DESIGNING HEAVEN'S WILL: THE JOB ASSIGNMENT IN THE CHINESE IMPERIAL CIVIL SERVICE INACIO´ BO´ AND LI CHEN Abstract. We provide an original analysis of historical documents to describe the as- signment procedures used to allocate entry-level civil service jobs in China from the tenth to the early twentieth century. The procedures tried to take different objectives into account through trial and error. By constructing a formal model that combines these procedures into a common framework, we compare their effectiveness in minimizing un- filled jobs and prioritizing high-level posts. We show that the problem was inherently complex such that changes made to improve the outcome could have the opposite effect. Based on a small modification of the last procedure used, we provide a new mechanism for producing maximum matchings under constraints in a transparent and public way. Keywords: Civil service assignment; Matching; Market design; History of civil service JEL: D73; J45; C78; D47; N15 arXiv:2105.02457v2 [econ.TH] 6 Sep 2021 B´o: China Center for Behavioral Economics and Finance, Southwestern University of Finance and Economics, Chengdu, China; email: [email protected]. Chen: Department of Economics, University of Gothenburg, Gothenburg, Sweden; email: [email protected]. Date: August, 2021. We thank Andrea Br´eard,Rustamdjan Hakimov, Philipp Heller, Yuan Ju, Dongwoo Lee, Herv´eMoulin, Luigi Pascali, Marek Pycia, Nadja Stroh-Maraun, and Utku Unver¨ for helpful comments. Special thanks to Rui Magone for assistance in our historical research of the Chinese civil service system. Financial support from the Anniversary Foundation of the School of Business, Economics and Law, University of Gothenburg, is gratefully acknowledged. 1 DESIGNING HEAVEN'S WILL 2 1. Introduction Bureaucrats are a core component of state capacity, as they are responsible for raising taxes, implementing policies, and delivering public services (Besley and Persson, 2009; Rauch and Evans, 2000). Studying the institutional rules that govern the appointments of these bureaucrats is therefore crucial to gain insights for understanding the functioning of the administration, as well as the impacts on the society's political and economic life. The civil service assignment in Imperial China provides a rich opportunity for this purpose. In particular, the assignment rules have evolved over time, in response to various challenges arising from the complexity in personnel as a result of its objectives and constraints. In this paper, we draw on historical documents and studies to present the first formal description for one of the earliest and longest-used assignment schemes that systematically assigned candidates to government jobs from the mid-tenth century to the early twentieth century in China. After describing in details various changes made to the assignment pro- cedure since its first introduction, we provide a unified theoretical framework for analyzing these procedures, which helps to understand the trade-offs behind each change. An important step in the evolution of the Chinese civil service was the introduction of a meritocratic selection system in the late sixth century that made it possible to select competent candidates from the general population to work for the state on various tasks at national, provincial, and prefectural levels. While the exam-based selection determined who would be qualified for the government jobs, the decisions regarding which jobs were taken by which candidates were not institutionalized until the mid-tenth century. Follow- ing the establishment of a professional career system around this period, recruitment via examinations expanded significantly, thus encouraging the use of more systematic rules to allocate newly recruited candidates to government jobs. There were a few challenges in finding the right candidates for jobs, that are not uncommon to today's world. First, given that there were candidates who obtained different levels of degrees, and jobs with different levels of importance, how to assign them systematically while ensuring the func- tioning of the bureaucracy? Second, appointing candidates to jobs in their home regions requires a careful balance between the benefit from the local knowledge and the threat of local capture. Last but not least, how to prevent the appointments from falling prey to corruption and influence-peddling? Our historical investigation identifies three criteria that were taken into consideration by the assignment procedures of the Chinese civil service in addressing the challenges mentioned above. First, the eligibility criterion, which defines for qualified candidates, depending on their competence measured by degrees, the types of government jobs they could be assigned to. Second, rule of avoidance, which prohibits candidates from being assigned to jobs located in their home regions. Finally, randomness, which was desirable DESIGNING HEAVEN'S WILL 3 when producing the matches, as it limits the impact of personal influences and balances the demands of different political groups. These three criteria were desirable properties|also resilient over time|when making the appointments, yet there were complicated questions regarding how to best implement them, as illustrated in the following quote from the court discussions between Emperor Chongzhen and his ministers in 1628. Curiously then, this important decision was thought to be best left to Heaven's Will|the drawing of lots. \Finding the right men for the grand secretariat benefits greatly the empire. I do not dare to make the decision myself, therefore, I ask for Heaven's will." | Sun(1777) 1 The first formal assignment procedure emerged around the mid-tenth century during the Song1 dynasty (960{1279).2 The Song1 procedure allowed candidates to express their preferred jobs and they were assigned one by one in public following an order determined by their degrees and exam results. This feature of sequential assignment was kept in all subsequent procedures|as it provided transparency, while several major changes were developed. The first change occurred around the late fourteenth century, in the wake of the tran- sition to the new Ming2 Dynasty. In the previous Song1 procedure, the preferences of candidates could result in a situation where a higher-degree candidate|eligible to both lower-level and higher-level jobs|was assigned to a lower-level job, while a higher-level job was left unassigned with a lower-degree candidate|eligible only to the lower-level job. In an effort to assign more candidates to jobs matching their competence, preferences were no longer taken into account. Instead, a job was decided for each of them after assessing the fit between the candidate and the job. We refer to this procedure as the First Ming2 procedure. The second change took place in the late sixteenth century, with the intention of reducing personal interference and balancing factional politics. The assignments were, for the first time, determined by drawing matches randomly from tubes. We refer to this procedure as the Second Ming2 procedure. While installing impartiality in the assignment process, the Second Ming2 procedure was criticized for, among other aspects, its failure in finding candidates with the right competence to jobs, a situation similar to what occurred under the Song1 procedure. Nevertheless, lots-drawing survived dynastic changes and became the norm in the fol- lowing centuries. Indeed, the focus of debates at that time shifted from whether lots- drawing should be used to how its performance could be improved. Amid this climate, 1Grand secretaries were cabinet members of the central administration. Lots-drawing was used mainly for assigning entry-level jobs which we will describe in more details later. It was however occasionally used for middle or high rank jobs. 2To assist readers when following the chronological order of the Chinese dynasties involved in our paper, we add a superscript of a number next to the dynasty to indicate the order: Song1 precedes Ming2 , which again precedes Qing3 . DESIGNING HEAVEN'S WILL 4 and soon after another dynastic transition, a partitioned lots-drawing system was intro- duced around the mid-seventeenth century|the third change, and once again with the objective of assigning more candidates to jobs matching their competence. In this proce- dure, which we refer to as the First Qing3 procedure, the assignment was partitioned into multiple smaller assignments, where each of them contained one type of job and a list of candidates who were eligible to them. This could prevent some of the mismatches of skills present in the previous procedure. The final change|which occurred in the early nine- teenth century|responded to a different concern that was known but not handled until then. The procedures used up until then could produce assignments that leave candidates and jobs unmatched, while alternative assignments could match more candidates to jobs. The change involved first matching candidates who had regions to avoid among the jobs present in the procedure. We refer to the last procedure as the Second Qing3 procedure. To understand the trade-offs behind these changes, we introduce a formal model that captures the key elements of different assignment procedures used in history. Two mea- sures are our focus when evaluating these procedures, minimizing the number of un- filled jobs, and prioritizing high-levels|favoring the match of high-level candidates, as measured by their degrees, to high-level jobs. These two objectives were mentioned in