Maximization Of Expected Value Research Articles

Maximizing the Success Probability of Policy Allocations in Online Systems

The effectiveness of advertising in e-commerce largely depends on the ability of merchants to bid on and win impressions for their targeted users. The bidding procedure is highly complex due to various factors such as market competition, user behavior, and the diverse objectives of advertisers. In this paper we consider the problem at the level of user timelines instead of individual bid requests, manipulating full policies (i.e. pre-defined bidding strategies) and not bid values. In order to optimally allocate policies to users, typical multiple treatments allocation methods solve knapsack-like problems which aim at maximizing an expected value under constraints. In the specific context of online advertising, we argue that optimizing for the probability of success is a more suited objective than expected value maximization, and we introduce the SuccessProbaMax algorithm that aims at finding the policy allocation which is the most likely to outperform a fixed reference policy. Finally, we conduct comprehensive experiments both on synthetic and real-world data to evaluate its performance. The results demonstrate that our proposed algorithm outperforms conventional expected-value maximization algorithms in terms of success rate.

Rationally irrational: When people do not correct their reasoning errors even if they could.

Why is it that sometimes people do not correct their reasoning errors? The dominating dual-process theories of reasoning detail how people (fail to) detect their reasoning errors but underspecify how people decide to correct these errors once they are detected. We have unpacked the motivational aspects of the correction process here, leveraging the research on cognitive control. Specifically, we argue that when people detect an error, they decide whether or not to correct it based on the overall expected value associated with the correction-combining perceived efficacy and the reward associated with the correction while considering the cost of effort. Using a modified two-response paradigm, participants solved cognitive reflection problems twice while we manipulated the factors defining the expected value associated with correction at the second stage. In five experiments (N = 5,908), we found that answer feedback and reward increased the probability of correction while cost decreased it, relative to the control groups. These cognitive control critical factors affected the decisions to correct reasoning errors (Experiments 2 and 3) and the corrective reasoning itself (Experiments 1, 4 and 5) across a range of problems, feedbacks, types of errors (reflective or intuitive), and cost and reward manipulations pre-tested and checked in five separate studies (N = 951). Thus, some people did not correct their epistemically irrational reasoning errors because they followed the instrumentally rational principle of the expected value maximization: They were rationally irrational. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

MEM-EX: An exemplar memory model of decisions from experience

Many real-world decisions must be made on basis of experienced outcomes. However, there is little consensus about the mechanisms by which people make these decisions from experience (DfE). Across five experiments, we identified several factors influencing DfE. We also introduce a novel computational modeling framework, the memory for exemplars model (MEM-EX), which posits that decision makers rely on memory for previously experienced outcomes to make choices. Using MEM-EX, we demonstrate how cognitive mechanisms provide intuitive and parsimonious explanations for the effects of value-ignorance, salience, outcome order, and sample size. We also conduct a cross-validation analysis of several models within the MEM-EX framework. We compare these to three alternative models; two baseline models built on the principle of expected value maximization, and another employing a suite of choice methods previously shown to perform well in prediction tournaments. We find that MEM-EX consistently outperforms these competitors, demonstrating its value as a tool for making quantitative predictions without overfitting. We discuss the implications of these findings for our understanding of the interplay between attention, memory, and experience-based choice.

Toward an attentional turn in research on risky choice.

For a long time, the dominant approach to studying decision making under risk has been to use psychoeconomic functions to account for how behavior deviates from the normative prescriptions of expected value maximization. While this neo-Bernoullian tradition has advanced the field in various ways—such as identifying seminal phenomena of risky choice (e.g., Allais paradox, fourfold pattern)—it contains a major shortcoming: Psychoeconomic curves are mute with regard to the cognitive mechanisms underlying risky choice. This neglect of the mechanisms both limits the explanatory value of neo-Bernoullian models and fails to provide guidance for designing effective interventions to improve decision making. Here we showcase a recent “attentional turn” in research on risk choice that elaborates how deviations from normative prescriptions can result from imbalances in attention allocation (rather than distortions in the representation or processing of probability and outcome information) and that thus promises to overcome the challenges of the neo-Bernoullian tradition. We argue that a comprehensive understanding of preference formation in risky choice must provide an account on a mechanistic level, and we delineate directions in which existing theories that rely on attentional processes may be extended to achieve this objective.

