Mathematical Social Sciences 109 (2021) 28–44 Contents lists available at ScienceDirect Mathematical Social Sciences journal homepage: www.elsevier.com/locate/mss Obfuscation maximization-based decision-making: Theory, methodology and first empirical evidence ∗ Caspar Chorus a, ,1, Sander van Cranenburgh a, Aemiro Melkamu Daniel a, Erlend Dancke Sandorf b, Anae Sobhani c, Teodóra Szép a a Department of Engineering Systems and Services, Delft University of Technology, Jaffalaan 5, 2628BX, Delft, The Netherlands b Economics Division Stirling Management School University of Stirling, Stirling, UK c Department of Human Geography and Spatial Planning in Utrecht University, Utrecht, The Netherlands article info a b s t r a c t Article history: Theories of decision-making are routinely based on the notion that decision-makers choose alternatives Received 8 January 2020 which align with their underlying preferences—and hence that their preferences can be inferred Received in revised form 18 August 2020 from their choices. In some situations, however, a decision-maker may wish to hide his or her Accepted 6 October 2020 preferences from an onlooker. This paper argues that such obfuscation-based choice behavior is likely Available online 21 October 2020 to be relevant in various situations, such as political decision-making. This paper puts forward a Keywords: simple and tractable discrete choice model of obfuscation-based choice behavior, by combining the Obfuscation well-known concepts of Bayesian inference and information entropy. After deriving the model and Signaling illustrating some key properties, the paper presents the results of an obfuscation game that was Choice behavior designed to explore whether decision-makers, when properly incentivized, would be able to obfuscate Preferences effectively, and which heuristics they employ to do so. Together, the analyses presented in this Hiding paper provide stepping stones towards a more profound understanding of obfuscation-based decision- making. ' 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). 1. Introduction in his3 choices. It may even be said, that the notion that choices are signals of underlying preferences – as formalized in the re- Models of rational decision-making are routinely based on the vealed preference axioms – lies at the heart of most empirical notion that agents base their choices on their latent, underly- work in decision-making; it is this assumption, which allows ing preferences—and/or their goals, motivations, desires, needs2; analysts to estimate preferences based on choice observations see prominent examples from the fields of social psychology (e.g. McFadden, 1974, 2001; Small and Rosen, 1981; Ben-Akiva (Ajzen and Fishbein, 1977; Ajzen, 1991), behavioral decision the- et al., 1985; McConnell, 1995; Train, 2009). ory (Edwards, 1954; Einhorn and Hogarth, 1981), mathematical The decision-making model presented in this paper adopts a psychology (Tversky, 1972; Swait and Marley, 2013), microeco- fundamentally different perspective, by postulating that in some nomics (Samuelson, 1948; Houthakker, 1950; Sen, 1971), micro- situations, a decision-maker may wish to hide the preferences econometrics (McFadden, 2001; Walker and Ben-Akiva, 2002; underlying his choices, from an onlooker. In other words, it cap- Arentze and Timmermans, 2009; Marley and Swait, 2017), the tures the notion that the decision-maker may in some situa- decision sciences (Bell et al., 1988; Keeney and Raiffa, 1993), tions wish to suppress the echo of his preferences. The rea- and artificial intelligence (Georgeff et al., 1998; Zurek, 2017). In sons for such obfuscation-based decision-making may include a other words, conventional models of decision-making routinely decision-maker's wish to protect his privacy, or to avoid legal postulate that a decision-maker's latent preferences echo through punishment or social shame. The proposed model of obfuscation- based decision-making is designed to be simple and tractable – it builds on the well-known concepts of Bayesian inference and ∗ Corresponding author. information entropy – while still being able to capture subtle E-mail address: [email protected] (C. Chorus). but important behavioral intuitions. In this paper, we will show 1 Except for first author, authors are listed in alphabetic order. 2 We are aware that several scholars have made useful distinctions between these and related concepts and have ordered them in (cognitive) hierarchies. 