DECISION MAKING INVOLVING SEQUENTIAL EVENTS: SOME EFFECTS OF DISAGGREGATED DATA AND DISPOSITIONS TOWARD RISK*

This paper concerns human processing of disaggregated data in a business decision setting involving sequential events. Subjects currently employed in trust banking institutions chose between two mutually exclusive alternatives in a series of decision trials. The outcome for each alternative was the result of a two-stage process; an unsuccessful outcome resulted from failure at either the first or second stage. The probabilities of success at each stage and the overall (joint) probability of success were provided for each alternative. Participants showed strongest preferences for an optimal (expected-value) strategy in processing the data; however, significant preferences for two suboptimal strategies also were observed. Preferences for suboptimal strategies were influenced by the magnitude of differences in the alternatives' joint probabilities of success, by the magnitude of differences in the alternatives' stage probabilities of success, and by subjects' dispositions toward risk.     

Sequential Estimation of Dynamic Discrete Games

This paper studies the estimation of dynamic discrete games of incomplete information. Two main econometric issues appear in the estimation of these models: the indeterminacy problem associated with the existence of multiple equilibria and the computational burden in the solution of the game. We propose a class of pseudo maximum likelihood (PML) estimators that deals with these problems, and we study the asymptotic and finite sample properties of several estimators in this class. We first focus on two‐step PML estimators, which, although they are attractive for their computational simplicity, have some important limitations: they are seriously biased in small samples; they require consistent nonparametric estimators of players' choice probabilities in the first step, which are not always available; and they are asymptotically inefficient. Second, we show that a recursive extension of the two‐step PML, which we call nested pseudo likelihood (NPL), addresses those drawbacks at a relatively small additional computational cost. The NPL estimator is particularly useful in applications where consistent nonparametric estimates of choice probabilities either are not available or are very imprecise, e.g., models with permanent unobserved heterogeneity. Finally, we illustrate these methods in Monte Carlo experiments and in an empirical application to a model of firm entry and exit in oligopoly markets using Chilean data from several retail industries.     

Bias‐Corrected Estimation in Continuous Sampling Plans

Continuous sampling plans (CSPs) are algorithms used for monitoring and maintaining the quality of a production line. Although considerable work has been done on the development of CSPs, to our knowledge, there has been no corresponding effort in developing estimators with good statistical properties for data arising from a CSP inspection process. For example, information about the failure rate of the process will affect the management of the process, both in terms of selecting appropriate CSP parameters to keep the failure rate after inspection at a suitable level, and in terms of policy, for example, whether the process should be completely inspected, or shut down. The motivation for this exercise was developing sampling protocols for Australia's Department of Agriculture and Water Resources for monitoring the biosecurity compliance of incoming goods at international borders. In this study, we show that maximum likelihood estimation of the failure rate under a sampling scheme can be biased depending on when estimation is performed, and we provide explicit expressions for the main contribution of the bias under various CSPs. We then construct bias‐corrected estimators and confidence intervals, and evaluate their performance in a numerical study.     

How Probabilistic Risk Assessment Can Mislead Terrorism Risk Analysts

Traditional probabilistic risk assessment (PRA), of the type originally developed for engineered systems, is still proposed for terrorism risk analysis. We show that such PRA applications are unjustified in general. The capacity of terrorists to seek and use information and to actively research different attack options before deciding what to do raises unique features of terrorism risk assessment that are not adequately addressed by conventional PRA for natural and engineered systems—in part because decisions based on such PRA estimates do not adequately hedge against the different probabilities that attackers may eventually act upon. These probabilities may differ from the defender's (even if the defender's experts are thoroughly trained, well calibrated, unbiased probability assessors) because they may be conditioned on different information. We illustrate the fundamental differences between PRA and terrorism risk analysis, and suggest use of robust decision analysis for risk management when attackers may know more about some attack options than we do.     

