Improving Subjective Probability Assessment for Planning and Control in Team-Like Organizations

ing from conflicting goals would seem to be appropriate when, for example, (1) no important conflicts exist or (2) the Central Authority has available to him schemes for dealing with conflicting goals in a manner such that these conflicts do not adversely affect organizational performance. Examples of such schemes are the reward-penalty schemes that are intended to resolve intraorganizational conflicts (see, e.g., Hass [1968], Baumol and Fabian [1964], Stedry [1967], Kriebel and Lave [1969], Ross [1973], and Winston [1964]). But the conflict-resolution schemes usually proposed typically ignore the effects of conflicts on the information provided by a given member of the organization to the Central Authority or to other members. The potential importance of these effects can be seen by noting that if a member has an opportunity to influence the types or contents of messages transmitted to other members (including the Central Authority), then that member can influence the actions of those other members. And that member may attempt to exert his influence so that the decision rules dictated by the Central Authority and the corresponding actions taken by the other members are closer to being personally optimal. This leads to a situation involving "dishonest" or "contaminated" reported information. This is a situation in which the information reported by a subordinate is, by the subordinate's choice, not an accurate reflection of the information 2 A pertinent game-theory treatment of such issues is given in Shubik [1962]. This content downloaded from 207.46.13.114 on Thu, 26 May 2016 06:20:24 UTC All use subject to http://about.jstor.org/terms 254 N. J. GONEDES AND Y. IJIRI possessed by the subordinate. If this occurs, suboptimization for the organization may result. :Presumably, the importance of each member's influence in this regard will depend upon the differences between his knowledge and the knowledge of the intended recipient of his messages, as well as the importance of the message to the intended recipient's actions. Thus, the importance of this influence will be determined by the design of the organization, since (under our assumptions) the design of an organization includes a complete specification of observation-rules, communication-rules, and all other decision-rules. Of course, the design of an organization, which is ultimately determined by the Central Authority, is itself conditional upon information supplied by the organization's members. This emphasizes the point that the problem of "contaminated" information cannot be avoided completely. "Contaminated" or "dishonest" information is not the only potential problem confronting the Central Authority. Since the Central Authority relies upon the members for information, his actions are dependent upon the "expertise" of each member. If a member is not very knowledgeable in the area for which he provides information, then the Central Authority will be relying upon information characterized by substantive deficiencies. And if there are goal conflicts within the organization, the members may have no motivation to increase their "expertise" in order to improve organizational performance. Under conditions of uncertainty, the kinds of information disseminated within an organization pertain to: (1) realizations of random variables and (2) distribution functions of random variables. The second type of information plays a critical role in the design of an organization because design selection is conditional upon distribution functions for the possible states of nature and, conditional upon each state, the consequences (e.g., monetary payoffs) associated with every feasible action. As indicated earlier, we are solely concerned with information pertaining to distribution functions. The problems of "contamination" and "substantive deficiencies" of information on distribution functions could be quite severe because this kind of information is usually in the form of subjectively assessed distribution functions. Thus, unlike the case of information pertaining to realizations, there may be little (if any) empirical evidence with which one may discern any contamination or substantive deficiency, given that a variety of subjective factors influenced the assessed distributions. That is, if there is any contamination or substantive deficiency, the assessed distribution functions reported by a member will be jointly determined by these factors and the member's degrees of belief, all of which are "private" to the member. The preceding remarks suggest that schemes for penalizing contaminated and/or substantively deficient assessments should be viewed as potentially useful ingredients of an overall system for controlling organizational performance. (If the cost of any such scheme exceeded its benefits, then, of This content downloaded from 207.46.13.114 on Thu, 26 May 2016 06:20:24 UTC All use subject to http://about.jstor.org/terms IMPROVING SUBJECTIVE PROBABILITY ASSESSMENT 255 course, it would not be included in. an optimal organizational design.) One of the most frequently proposed approaches for precisely this purpose is the use of scoring rules, which are supposed to encourage "honest'' as well as "improved" probability assessments. Scoring rules will be discussed in the following two sections. We shall also point to some particularly severe limitations of scoring rules, and then propose an alternative scheme for dealing with "contaminated" and "substantively deficient" probability assessments. The discussion in section 3 considers the scoring rule scheme and our alternative scheme only with respect to the problem of contamination. In section 4, we indicate that both of these schemes attack the problem of substantive deficiencies in the same way that they attack contamination. We shall also indicate, however, that the speed with which these problems are alleviated may be quite different for both schemes. Indeed, when the issue of speed is considered, one can easily envisage cases in which it is easier to deal with a completely dishonest and knowledgeable subordinate than with a completely honest and less knowledgeable subordinate. 3. Dealing with Contamination SCORING RULES: DISCUSSION AND ILLUSTRATION3 For simplicity, we shall deal with one subordinate who is supposed to provide to the Central Authority an assessed distribution function for one random variable. Denote the random variable by x and assume that P (X E S) = 1, where S is a set of possible, values of x and P(.) denotes probability. Let Et, i = 1, 2, * n constitute an n-fold partition of S such that U"==1 Ei = S andEi nEj is empty for all i # j. Let p = (p, P2, * * p,,) denote the vector containing the subordinate's honest assessments of P(xt E Ei), i = 1, 2, * *, n. That is, for each i, pi = P(x e En) is the subordinate's honest assessment. Let r = (ri, r2, **, r, ) denote the vector of probabilities that the subordinate plans to report to the Central Authority. In view of the discussion of the preceding section, r = p may not be true. For example, an R & D manager may assess the probability of making a breakthrough with a project to be 0.3. That is, p = (0.3, 0.7), where the first component of p is the assessed probability of a breakthrough and the second component is the probability of no breakthrough. But if he is overly anxious to receive an allocation of funds for the project, the R & D manager may report a probability of breakthrough equal to 0.8. That is, r = (0.8, 0.2). A more elaborate example of this kind of, "dishonest" or "contaminated" reporting will be presented after scoring rules are discussed. A scoring rule is a function of the reported assessment r and the actual realization of x; this function defines the reward, or "score," to be received 3 Additional material on scoring rules may be found in Hendrickson and Buehler [1971]; Savage [1971]; Stael von Holstein [1970a, 1970b]; Winkler [1967b, 1969, 1971]; and Hampton et al. [1973]. This content downloaded from 207.46.13.114 on Thu, 26 May 2016 06:20:24 UTC All use subject to http://about.jstor.org/terms 256 N. J. GONEDES AND Y. IJIRI by the subordinate given his reported assessment, r, and the realization of x. Denoting the scoring rule by Sk (r), k = 1, 2, * , n, the subordinate receives the score Sk(r) if he reports r and if the realization is x E Ek, k1, 2,**, n. The expected score of the subordinate (as of the time of reporting) is: