آموزش بوسیله کمک: یک مدل عقلانیت محدود مشاوره

Within an organization, a bounded rational principal organizes a promotion contest based on a sequence of tests regarding candidates’ relative performances. We assume the principal to suffer from limited ability to rank the performances, only identifying the best in each test. Furthermore, he satisfies the expected profit from promotion, designing the contest such that expected gains do not decrease with the information generated by additional tests. Then, mentoring is shown to improve the information about candidates’ ability when the principal offers help to the current best candidate provided by a manager promoted after a similar contest.

Mentoring relations involving newcomers and senior managers have never been formally modeled in economic theory even though sociological and management literature has demonstrated their empirical relevance. For example, Collins and Scott, 1978, Ochberg et al., 1986 and Chao, 1997 study various professional environments identifying the extent of relations between mentors and protégés and show that mentored workers experience greater future rewards or career success than non-mentored ones. This paper presents a model that endogenizes the formation of mentor–protégé relations and shows how mentoring can improve the promotion process of workers in organizations. In a pioneering study, Kram (1985) underlines the career enhancing functions of mentoring. These functions are coaching, sponsorship and teaching, all of which conspire to increase skills, signal ability and prepare the protégé for advancement. Accordingly, we interpret mentoring as the set of activities by which a mentor can help workers to increase their productivity. Laband and Lentz (1995) discuss two rational explanations for the use of mentor–protégé relations in organizations. The first is based on the transfer and accumulation of firm specific human capital. The second relates mentoring to job matching theory. To identify the best workers, firms invest time and knowledge of senior managers to cooperate with the promising workers. This cooperation generates information about the quality of job matches and can improve on the matching of workers to jobs. Our contribution clearly belongs to the job-matching interpretation. We consider a principal who organizes a promotion contest that is, a sequence of tests regarding relative performances of candidates. The tests are based on the workers’ performance during the normal course of production. Though the recorded performances are imperfect signals of ability, they help disclose for each candidate the likelihood of being the best. After each test, the beliefs of the principal are then revised according to the result. So, test after test, he learns about the relative ability of all contestants in order to limit the risk of inefficient assignment of workers. The principal here is assumed to be boundedly rational for the following two reasons: 1. The problem of the promotion decision in the contest arises from the imperfect nature of the information conveyed by the recording of workers’ performance. This imperfection does not only stem from the uncertainty about workers’ ability but also from the principal’s inability to cardinally measure or totally rank their performances. Since a promotion contest may include more than two contestants but the principal only identifies the winner, then his ability to rank is obviously bounded. 2. The principal only tries to increase (and not to maximize) the expected profit after the promotion. Under the assumption of positive correlation between the current performance of candidates and their future performance if promoted, looking for a higher expected profit is perfectly equivalent for the principal to increasing (and not to maximizing) his final confidence in the promoted worker, i.e. the leader at the end of the contest (Simon, 1955). It is then natural to wonder if a procedure with repeated identical tests and aggregated records of performance always increases the expected profit. Let us consider the following problem: anticipating a vacancy in the next period, the principal gathers previous information about two candidates, Bob and Bruce, after nine tests, and finally promotes one of them after a last identical 10th. Suppose that Bob has won six times and Bruce three. Then, it is clear that whatever happens during the 10th test, Bob will be promoted with a minimum of six victories against Bruce’s maximum of four. Moreover, it is also obvious that the principal’s confidence — when defined as a victory frequency — regarding Bob as the best worker may have decreased (e.g. from 2/3 to 3/5 if Bruce wins the last test). Hence, the informative content of this last test is weak since the promoted worker remains the same (Bob) while his expected contribution to future profits can be worse. More generally, for any contest involving n candidates, we show that there never exists an identical final test always insuring a higher expected profit (see Theorem 1). It is also natural to wonder if the principal can nevertheless improve on learning about the workers’ ability by changing the design of the last test, that is modifying its informative value. We answer in proving that the principal must bias the final test. In our framework, biasing consists of helping the worker known to have been the best performer in the past, namely the leader. This help corresponds to vertical cooperation with a mentor, i.e. a senior worker already promoted, whose mentoring is such that it can alter the informative value of the test. Within such a biased test, two outcomes are possible. If the mentored worker wins, he remains the leader and the principal’s final confidence is enhanced. Otherwise, if a non-mentored worker wins the biased test, this victory is understood as a stronger signal of his ability because the quality of the contestants’ field is increased. Thus, the principal always becomes more confident about the winner of the final biased test than he was about the previous leader (see Theorem 2 and Theorem 3). The idea of using a bias to improve the quality of information obtained from imperfect signals has been applied to various contexts (see Calvert, 1985, Koh, 1994 and Billot, 1998). Close to our context, Meyer (1991) considers the problem of a promotion contest between two agents. Meyer proposes a cardinal bias for the final test which strictly maximizes the principal’s confidence about the winner. Besides, she argues that a possible way of implementing the bias could be to modify the contents of the leader’s job. This interpretation is intuitive and especially attractive in terms of job design. Nevertheless, her framework does not allow for a change in the tasks devoted to the leader. Formally, the modeling of Meyer’s bias is perfectly cardinal, operating as if the supervisors were giving a positive handicap to the leader of the competition. This is different from our case because we focus on cooperation between workers and show that the bias can be implemented by a vertical cooperation similar to mentoring. Moreover, in Meyer’s model, the principal deviates from standard notions of rationality only in the sense that he has problems gathering the information within the organization. Nevertheless, there is no limitation in his instrumental rationality since he still maximizes the expected output of the promoted worker. In our framework, bounded rationality is instrumental and cognitive since the principal neither maximizes the expected output nor gathers full information. The remainder of the paper is organized as follows. Section 2 deals with the rules of the promotion contest and the principal’s beliefs. Section 3 stresses the need for changing the contest design in proving the irrelevance of any final test identical to the previous ones. Section 4 studies the optimal design of the biased contest, endogenizes mentoring relations and discusses their empirical relevance. Finally, Section 5 summarizes the results and concludes with possible extensions of the discrete choice framework within organization theory.