Opportunism in Capital Budget Recommendations: The Effects of Past Performance and Its Attributions*

This study uses an experiment to examine the separate and combined effects of managers' loss aversion and their causal attributions about their divisions' performance on tendencies to make goal‐incongruent capital budget recommendations. We find that managers' recommendations are biased by their loss aversion. In particular, managers of high‐performing divisions are more likely than managers of low‐performing divisions to propose investments that maximize their division's short‐term profits at the expense of the firm's long‐term value. We also find that managers' recommendations are biased by their causal attributions. In particular, managers are more likely to propose investments that maximize their division's short‐term profits at the expense of the firm's long‐term value when they attribute their division's performance to external causes (e.g., task difficulty or luck) rather than to internal causes (e.g., managerial ability or effort). Further, the effects of causal attributions are greater for managers of high‐performing divisions than for managers of low‐performing divisions. The study's findings are important because loss aversion and causal attributions are often manifested in firms. Thus, they may bias managers' decisions, which in turn may be detrimental to the firms' long‐term value.     

Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models

This paper proposes a new nested algorithm (NPL) for the estimation of a class of discrete Markov decision models and studies its statistical and computational properties. Our method is based on a representation of the solution of the dynamic programming problem in the space of conditional choice probabilities. When the NPL algorithm is initialized with consistent nonparametric estimates of conditional choice probabilities, successive iterations return a sequence of estimators of the structural parameters which we call K–stage policy iteration estimators. We show that the sequence includes as extreme cases a Hotz–Miller estimator (for K=1) and Rust's nested fixed point estimator (in the limit when K→∞). Furthermore, the asymptotic distribution of all the estimators in the sequence is the same and equal to that of the maximum likelihood estimator. We illustrate the performance of our method with several examples based on Rust's bus replacement model. Monte Carlo experiments reveal a trade–off between finite sample precision and computational cost in the sequence of policy iteration estimators.     

The Quantitative Estimation of IT‐Related Risk Probabilities

How well can people estimate IT‐related risk? Although estimating risk is a fundamental activity in software management and risk is the basis for many decisions, little is known about how well IT‐related risk can be estimated at all. Therefore, we executed a risk estimation experiment with 36 participants. They estimated the probabilities of IT‐related risks and we investigated the effect of the following factors on the quality of the risk estimation: the estimator's age, work experience in computing, (self‐reported) safety awareness and previous experience with this risk, the absolute value of the risk's probability, and the effect of knowing the estimates of the other participants (see: Delphi method). Our main findings are: risk probabilities are difficult to estimate. Younger and inexperienced estimators were not significantly worse than older and more experienced estimators, but the older and more experienced subjects better used the knowledge gained by knowing the other estimators' results. Persons with higher safety awareness tend to overestimate risk probabilities, but can better estimate ordinal ranks of risk probabilities. Previous own experience with a risk leads to an overestimation of its probability (unlike in other fields like medicine or disasters, where experience with a disease leads to more realistic probability estimates and nonexperience to an underestimation).     

The Importance of Social Embeddedness: Churn Models at Mobile Providers

This article argues the importance of social embeddedness at mobile providers by examining the effects of customers’ network topological properties on churn probability—the probability of a customer switching from one telecommunication provider to another. This article uses data from regional snowball sampling—the only practically feasible network sampling method—to identify groups with significantly different churn ratios for customers with different network topological properties. Clear evidence indicates that individual network characteristics (node‐level metrics) have considerable impact on churn probabilities. The inclusion of network‐related measures in the churn model allows a longer‐term projection of churners and improves the predictive power of the model. With no possibility to carry out repeated sampling, sample stability was checked through simulation results. On the one hand, this article highlights the importance and effectiveness of the provider's tailored marketing campaigns by showing that customers targeted by direct marketing campaigns are less threatened by churn than nontargeted customers. On the other, this article shows that social embeddedness blocks the impact of the very same marketing efforts. This article forwards the idea that social embeddedness, also prevalent in vendor switching, can be extended to understanding the development of professional societies threatened by membership churn.     