Was Sarbanes–Oxley Costly? Evidence from Optimal Contracting on CEO Compensation

ABSTRACTThis paper investigates the effects of regulatory interventions on contracting relationships within firms by examining the impacts of the Sarbanes–Oxley (SOX) Act on CEO compensation. Using panel data of the S&P 1500 firms, it quantifies welfare gains from a principal–agent model with hidden information and hidden actions. It finds that SOX: (1) reduced the conflict of interest between shareholders and their CEOs, mainly by reducing shareholder loss from CEOs deviating from their goal of expected value maximization; (2) increased the cost of agency, or the risk premium CEOs are paid to align their interests with those of shareholders; (3) increased administrative costs in the primary sector (which includes utilities and energy) but the effect in the other two broadly defined sectors, services and consumer goods, was more nuanced; and (4) had no effect on the attitude of CEOs toward risk.

Detectability, duality, and surplus extraction

We study surplus extraction in the general environment of McAfee and Reny (1992), and provide two alternative proofs of their main theorem. The first is an analogue of the classic argument of Crémer and McLean (1985, 1988), using geometric features of the set of agents' beliefs to construct a menu of contracts extracting the desired surplus. This argument, which requires a finite state space, also leads to a counterexample showing that full extraction is not possible without further significant conditions on agents' beliefs or surplus, even if the designer offers an infinite menu of contracts. The second argument uses duality and applies with an infinite state space, thus yielding the general result of McAfee and Reny (1992). Both arguments suggest methods for studying surplus extraction in settings beyond the standard model, in which the designer or agents might have objectives other than risk neutral expected value maximization.

A Qualified Defence of Expected Value Maximization

A Qualified Defence of Expected Value Maximization

Revisiting the Open Sampling format: Improving risky choices through a novel graphical representation

When making risky choices, people often fall short of the norm of expected value (EV) maximization. Previous research has shown that presenting options in the Open Sampling (OSa) format, a 10-by-10 matrix of randomly arranged outcomes, can improve choices and reduce decision times. First, the current research aims to replicate and extend the findings on the OSa format. To this end, we compare OSa to the common description-based format as well as further graphical representations, and investigate the resulting accordance with EV maximization and decision time. Second, we study whether people lower (vs. higher) in numeracy, the ability to use probabilistic and mathematical concepts, particularly benefit from a graphical representation of options. We conducted five high-powered studies (total N = 1,575) in which participants chose repeatedly between two risky gambles, using different populations and gamble-problem sets. Overall, we could not find a benefit of the OSa format in terms of EV accordance in any of the five studies. However, three studies also tested a novel variant of the OSa format with grouped outcomes and found that it consistently improved EV accordance compared with all other formats. All graphical formats led to faster decisions without harming decision quality. The effects of presentation format were not moderated by numeracy in three of the four studies that assessed numeracy. In conclusion, our research introduces a new presentation format which consistently improves risky choices and can also be used to communicate risks in applied contexts such as medical decision making.

On the Value of Alert Systems and Gentle Rule Enforcement in Addressing Pandemics.

The COVID-19 pandemic poses a major challenge to policy makers on how to encourage compliance to social distancing and personal protection rules. This paper compares the effectiveness of two policies that aim to increase the frequency of responsible health behavior using smartphone-tracking applications. The first involves enhanced alert capabilities, which remove social externalities and protect the users from others’ reckless behavior. The second adds a rule enforcement mechanism that reduces the users’ benefit from reckless behavior. Both strategies should be effective if agents are expected-value maximizers, risk averse, and behave in accordance with cumulative prospect theory (Tversky and Kahneman, 1992) or in accordance with the Cognitive Hierarchy model (Camerer et al., 2004). A multi-player trust-game experiment was designed to compare the effectiveness of the two policies. The results reveal a substantial advantage to the enforcement application, even one with occasional misses. The enhanced-alert strategy was completely ineffective. The findings align with the small samples hypothesis, suggesting that decision makers tend to select the options that lead to the best payoff in a small sample of similar past experiences. In the current context, the tendency to rely on a small sample appears to be more consequential than other deviations from rational choice.

Choice bracketing and experience‐based choice

AbstractWe examine how choice bracketing affects expected value maximization in experience‐based choice. Experience‐based choices are a series of individual choices made sequentially, for which feedback follows each choice, and are thus naturally bracketed narrowly. Previous research broadly bracketed multiple experience‐based choices for decision makers by aggregating the choices (such that each choice pertained to multiple individual choices) or by reducing feedback frequency. We find that decision makers prompted to actively broad‐bracket experience‐based choices in the presence of immediate feedback on individual choices (which prompts narrow bracketing) are more likely to choose expected value maximizing options than decision makers prompted to narrow‐bracket these choices. This pattern replicated across four studies, using different manipulations of choice bracketing, forms of feedback (partial or full), payoffs (hypothetical or incentive‐compatible payoff), subject populations, and when the choices and outcome distribution involved prices or time. We discuss the theoretical and practical implications of our findings.

