rules. More numerous cases are showcased solely in Islamic inheritance law than problems compiled and examined from the Talmud in the existing microeconomics literature. However, the relevant microeconomics literature has not yet referenced these problems or the distribution methods delineated in Islamic law. Similarly, scant studies in the relevant Islamic law literature have systematically compiled or investigated these types of legal disputes. To date, scholars have evaluated disputes and solutions only through sociopolitical and historical perspectives.
This study presents three cases from Al-Sarakhsi’s Mabsut and describes the solutions proposed by the jurists of that time. These conflicts from Islamic history can be modeled as fair division problems and classical division rules are applied to them. The solutions derived by applying classical division rules are compared with the solutions suggested by the eminent jurists of the past to determine the similarities and differences. Subsequently, this study attempts to exemplify the historical solutions as generalizable sharing rules, determining their generalizability according to justifications found in the relevant Islamic law sources. The properties utilized for the characterizations are also scrutinized for compliance with Islamic principles and are adapted in a manner consistent with Islamic values. Thus, legal disputes discussed politically and historically for centuries are examined from an unaddressed perspective and axiomatically evaluated.
The rules frequently employed by studies to resolve current and historical disputes include the concede-and-divide principle known for its solution to the contested garment problem mentioned in the Talmud, the Ibn Ezra rule named after Abraham Ibn Ezra (d.1089/1092-1164/1167), and the Maimonides Rule named after Maimonides (d.1138-1204). Different researchers have characterized these rules using certain sets of properties. The present study employs the axiomatic approach, a methodology adopted in the existing literature, and defines Abu Hanifa’s and Abu Yusuf’s solutions for the given legal disputes as generalizable rules. The application of the classical fair division rules to the disputes yielded the following results. The concede-and-divide rule postulated a solution identical to that of Abu Hanifa and the Ibn Ezra rule proposed the same solution as Abu Yusuf’s method. The existing research has examined the compatibility of the properties that characterize the concede-and-divide rule and the Ibn Ezra rule with Islamic principles and has shown that both doctrines can be characterized using the same sets of properties adapted to the Islamic context. Similarly, Abu Hanifa’s method has been proven equivalent to the concede-and-divide rule in the context of claim problems and Abu Yusuf’s method equals the Ibn Ezra rule in the context of the adapted claim problem.
In conclusion, this study compiled cases that can be examined in the context of fair division problems and the solutions posited for them in related reliable Islamic law sources. Disputes are modeled by adjusting them to relevant contexts, defining the generalizable solutions among them as rules, and characterizing them through their properties. Classical rules of the fair division are adapted and applied to these disputes, and the solutions proposed by them are axiomatically compared against the solutions obtained by this study. The referenced properties are adapted to the Islamic context because of their similarities and the relevant Islamic allocations are characterized.