3 For ease of communication, we refer to the decision-maker as ``he'' and to These distinctions and hierarchies are subject to considerable academic debate. the onlooker as ``she'' throughout this paper, although either the agent and/or In this paper we do not take a standpoint in this debate. the onlooker may be conceived to be human or artificial (``it''). https://doi.org/10.1016/j.mathsocsci.2020.10.002 0165-4896/' 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). C. Chorus, S. van Cranenburgh, A.M. Daniel et al. Mathematical Social Sciences 109 (2021) 28–44 that although the notion of obfuscation clearly goes against a the attribute is of the highest importance to the decision-maker. fundamental premise underlying most decision theories, it is still Scores xkj which are stacked in a K by J matrix X reflect how each possible to do meaningful normative and empirical analyses with particular alternative scores on each particular attribute; the non- a properly specified obfuscation model. negative attribute-weights imply that higher scores are preferred The notion of obfuscation-based decision-making is conceptu- over lower ones. The aggregated utility associated with choosing D PK D · ally related to principal–agent interaction and mechanism alternative aj equals uj kD1 ujk, where ujk βk xkj. Note design (Hurwicz, 1973), strategic ambiguity in political decision- that this aggregation reflects a classical linear-additive multi- making (Page, 1976; Kono, 2006), truth serums (Prelec, 2004), attribute utility approach; other aggregation procedures may be incentive compatibility (Carson and Groves, 2007), preference- considered as well. Denote the K-dimensional vector containing falsification (Frank, 1996; Kuran, 1997), deception by artificial the weights of all attributes as β, which defines the decision- agents (Castelfranchi, 2000), privacy protection (Brunton et al., maker's preferences. The decision-maker's beliefs are defined as 2017) and covert signaling (Smaldino et al., 2018). follows: Despite this abundance of related work, this – to the best of 1. He is being watched by an onlooker. the authors' knowledge – is the first paper to provide a model 2. The onlooker observes A, G, and X; she has the same of the decision-making behavior of an agent that wishes to hide perception of these vectors and matrix as the agent himself. from an onlooker the latent underlying preferences that govern 3. The onlooker has uninformative prior probabilistic beliefs his choices. It is important to note at this point, that obfuscation P .β/ about the weights attached by the agent to different – i.e., hiding preferences from onlookers – is fundamentally dif- attributes. She knows that each weight is an element from ferent from the much more widely studied notion of deception the set f0; 1; 2;:::; Mg. The onlooker's multidimensional (e.g. Eriksson and Simpson, 2007; Van't Veer et al., 2014; Biziou- uninformative prior thus consists of probabilities of size van-Pol et al., 2015; Danaher, 2020). We conceive deception in 1=(M C 1)K for each of the (M C 1)K possible states of the terms of an agent trying to mislead the onlooker into making world, where each state is characterized by a realization of her believe that a particular set of preferences underlies his each of the K weights βk. choices while in reality, another set of preferences governed his 4. The onlooker observes one choice by the decision-maker decision-making. In contrast, an obfuscating agent has no `target' from A, and uses that observation to update her beliefs set of preferences towards which he wants to steer the onlooker's about weights β, into posterior probabilities; she does so beliefs; he merely wants to present the onlooker with as little as using Bayes' rule. Her posterior probabilities, after having possible information regarding his preferences. Put colloquially: a observed the decision-maker's choice for alternative aj, are deceiving agent wants the onlooker to give the wrong answer to given by: the question ``why did he do that?'', while an obfuscating agent ( ) wants the onlooker to say ``I do not know''. P ajjβ · P .β/ P (βja ) D (1) The remainder of this paper is structured as follows: Sec- j P ( j ) · β2B P aj β P .β/ tion2 presents a model of obfuscation-based decision-making and illustrates some of its workings using a concrete, numerical Here B represents the domain of β (i.e., it contains all C K ( j ) example. Section3 presents the results of an obfuscation game, (M 1) states of the world), and P aj β is given by the well-known Logit-formulation (Luce, 1959; McFadden, designed to take a first step towards empirical validation of 1974) which stipulates that the probability of choosing an the obfuscation model. Section4 concludes, and presents direc- action given a set of preferences increases when the utility tions for further research.