The formation of preference in risky choice.

A key question in decision-making is how people integrate amounts and probabilities to form preferences between risky alternatives. Here we rely on the general principle of integration-to-boundary to develop several biologically plausible process models of risky-choice, which account for both choices and response-times. These models allowed us to contrast two influential competing theories: i) within-alternative evaluations, based on multiplicative interaction between amounts and probabilities, ii) within-attribute comparisons across alternatives. To constrain the preference formation process, we monitored eye-fixations during decisions between pairs of simple lotteries, designed to systematically span the decision-space. The behavioral results indicate that the participants' eye-scanning patterns were associated with risk-preferences and expected-value maximization. Crucially, model comparisons showed that within-alternative process models decisively outperformed within-attribute ones, in accounting for choices and response-times. These findings elucidate the psychological processes underlying preference formation when making risky-choices, and suggest that compensatory, within-alternative integration is an adaptive mechanism employed in human decision-making.

Do people exploit risk\u2013reward structures to simplify information processing in risky choice?

The high rewards people desire are often unlikely. Here, we investigated whether decision-makers exploit such ecological correlations between risks and rewards to simplify their information processing. In a learning phase, participants were exposed to options in which risks and rewards were negatively correlated, positively correlated, or uncorrelated. In a subsequent risky choice task, where the emphasis was on making either a ‘fast’ or the ‘best’ possible choice, participants’ eye movements were tracked. The changes in the number, distribution, and direction of eye fixations in ‘fast’ trials did not differ between the risk–reward conditions. In ‘best’ trials, however, participants in the negatively correlated condition lowered their evidence threshold, responded faster, and deviated from expected value maximization more than in the other risk–reward conditions. The results underscore how conclusions about people’s cognitive processing in risky choice can depend on risk–reward structures, an often neglected environmental property.

Risk taking on behalf of others: The role of social distance

Individuals take decisions on behalf of others in many different contexts. In this paper, we focus on lotteries with negative expected value and study if (and how) risky choices made on behalf of another person differ i) compared to decisions which do not affect anyone else, and ii) depending on the social distance between who makes the decision and who is affected by it. Our results show that social distance (i.e., whether the person affected by one’s decision is an unknown stranger or a friend) is an important determinant when people decide on behalf of others. Moreover, when deciding on behalf of a friend rather than only for themselves or a stranger, average individual behavior is closer to expected value maximization, exhibiting less risk taking. These findings suggest that responsibility for others’ outcome and the empathy gap affect the decision making process, particularly when the social distance is shortened. The results are robust to different feedback frequencies. Controlling for order effects shows that experiencing a decrease in social distance is crucial in activating this mechanism.

Noisy preferences in risky choice: A cautionary note.

We examine the effects of multiple sources of noise in risky decision making. Noise in the parameters that characterize an individual’s preferences can combine with noise in the response process to distort observed choice proportions. Thus, underlying preferences that conform to expected value maximization can appear to show systematic risk aversion or risk seeking. Similarly, core preferences that are consistent with expected utility theory, when perturbed by such noise, can appear to display nonlinear probability weighting. For this reason, modal choices cannot be used simplistically to infer underlying preferences. Quantitative model fits that do not allow for both sorts of noise can lead to wrong conclusions.

Neural Mechanisms Underlying Compensatory and Noncompensatory Strategies in Risky Choice

Individuals may differ systematically in their applied decision strategies, which has critical implications for decision neuroscience but is yet scarcely studied. Our study's main focus was therefore to investigate the neural mechanisms underlying compensatory versus noncompensatory strategies in risky choice. Here, we compared people using a compensatory expected value maximization with people using a simplified noncompensatory loss-minimizing choice strategy. To this end, we used a two-choice paradigm including a set of "simple" items (e.g., simple condition), in which one option was superior on all attributes, and a set of "conflict" items, in which one option was superior on one attribute but inferior on other attributes. A binomial mixture analysis of the decisions elicited by these items differentiated between decision-makers using either a compensatory or a noncompensatory strategy. Behavioral differences were particularly pronounced in the conflict condition, and these were paralleled by neural results. That is, we expected compensatory decision-makers to use an integrated value comparison during choice in the conflict condition. Accordingly, the compensatory group tracked the difference in expected value between choice options reflected in neural activation in the parietal cortex. Furthermore, we expected noncompensatory, compared with compensatory, decision-makers to experience increased conflict when attributes provided conflicting information. Accordingly, the noncompensatory group showed greater dorsomedial PFC activation only in the conflict condition. These pronounced behavioral and neural differences indicate the need for decision neuroscience to account for individual differences in risky choice strategies and to broaden its scope to noncompensatory risky choice strategies.