Setting Tolerable Misstatements When Auditing Aggregated Accounts*

Generally accepted auditing standards require auditors to plan audits of clients' account balances. If accounts are to be sampled, then part of this planning must include setting the tolerable misstatement for each account or class of transactions to be sampled. Although classical sampling approaches provide certain advantages, they have not been widely used because they are viewed as complex and difficult to implement. We present a remedy to these difficulties in an efficient, easily implemented optimal solution method for the problem of setting tolerable misstatements given constraints on tolerable misstatements for individual account balances as well as the overall audit. Further, our method suggests when the materialities of certain accounts or the materiality of the overall audit are irrelevant to the problem. Several example auditing problems demonstrate both our solution approach and the settings in which our approach provides a more effective or more efficient sampling plan than that provided by monetary unit sampling.     

The Effects of Hindsight Bias on Jurors' Evaluations of Auditor Decisions*

Hindsight bias refers to the tendency of individuals with outcome knowledge (hindsight) to alter their perception of an event such that, ex-post, one's assumed ability to predict an event is greater than one's ex-ante ability. Auditors must make decisions without knowledge of an eventual outcome, but auditor liability is determined from a perspective that includes outcome knowledge. A behavioral experiment was conducted with 92 prospective jurors. Jurors were presented with a case in which auditors performed an audit of a client company and subsequently issued the standard, favorable audit report. Outcome knowledge was manipulated as: (1) no outcome (control group), (2) negative outcome (bankruptcy and subsequent lawsuit), and (3) negative outcome with a debiasing strategy. Results indicate that outcome knowledge biased jurors' evaluations of the auditor's judgment. Additional analysis revealed that the results are consistent with a cognitive interpretation of hindsight bias. The debiasing strategy was found to be effective in mitigating hindsight bias.     

An Experimental Study of the Effectiveness of Three Debiasing Techniques*

Subjective probability distributions constitute an important part of the input to decision analysis and other decision aids. The long list of persistent biases associated with human judgments under uncertainy [16] suggests, however, that these biases can be translated into the elicited probabilities which, in turn, may be reflected in the output of the decision aids, potentially leading to biased decisions. This experiment studies the effectiveness of three debiasing techniques in elicitation of subjective probability distributions. It is hypothesized that the Socratic procedure [18] and the devil's advocate approach [6] [7] [31] [32] [33] [34] will increase subjective uncertainty and thus help assessors overcome a persistent bias called “overconfidence.” Mental encoding of the frequency of the observed instances into prespecified intervals, however, is expected to decrease subjective uncertainty and to help assessors better capture, mentally, the location and skewness of the observed distribution. The assessors' ratings of uncertainty confirm these hypotheses related to subjective uncertainty but three other measures based on the dispersion of the elicited subjective probability distributions do not. Possible explanations are discussed. An intriguing explanation is that debiasing may affect what some have called “second order” uncertainty. While uncertainty ratings may include this second component, the measures based on the elicited distributions relate only to “first order” uncertainty.     

随机抽样算法在多项目调度中的应用

针对资源约束下的多项目调度问题,扩展了单项目进度生产机制,并在此基础上设计了多项目调度的随机抽样算法。通过对比分析,说明不同的任务优先规则对随机抽样算法具有不同的影响,其中采用MINSLK等优先规则的随机抽样算法能够有效地缩短项目平均工期。与其他多项目调度启发式算法的比较和统计检验,说明随机抽样算法显著优于这些常用的启发式算法。     

A Mechanism for Eliciting Probabilities

This paper describes a direct revelation mechanism for eliciting agents' subjective probabilities. The game induced by the mechanism has a dominant strategy equilibrium in which the players reveal their subjective probabilities.     

Appointment Scheduling with No‐Shows and Overbooking

We study an overbooking model for scheduling arrivals at a medical facility under no‐show behavior, with patients having different no‐show probabilities and different weights. The scheduler has to assign the patients to time slots in such a way that she minimizes the expected weighted sum of the patients' waiting times and the doctor's idle time and overtime. We first consider the static problem, where the set of patients to be scheduled and their characteristics are known in advance. We partially characterize the optimal schedule and introduce a new sequencing rule that schedules patients according to a single index that is a function of their characteristics. Then we apply our theoretical results and conclusions from numerical experiments to sequential scheduling procedures. We propose a heuristic solution to the sequential scheduling problem, where requests for appointments come in gradually over time and the scheduler has to assign each patient to one of the remaining slots that are available in the schedule for a given day. We find that the no‐show rate and patients' heterogeneity have a significant impact on the optimal schedule and should be taken under consideration.     

Is Allocation Affected by the Perception of Others' Irresponsible Behavior and by Ambiguity?

The article examines how the perception of others' irresponsible behavior and ambiguity regarding probabilities affect allocation among potential beneficiaries. To elicit these views, we conducted a survey where the participants were first asked to make an allocation of a fixed sum of money between a hereditary cancer, where chance plays a central role, and a lifestyle‐related cancer, where individual lifestyle decisions are more important. Our estimation results show that a substantial share of the respondents allocate significantly more to the hereditary cancer. This may indicate that these respondents care about others' irresponsible behavior. Then, we elicited perceptions of cancer hazards in the form of imprecise probabilities and examined the interplay between allocating behavior and risk perceptions. Finally, we investigated the effects of various socioeconomic characteristics, and of awareness of highly publicized cancer cases, on respondents' allocations.     

Strategic Assessment Model (SAM): A Multiple Criteria Decision Support System for Evaluation of Strategic Alternatives*

The evaluation of strategic alternatives is a particularly difficult task. This difficulty is due to the complexities inherent in the evaluation process and the lack of structured information. The evaluation process must consider a multitude of relevant information from both the internal and external environments of the organization. Various analytical and normative models have helped decision makers utilize large volumes of information in strategic evaluation; however, most of these models have some limitations. We present a multiple criteria decision support system, called strategic assessment model (SAM), that addresses some of the limitations inherent in the existing models. SAM captures the decision maker's beliefs through a series of sequential, rational, and analytical processes. The environmental forces—decomposed into internal, task, general opportunities, and threats—are used along with the analytic hierarchy process (AHP), subjective probabilities, the entropy concept, and utility theory to enhance the decision maker's intuition in evaluating a set of strategic alternatives.     

Resource Distribution in Multiple Attacks with Imperfect Detection of the Attack Outcome

This article extends the previous research of consecutive attacks strategy by assuming that an attacker observes the outcome of each attack imperfectly. With given probabilities it may wrongly identify a destroyed target as undestroyed, and wrongly identify an undestroyed target as destroyed. The outcome of each attack is determined by a contest success function that depends on the amount of resources allocated by the defender and the attacker to each attack. The article suggests a probabilistic model of the multiple attacks and analyzes how the target destruction probability and the attacker's relative resource expenditure are impacted by the two probabilities of incorrect observation, the attacker's and defender's resource ratio, the contest intensity, the number of attacks, and the resource distribution across attacks. We analyze how the attacker chooses the number of attacks, the attack stopping rule, and the optimal resource distribution across attacks to maximize its utility.     

Utilitarian Preferences With Multiple Priors

This paper proposes a method for aggregating individual preferences in the context of uncertainty. Individuals are assumed to abide by Savage's model of Subjective Expected Utility, in which everyone has his/her own utility and subjective probability. Disagreement on probabilities among individuals gives rise to uncertainty at the societal level, and thus society may entertain a set of probabilities rather than only one. We assume that social preference admits a Maxmin Expected Utility representation. In this context, two Pareto‐type conditions are shown to be equivalent to social utility being a weighted average of individual utilities and the social set of priors containing only weighted averages of individual priors. Thus, society respects consensus among individuals' beliefs and does not add ambiguity beyond disagreement on beliefs. We also deal with the case in which society does not rule out any individual belief.