The model we propose in this paper is, to our knowledge, the first theoretic approach formally establishing that mentor–protégé relations can be beneficial to the organization. Two remarks can be made in relation to connected literature as follows: 1. The main result, as an extension of the Meyer’s idea, allows us to interpret the learning behavior of the principal in the context of the job design literature. Earlier literature studying the optimal choice of the job contents as a part of the motivation system show that cooperation and coordination between workers of the same hierarchical rank can complement incentive compensation policies (see Holmstrom and Milgrom, 1991 and Valsecchi, 1996). Analogous to this ‘incentive’ argument for cooperation, our contribution establishes the importance of work organization for the selection. 2. Mentoring as an integral part of a selection process according to our model, serves also as a means of creating long term employment relations between the workers and their firm in line with human capital theory. The implementation of a vertical cooperation, as learning by doing, naturally increases the productive knowledge of the worker. Moreover, after the promotion, a worker is regarded as a specific asset for the organization since promoted workers’ reputation can be used to optimally bias future promotion contests. Such a specific human capital reinforces the link between senior workers and the organization. In some sense, expected gains from efficient screening with mentoring are similar to those generated by use of Old Boys Networks to proceed to external hiring (see Simon and Warner, 1992). From a methodological viewpoint, a new feature of our contribution is the modeling of the selection problem in a discrete choice style. For further research, this family of probabilistic models seems to be useful for describing imperfect decision making within the context of organization theory. A natural extension of this paper is to model the promotion process when supervisors record the results of repeated quota-like tests in order to analyze the properties and relative advantage of the two systems of selection: the tournaments and quotas (see Lazear and Rosen (1981) for tournaments and Drago and Turnbull (1991) for quotas). An appropriate tool for that purpose could be the Tversky’s selection model of discrete alternatives (Tversky, 1972), based on binary experiments about specific attributes.