Why contextual preference reversals maximize expected value.

Contextual preference reversals occur when a preference for one option over another is reversed by the addition of further options. It has been argued that the occurrence of preference reversals in human behavior shows that people violate the axioms of rational choice and that people are not, therefore, expected value maximizers. In contrast, we demonstrate that if a person is only able to make noisy calculations of expected value and noisy observations of the ordinal relations among option features, then the expected value maximizing choice is influenced by the addition of new options and does give rise to apparent preference reversals. We explore the implications of expected value maximizing choice, conditioned on noisy observations, for a range of contextual preference reversal types—including attraction, compromise, similarity, and phantom effects. These preference reversal types have played a key role in the development of models of human choice. We conclude that experiments demonstrating contextual preference reversals are not evidence for irrationality. They are, however, a consequence of expected value maximization given noisy observations.

How short- and long-run aspirations impact search and choice in decisions from experience

To what extent do people adapt their information search policies and subsequent decisions to the long- and short-run consequences of choice environments? To address this question, we investigated exploration and exploitation policies in choice environments that involved single or multiple plays. We further compared behavior in these environments with behavior in the standard sampling paradigm. Frequently used in research on decision from experience, this paradigm does not explicitly implement the choice in terms of the short or long run. Results showed that people searched more in the multi-play environment than in the single-play environment. Moreover, the substantial search effort in the multi-play environment was conducive to choices consistent with expected value maximization, whereas the lesser search effort in the single-play environment was compatible with the goal of maximizing the chance of winning something. Furthermore, choice and search behaviors in the sampling paradigm predominantly echoed those observed in the single-play environment. This suggests that, when not instructed otherwise, participants in the sampling paradigm appear to favor search and choice strategies that embody short-run aspirations. Finally, the present findings challenge the revealed preference approach in decisions from experience, while also suggesting that information search may be an important and potentially even better signal of preference or aspirations than choice.

The Microeconomics of Choice under Risk and Uncertainty: Where Are We?

Financial decision-making is not straightforward, in part, because such decisions generally involve comparing financial assets the payoffs from which are subject to risk and uncertainty. Given that situation, two questions naturally arise: How do economic agents go about the business of making choices in the face of risk and uncertainty? And, how should economic agents make choices in the face of risk and uncertainty? This paper concentrates on the first of these questions and discusses some of the main attempts made by economic theory to understand how economic agents go about the business decision-making under conditions of risk and uncertainty. Theoretical possibilities considered in the context of decisions under conditions of risk include: Expected value maximization, Expected utility maximization, Rank dependent utility maximization, Prospect theory, and the Topology of fear approach to decision-making in the face of catastrophic risk. This paper also considers empirical tests of these theoretical possibilities and some of the anomalies and responses thrown up by those tests such as: Allais Paradox, Discovered Preference Hypothesis, and the choice behaviour of CEOs when faced with risk. The paper concludes with a brief excursion into choice under uncertainty where, unlike in risky choice situation, the existence of objective probabilities over states of the world cannot be relied on. In that context, the author briefly canvases the Subjective Expected Utility approach — which is unable in general to account for ambiguity aversion — Choquet utility, Wald's Multiple Priors, and the Case Based approach This paper highlights the fact that the rich and fascinating field of decision-making under risk and uncertainty is characterized by a constant interplay between theoretical conjecture, empirical testing, and theoretical refinement. Such interplay is mirrored by this paper and contributions in the Colloquium Section of this Issue, where the thoughts of practitioners and academics interact.

An incentive compatible scoring rule for ordinal judgments of expected utility maximizers

This note introduces a scoring rule for ordinal likelihood judgments based on the linear scoring rule. If the ordinal judgments are strict, the scoring rule is incentive compatible for expected utility maximizers as long utility is increasing in wealth. When allowing for non-strict judgments, the scoring rule is no longer incentive compatible for all expected utility maximizers, but still incentive compatible for expected value maximizers. In both cases the scoring rule fulfills the Relevance Principle and is thus simple to implement experimentally.

The Infectiousness of Nihilism

In “Rejecting Ethical Deflationism,” Jacob Ross argues that a rational decision maker is permitted, for the purposes of practical reasoning, to assume that nihilism is false. I argue that Ross’s argument fails because the principle he relies on conflicts with more plausible principles of rationality and leads to preference cycles. I then show how the infectiousness of nihilism, and of incomparability more generally, poses a serious problem for the larger project of attempting to incorporate moral uncertainty into expected value maximization style reasoning.