Blockchain Papers

Dustin Weiss, Robert Gaudiosi, Z. Ivy Zhou, Robert I. Webb

This paper examines intraday Bitcoin spot returns and trading activity around the expiration of Deribit Bitcoin options. Using data from spot exchanges and Deribit perpetual futures, we document a statistically and economically significant return reversal around expiration. The effect concentrates on days with elevated at-the-money open interest and is strongest when cumulative gamma exposure is negative, which is consistent with positive feedback trading pressure induced by option market makers hedging net short exposure. Trading activity also rises around expiry in Deribit perpetual futures and in the spot exchanges used to determine the Deribit settlement price. These intraday price effects are economically meaningful, implying annual wealth transfers of approximately USD 50 million between option writers and holders. Overall, the findings highlight the role of daily option expirations in shaping short-horizon price formation in Bitcoin markets and have implications for regulated investment products that rely on spot-market reference prices.

Navid Bahmani, Amit Bhatnagar, Minakshi Trivedi

No abstract is available for this record.

Alwin Estareja, Ramona Rupeika-Apoga

No abstract is available for this record.

Muhammed Ismail

In this paper, I prove that sublinear regret across the environment Class C requires six functional properties, that these properties are mutually independent, and that they compose into a directed informational chain closing back on itself — a six-link cycle whose final link is grounded in an explicit Doob martingale construction over cycles of play. All six properties are defined functionally — as conditions on the distributions a decision-maker induces over actions and canonical summaries — so the results are invariant under implementation and apply to any decision-making system that can be modelled within the class: a person, an institution, or a machine. Every theorem in this paper, without exception, is checked line by line in the Lean 4 proof assistant against Mathlib: the formalization (~12,700 lines) contains zero `sorry`, zero custom axioms, and zero opaque definitions. Class C is the union of all POMDPs satisfying at least one of six structural properties covering the fundamental qualitative dimensions of adaptive hardness: reward ambiguity (P1), absorbing traps (P2), local optima (P3), deterministic optimality (P4), constrained feasibility (P5), and nonstationarity (P6). * Part I (Necessity). I define six primitives X1–X6 as purely functional properties of decision rules: Objective Tracking, Cross-Context Safety Transfer, Global Attractor Exploration, Policy Simplification, Feasibility Projection, and Feedback Adaptation. For each, I construct an explicit environment in C and prove an unconditional Ω(T) regret lower bound for any decision-maker lacking that primitive.* Part II (Independence). For every ordered pair (i,j) with i≠j, I exhibit an explicit decision rule possessing Xj but lacking Xi that suffers Ω(T) regret on the matching environment. All thirty directed-pair results are shown to follow from one master theorem, verified on a single compound environment with full non-interference analysis.* Part III (Sequential Dependence). Necessity is domain-invariant — a structural failure is a structural failure no matter what "success" means to the decision-maker — which is why Parts I and II hold unconditionally. Sufficiency is not: what counts as success is supplied by the domain, not by the theorem, so a single closed-form sufficiency result covering every domain at once would have to either fix one arbitrary notion of success and stop being general, or say nothing of substance. Part III proves exactly what generalizes. I prove six Information Enhancement Theorems establishing that the six primitives compose into a directed information chain: possessing Xi strictly increases the mutual information available toward any goal variable at Xi+1's task. Each of the six links is established outright — a forward theorem, a reverse theorem, and a non-reversibility result — with the exact point where a domain's own definition of success enters the chain named explicitly, as an Implementation Obligation, rather than assumed away. The closing link, X6→X1, is grounded in an actual Doob martingale construction: given that the cycle-indexed posterior is a martingale, it converges almost surely to the truth across cycles — the precise sense in which the chain accumulates rather than resets. To this paper's knowledge, no prior formalization unifies this many independently-proven-necessary structural properties into a single machine-checked class with proven mutual independence across all of them. All mathematical work is provided in full transparency and independent verification is highly encouraged: the complete Lean formalization, with a passing build and every theorem cross-referenced to its exact identifier, is at github.com/M-Ismail-ZA/IsmailsPrimitives. For any feedback or collaboration, please contact me via the email address listed on the paper. Updated: 3 July 2026 (V6.1).

Sinja Müser, Moritz Hemmerich, Florian Schmitz

Cryptocurrencies have found their way into the financial market as a serious alternative in recent years. In particular, Bitcoin is increasingly coming into focus. Currently, however, little is known why people invest in cryptocurrency or not. The present study seeks to shed light on individual difference variables potentially associated with these investment decisions. This includes personality traits, knowledge, and attitudes toward the social and political environment. The effective sample comprised 603 respondents who completed an online survey. Based on the proportion of their financial portfolio invested into Bitcoin, participants were divided into three groups: Non-Bitcoiners, Bitcoin Enthusiasts, and Bitcoin Maximalists. Group comparisons and prediction models indicated that Bitcoiners differed substantially from Non-Bitcoiners in justice-related attitudes as well as in specific knowledge about this cryptocurrency. By contrast, general political attitudes or reinforcement sensitivity did not differ much, and there was hardly a difference in basic dimensions of personality and general knowledge.

Mohamad El Haj, Ahmed A. Moustafa

Introduction: Cryptocurrency investment and trading are rapidly growing activities due to the development of applications and platforms that offer fast, continuous, and easy entry into the cryptocurrency world. To understand decision making in cryptocurrency holders, we assessed temporal discounting, that is, whether Bitcoin holders disregard rewards if they are distant in time and overvalue rewards if they are more immediate. Further, we compared performance between short-term investors (i.e., day-traders) vs. long-term investors. Methods: Using an online survey, we invited 144 Bitcoin holders to answer temporal discounting questionnaires dealing with money ("Which do you prefer, that you get right now 20 USD in cash or 100 USD in a month?") and Bitcoin ("Which do you prefer, that you get right now 0.1 or 1 Bitcoin in a month?"). Results: Analysis demonstrated no significant differences between temporal discounting for money and Bitcoin. However, and critically, higher temporal discounting for both money and Bitcoin was observed in short-term investors compared with long-term investors. In a similar vein, significant positive correlations were observed between day trading and temporal discounting for both money and Bitcoin. Discussion: These findings demonstrate how Bitcoin holders with short-term time horizons tend to prioritize immediate rewards over larger but delayed rewards. Future research can assess the neural basis of temporal discounting for cryptocurrencies.

Bambang Leo Handoko, Agustinus Winoto, Faris Kasenda, Citra Amanda · 5 authors

Investing in cryptocurrencies is one of the instruments that is increasingly in demand by individual investors today. Investors are starting to aim for other advantages of investing in cryptocurrencies besides capital gains, which is the benefits of getting airdrops. Through this research, we want to examine what factors influence investors' intention to invest through the cryptocurrency airdrops program. We take these factors from the behavioral finance approach. We use heuristic behavior, prospect theory and role of personality variables. Our research is a causal quantitative research. We collected primary data from a questionnaire distributed to experienced individual investors participating in one of the cryptocurrency airdrops programs. We use hypothesis testing with ordinary least square analysis. The research result is that heuristic behavior, prospect theory, and role of personality each has significant influence on investor decision making in cryptocurrency airdrops.

Joachim I. Krueger

Steven Pinker, being a public intellectual, may expect readers of his Rationality: What It Is, Why It Seems Scarce, Why It Matters (RAT) to bring certain hopes and expectations to the task. They know Pinker as a distinguished expert on linguistics, communication, and cognitive science, a scholar with a deep knowledge of many theories from evolution to cognitive dissonance, a child of the Enlightenment and a prophet of progress. They will not be disappointed.Readers with sensitivity and memory may recall that Pinker sometimes oversells his message. How the Mind Works (Pinker, 1997), for example, was a wild and fun ride through the cognitive science of that time, but it did not reveal how the mind really works. As far as I can see, there are two main reasons for this shortcoming. One reason is the impossibility of omniscience (Felin, Koenderink, & Krueger, 2017). We will never know how the mind really works. What we can have are incrementally better models of it. In RAT, Pinker does better. He notes the impossibility of defining rationality in rational terms without begging the question. Yet he pragmatically forges ahead, and this is his genius.The other reason for why RAT goes a bit too far lies in its curated presentation of the relevant science. In How the Mind Works, Pinker's discussion of the social mind was based on the work of a handful of authors with an evolutionary point of view and homes in Santa Barbara. In RAT, Pinker casts a broader net but still anchors his story on a familiar cast of pioneers, namely Robyn Dawes, Paul Slovic, Daniel Kahneman, and Amos Tversky. Pinker knows that there is an ongoing debate over the nature of rationality and the proper role of normative models of thinking (Chater et al., 2018). Yet he sidesteps these difficult issues in order to tell a story of how the concept of rationality can be understood and how its practice can be improved. This story requires some omissions, and their shadow reflects the dark side of his genius. Given these caveats, my recommendation is to read the book but to do so with an attitude of properly curbed enthusiasm. That would be the rational approach.In his penultimate chapter Pinker asks, “What is wrong with people?,” and he knows that his readers have been waiting for him to raise this question. Pinker also knows that he can't answer it because he—as anyone would—has failed to define rationality without question-begging. So why do we care about a big question when all we can do is answer little ones, such as “Under what conditions do people neglect base rates?” Is it rational to think that many little answers will add up to a big one? As a connoisseur of Hume, Pinker knows that this question is a version of the induction problem. When a large number of little questions have been answered, another one may come along to frustrate us. Yet the effort to chip away at the big issue is not for nothing. Identifying limited questions and answering them is fun and profitable.Like Pinker, I have enjoyed the ride on the rationality train. My favorite example of a thought problem that puzzled many great Renaissance minds until Fermat and Pascal came along to solve it is “The problem of points” (Krueger, 2000). Suppose Steven and Joachim use a fair coin, bet on opposite sides, and agree to throw it until one of them has won six times. This person will get the $20 that Dominic has kindly provided. However, at the point where Steven has won five rounds and Joachim has won three rounds, Dominic is called to editorial duty and terminates the game. What is a fair distribution of the $20? As it turns out, 7/8 of the money should go to Steven because the only way I could win under the agreed-upon conditions would be to score another three wins in a row. Few people understand this intuitively, but Fermat's math leaves no doubt that the rational solution is also a moral one, and for once the tug of war between the sweet and the smart is relaxed.The problem of points, the solution of which was a crucial step toward the modern understanding of probability, is an example of significant, if limited, progress. Alas, the tug often asserts itself and leaves us in tragic dilemmas where rational individuals bring forth their own destruction. For example, Pinker is pessimistic about our prospects in the prisoner's dilemma and its derivates (e.g., commons dilemmas). For an optimist like Pinker, this is a surprising surrender. In fact, one ray of hope in the prisoner's dilemma is social projection, an inductive inference that was once considered irrational. Yet when people reasonably assume that other reasonable people will choose as they themselves do, mutual cooperation becomes more likely than the presumably rational catastrophe of mutual defection (Krueger, 2013). The dilemma of trust, not discussed by Pinker, also illustrates this point. Classic game theory holds that rational agents will not trust strangers on the assumption that there is no incentive to reward trust with trustworthiness. Yet a proscription of trust is self-defeating and thus irrational—as is a prescription of trust. The rational attitude is to gather available cues (e.g., self-other similarities) as well as moral considerations (e.g., the golden rule) and social projection. With that the leap of trust can be framed as a decision under calculated uncertainty (Evans, Ong, & Krueger, 2021).In Chapters 3 to 9, the main body of RAT, Pinker surveys engaging examples of problems posed and problems solved, thereby illustrating the many and diverse tools critical thinkers find in their boxes. Here are some of them in super-short shrift: Chapter 3 reviews the elements of logic, and this is just as well because “logic” is as close as one gets to the term “rationality” in the Greek language. The ur-term is “logos,” which we first find in Heraclitus as a reference to the hidden order of the universe. Aristotle used it to refer to how we think, or should think, about the world. Like Socrates and Plato before him, he figured that we need help. The chasm between thinking as it is and thinking as it should be had opened up and it stills yawns at us today. Pinker, like Dawes (1988) and many other pioneers, knows that the mastery of logic does not eliminate the question “What is wrong with people?” because villains can be perfectly logical in the pursuit of their villainy.Chapter 4 confronts human ignorance and its management with an introduction to probability and randomness. Probabilistic thinking is the poor human's retreat when high rationality in the form of “true knowledge” fails. Now that we know so little, how can we still be rational? The obvious task seems to be gathering more data, making coherent inferences, and detecting randomness wherever it may lurk. Yet there are ironic puzzles, such as deliberate ignorance, when people elect to hide information from themselves although they might have it for free. As it turns out, such self-blinding need not be irrational, in the tradition of King Oedipus's self-mutilation, but a rational response to an environment that has no compassion (Krueger et al., 2020).Chapter 5 is written in reverence of the Reverend Bayes, who sought an inductive proof of the existence of God and failed. For all its elegance, Bayes's theorem's ability to nudge us toward true beliefs depends on the quality of the assumptions that go into it, that is, the priors. When we ask “What is wrong with people,” we may find that they overadjust or underadjust their beliefs in light of evidence, but the deep problem is that many people with contrasting priors are willing to diverge rather than converge with their beliefs after evidence. Pinker refers to Stanovich's (2021) book on “myside bias” (reviewed in this issue), but his faith in Bayes remains intact.Chapter 6 follows the bending arc of the utility function and its implications for rational choice. Pinker follows the tradition of marveling at the beauty of utility theory's axioms and noting that we'd be better off in our goal pursuit by observing them. At least we'd be protecting ourselves from being turned into money pumps by exploiters who are more rational and less scrupulous than we are (Grüning & Krueger, 2021). Kahneman and Tversky (1979) delivered what should have been the coup de grâce to the utility paradigm by showing how preference reversals emerge from the human ability to adapt to current circumstances and their differential treatment of gains and losses. However, organisms that don't adapt (even fungi habituate to mild toxins) or that reduce their loss aversion to match their love of gains in absolute terms might not live long enough to see the next equinox.Chapter 7 discusses the management of errors. Signal detection theory (SDT) was created to help radar operators decide whether a blip on the screen represented a Stuka formation or a flock of geese, a situation in which human sensibilities prefer to tolerate a few more false positives if that means fewer Stukas will be missed (Swets, Dawes, & Monahan, 2000). Beyond the radar screen lies a reality: The Stukas are either coming or they are not. Being able to tell the differencewith a large d' is a way of having knowledge and thus of being rational. The beta parameter, that is, the threshold one sets for sounding the “Stuka!” alarm, is of interest only when d' is low. It is here that the trade-off between the two types of errors must be adjudicated in light of preferences and values. Pinker then presents the Neyman–Pearson theory of statistical decision making as if it were a version of SDT, although it was its predecessor (Neyman & Pearson, 1933). A critical difference is that the size of a statistical effect is a random variable. It's rather like asking, “How many Stukas are there?” If there is only one, we may not care, but our theory says there are four (i.e., a formation). Any power analysis, which nowadays fashionably and ritualistically prefaces every Result section of a psychology article, is conditioned on a theorized (i.e., unobserved) effect size. Whereas SDT yields d' as a measure of discriminative sensitivity, the Neyman–Pearson theory of statistical testing assumes a d', as well as a false positive and a false negative rate, and then yields a probability of the data under the assumption that d' = 0. Which theory is more rational?Chapter 8 surveys the essentials of game theory and presents rationality as John von Neumann saw it. This view leads to despair because when rational goals yield irrational outcomes, we have tragedy. When individually rational agents find themselves in noncooperative games such as the prisoner's dilemma or chicken, they can do no better than avoid exploitation (chicken) or face mutual destruction (prisoners). The failure of game theory highlights the failure of individualized notions of rationality when collective welfare is at stake. To frame rationality at the supraindividual level requires the surrender of methodological individualism, one of the sacred tenets of the Enlightenment. Both Pinker and I hesitate to accept the need for a methodological collectivism, but there may be no way around it.Chapter 9 seems mildly out of place because it covers familiar questions about correlation and causation. Pinker takes the conventional line of prioritizing causation. Chains of cause and effect are the cement of the universe, although we know from Hume that we cannot prove this. Correlation is a trickster because it enables sloppy causal reasoning. The rational person knows how to extract credible causal claims from correlation with the help of other cues such as precedence or mechanism. One may counter that, because causation cannot be observed but only inferred, a rational person can be imagined who is not interested in causal explanations but who has a good fix on the available correlations and is able to predict what will happen next. Data scientists and machine learners seem to be betting on this model of rationality (Krueger, 2020).Late in his distinguished career, German sociologist Helmut Schelsky (1975) diagnosed and bemoaned the rise of a priestly caste on campus. These self-anointed priests took it upon themselves, Schelsky argued, to tell the rest of society, and thus its productive classes, what was wrong with their perceptions and actions and what they should do to overcome their “false consciousness.” After the Enlightenment had broken the power of the seminary to control thinking, the power of the seminar took its place. Today, we see a similar situation in cognitive psychology. Reasoning errors are revealed—or rather designed—to bring forth in the audience the humbling Aha! experience of “How could we be so stupid!” The omniscient lecturer then offers a path toward salvation. “Think again,” they might say (Grant, 2021), or think that which is not on your mind (Kahneman, 2011), or learn to think like us, the scientists (Pinker, 2021). Much like Schelsky's estranged colleagues from the Frankfurt School, today's cognitive scientists of the Kahneman school treat their audience to a domination–submission ritual. We tell you what's wrong with you, they declare, and you will thank us (and pay us) for it. The false consciousness lies in the audience's cheerful acceptance of this game.Arguably, the greatest achievement of psychological science is the demystification of the workings of the visual system. Visual illusions are endlessly fascinating in their weirdness and instructive in what they teach us about this masterpiece of nature. Tversky and Kahneman's (1974) greatest rhetorical trick was to suggest that cognitive illusions are analogs of visual illusions. Nothing could be further from the truth. Pinker wisely notes that to reveal the nuttiness of a belief is to challenge the believer to act on it, but he still is lulled by the Sirens’ song of the visual illusion metaphor. If the metaphor were true, there would be no irrationality. The so-called cognitive illusions would be the features of the system, not its bugs. This is a conclusion I do not wish to defend. Irrationality does exist, and it is all around us.Pinker comes closest to a solution, I think, when he early on in RAT tells how the Ju/’hoansi Bushmen of the Kalahari reason about their environment with exquisite cognitive skill. Their abilities meet the demands of their ecology, to the detriment of the springbok. Most contemporary people live in a world in which their skills are not aligned with their ecology, and this is partly the fault of the academic priests who design wicked puzzles in their labs or on their Qualtrics platforms (Lejarraga & Hertwig, 2021). Perhaps it is time to chill about individualist rationality, take a more ecological perspective (Hertwig, Leuker, Pachur, Spiliopoulos, & Pleskac, 2021), and not forget to have a good laugh (Kazantzakis, 1952).

Rongxin Chen, Gabriele M. Lepori, Chung-Ching Tai, Ming‐Chien Sung

Research on human attention indicates that objects that stand out from their surroundings, i.e., salient objects, attract the attention of our sensory channels and receive undue weighting in the decision-making process. In the financial realm, salience theory predicts that individuals will find assets with salient upsides (downsides) appealing (unappealing). We investigate whether this theory can explain investor behaviour in the cryptocurrency market. Consistent with the theory's predictions, using a sample of 1738 cryptocurrencies, we find that cryptocurrencies that are more (less) attractive to “salient thinkers” earn lower (higher) future returns, which indicates that they tend to be overpriced (underpriced). On average, a one cross-sectional standard-deviation increase in the salience theory value of a cryptocurrency reduces its next-week return by 0.41%. However, the salience effect is confined to the micro-cap segment of the market, and its size is moderated by limits to arbitrage.

William J. Luther

By William Luther. How might we reconcile the regression theorem with the emergence of bitcoin? Luther responds to Pickering's argument that the "purpose and requirements of the regression theorem" have been misinterpreted.

Kofi Agyarko Ababio

This paper investigates if real investors other than rational investors could add value to their investment portfolios considering their mentality and psychology. The universe of assets constitutes 21 cryptocurrencies (37 international equities) and covers, respectively, the period from August 1, 2016, to March 31, 2018 (January 7, 2002, to March 23, 2018). The cumulative prospect theory and variant specifications were utilized to validate and compare the classification and selection of assets driven by some decision theories. The results of optimization analysis of all the formulated portfolios constituting assets from both markets showed that portfolios constituting assets with lower cumulative prospect theory values outperformed their counterpart with higher cumulative prospect theory values. The superiority of the cumulative prospect theory was established as an empirically corroborated theory of decision-making with rich psychological content. The findings of this paper are crucial for finance practitioners as they showcase an intuitive and coherent manner to guide fund managers, investors and other economic agents in their investment practices.

Philip A. Ebert, Martin Smith, Ian Durbach

The notion of risk plays a central role in economics, finance, health, psychology, law and elsewhere, and is prevalent in managing challenges and resources in day-to-day life. In recent work, Duncan Pritchard (2015, 2016) has argued against the orthodox probabilistic conception of risk on which the risk of a hypothetical scenario is determined by how probable it is, and in favour of a modal conception on which the risk of a hypothetical scenario is determined by how modally close it is. In this article, we use Pritchard's discussion as a springboard for a more wide-ranging discussion of the notion of risk. We introduce three different conceptions of risk: the standard probabilistic conception, Pritchard's modal conception, and a normalcy conception that is new (though it has some precursors in the psychological literature on risk perception). Ultimately, we argue that the modal conception is ill-suited to the roles that a notion of risk is required to play and explore the prospects for a form of pluralism about risk, embracing both the probabilistic and the normalcy conceptions. We take the view that a risk judgment always implicates a body of evidence, which we refer to as the background evidence. In cases where the background evidence is not made explicit, we take it to be supplied by the context of utterance and, in typical cases, to be the evidence possessed by the one making the judgment. That is, we are inclined towards a contextualist semantics for utterances such as 3 and 4, on which their truth conditions feature an evidence parameter, the value of which is fixed by the context. The semantics of such utterances is not, however, our primary concern here. As well as making categorical risk judgments such as the above, we often make comparisons. While we may judge that the risk of a plane crash is very low, we may also judge that there is a higher risk of a car crash on the way to the airport. As well as judging that there's a high risk of food poisoning at a particular restaurant, we might also judge that there is a lower risk of food poisoning at the restaurant next door. Moreover, while we often speak about the riskiness of feared events, such as plane crashes, food poisoning, etc., we can also assess the risk of states of affairs. For instance, before drilling into the wall of a 1970s West Australian house, one might assess the risk that the wall contains asbestos, or jurors in a criminal trial, when contemplating a guilty verdict, might consider the risk that the defendant is innocent, or a mountaineer may ponder the risk that the snow conditions are unfavourable for a climb. 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Malte Preuß

Economic preferences and personality traits are fundamental explanatory factors in understanding individual decision-making. They explain the heterogeneity within human behavior and are the reason why individuals differ in their actions although the preliminaries are the same. Labor market behavior, educational choices, investment decisions as well as fertility and health outcomes are only a few examples in which inherent characteristics play a key role. These findings rely on one joint assumption: preferences and personality traits do not change across the working age. The point in time when preferences are defined and measured is thus irrelevant. However, if this assumption is violated, theoretical models and empirical studies face the threat of endogeneity biases: preferences do not only affect life's outcomes, life's outcomes may also affect preferences. Testing the exogeneity assumption is thus obligatory. Herein, the present thesis makes its contribution and presents three different studies on the stability of economic preferences and personality traits. The first study in this thesis focuses on the stability of time preferences. So far, evidence on their stability is scarce and considerably restricted by very short time frames, very small sample sizes, or both. The Dutch Household Survey enables these obstacles to be circumvented and the long-term stability of time preferences within a representative sample to be analyzed. By relying on the `consideration of future consequences’ scale -- a behaviorally validated survey measure on time preferences -- this thesis finds that time preferences have, compared to other economic attitudes, a relatively low intra-individual stability. However, the analysis reveals that individuals' valuation of future utility neither varies with age nor changes persistently with past life experiences. Similar findings result from a replication of the analysis with the German Socio-Economic Panel and its ultra-short survey items on patience and impulsiveness. The thesis, therefore, comes to the conclusion that time preferences are stable in the long run but subjected to measurement issues. The second study focuses on the determinants of risk-taking. Using German panel data, we find that people become more risk-averse when losing work. The immediate income loss does not mediate this effect. Risk aversion also seems unrelated to the loss of non-monetary benefits of work. However, the study finds that risk aversion responds more strongly to losing work the more future income is at stake, and the effect manifests itself on the eve of job loss even when people have not yet suffered from the consequences of the event. Lower future income expectations and more uncertainty about future incomes may thus explain the effect of job loss on risk attitude. Nevertheless, the effect is not persistent. After some time, individuals turn back to their initial level of risk attitude. The last chapter of this thesis tests the stability of locus of control, a measure that depicts how much people believe in their ability to affect life outcomes. Using the German Socio-Economic Panel, we find that a job loss due to a plant closure has no long-lasting effect on locus of control. The common assumption of its stability is thus not rejected. However, during unemployment, control perception decreases significantly. The effect holds true independent from unemployment duration or socio-demographic characteristics and vanishes as soon as the unemployed find a new job. In conclusion, measurement of locus of control is affected by unemployment but not the trait itself. Using this trait as the explanatory variable can thus lead to biased estimations if this temporary deviation in measurement is not accounted for. In conclusion, the present thesis neither rejects the stability assumption nor claims that preferences or personality are perfectly stable. All measures analyzed change with time. But, interpreting this instability as proof of endogenous preferences or personality traits appears unjustified. Each of the studies proposes alternative, less controversial interpretations of instability.

Yibeltal Assefa, Yogan Pillay, Wim Van Damme

Sander Greenland and Charles Poole1 accept that P values are here to stay but recognize that some of their most common interpretations have problems. The casual view of the P value as posterior probability of the truth of the null hypothesis is false and not even close to valid under any reasonable model, yet this misunderstanding persists even in high-stakes settings (as discussed, for example, by Greenland in 2011).2 The formal view of the P value as a probability conditional on the null is mathematically correct but typically irrelevant to research goals (hence, the popularity of alternative—if wrong—interpretations). A Bayesian interpretation based on a spike-and-slab model makes little sense in applied contexts in epidemiology, political science, and other fields in which true effects are typically nonzero and bounded (thus violating both the “spike” and the “slab” parts of the model). I find Greenland and Poole’s1 perspective to be valuable: it is important to go beyond criticism and to understand what information is actually contained in a P value. These authors discuss some connections between P values and Bayesian posterior probabilities. I am not so optimistic about the practical value of these connections. Conditional on the continuing omnipresence of P values in applications, however, these are important results that should be generally understood. Greenland and Poole1 make two points. First, they describe how P values approximate posterior probabilities under prior distributions that contain little information relative to the data: This misuse [of P values] may be lessened by recognizing correct Bayesian interpretations. For example, under weak priors, 95% confidence intervals approximate 95% posterior probability intervals, one-sided P values approximate directional posterior probabilities, and point estimates approximate posterior medians. I used to think this way, too (see many examples in our books), but in recent years have moved to the position that I do not trust such direct posterior probabilities. Unfortunately, I think we cannot avoid informative priors if we wish to make reasonable unconditional probability statements. To put it another way, I agree with the mathematical truth of the quotation above, but I think it can mislead in practice because of serious problems with apparently noninformative or weak priors. Second, the main proposal made by Greenland and Poole is to interpret P values as bounds on posterior probabilities: [U]nder certain conditions, a one-sided P value for a prior median provides an approximate lower bound on the posterior probability that the point estimate is on the wrong side of that median. This is fine, but when sample sizes are moderate or small (as is common in epidemiology and social science), posterior probabilities will depend strongly on the prior distribution. Although I do not see much direct value in a lower bound, I am intrigued by Greenland and Poole’s1 point that “if one uses an informative prior to derive the posterior probability of the point estimate being in the wrong direction, P0/2 provides a reference point indicating how much the prior information influenced that posterior probability.” This connection could be useful to researchers working in an environment in which P values are central to communication of statistical results. In presenting my view of the limitations of Greenland and Poole’s1 points, I am leaning heavily on their own work, in particular on their emphasis that, in real problems, prior information is always available and is often strong enough to have an appreciable impact on inferences. Before explaining my position, I will briefly summarize how I view classical P values and my experiences. For more background, I recommend the discussion by Krantz3 of null hypothesis testing in psychology research. WHAT IS A P VALUE IN PRACTICE? The P value is a measure of discrepancy of the fit of a model or “null hypothesis” H to data y. Mathematically, it is defined as Pr(T(yrep)>T(y)|H), where yrep represents a hypothetical replication under the null hypothesis and T is a test statistic (ie, a summary of the data, perhaps tailored to be sensitive to departures of interest from the model). In a model with free parameters (a “composite null hypothesis”), the P value can depend on these parameters, and there are various ways to get around this, by plugging in point estimates, averaging over a posterior distribution, or adjusting for the estimation process. I do not go into these complexities further, bringing them up here only to make the point that the construction of P values is not always a simple or direct process. (Even something as simple as the classical chi-square test has complexities to be discovered; see the article by Perkins et al4). In theory, the P value is a continuous measure of evidence, but in practice it is typically trichotomized approximately into strong evidence, weak evidence, and no evidence (these can also be labeled highly significant, marginally significant, and not statistically significant at conventional levels), with cutoffs roughly at P = 0.01 and 0.10. One big practical problem with P values is that they cannot easily be compared. The difference between a highly significant P value and a clearly nonsignificant P value is itself not necessarily statistically significant. (Here, I am using “significant” to refer to the 5% level that is standard in statistical practice in much of biostatistics, epidemiology, social science, and many other areas of application.) Consider a simple example of two independent experiments with estimates (standard error) of 25 (10) and 10 (10). The first experiment is highly statistically significant (two and a half standard errors away from zero, corresponding to a normal-theory P value of about 0.01) while the second is not significant at all. Most disturbingly here, the difference is 15 (14), which is not close to significant. The naive (and common) approach of summarizing an experiment by a P value and then contrasting results based on significance levels, fails here, in implicitly giving the imprimatur of statistical significance on a comparison that could easily be explained by chance alone. As discussed by Gelman and Stern,5 this is not simply the well-known problem of arbitrary thresholds, the idea that a sharp cutoff at a 5% level, for example, misleadingly separates the P = 0.051 cases from P = 0.049. This is a more serious problem: even an apparently huge difference between clearly significant and clearly nonsignificant is not itself statistically significant. In short, the P value is itself a statistic and can be a noisy measure of evidence. This is a problem not just with P values but with any mathematically equivalent procedure, such as summarizing results by whether the 95% confidence interval includes zero. GOOD, MEDIOCRE, AND BAD P VALUES For all their problems, P values sometimes “work” to convey an important aspect of the relation of data to model. Other times, a P value sends a reasonable message but does not add anything beyond a simple confidence interval. In yet other situations, a P value can actively mislead. Before going on, I will give examples of each of these three scenarios. A P Value that Worked Several years ago, I was contacted by a person who suspected fraud in a local election.6 Partial counts had been released throughout the voting process and he thought the proportions for the various candidates looked suspiciously stable, as if they had been rigged to aim for a particular result. Excited to possibly be at the center of an explosive news story, I took a look at the data right away. After some preliminary graphs—which indeed showed stability of the vote proportions as they evolved during election day—I set up a hypothesis test comparing the variation in the data to what would be expected from independent binomial sampling. When applied to the entire data set (27 candidates running for six offices), the result was not statistically significant: there was no less (and, in fact, no more) variance than would be expected by chance alone. In addition, an analysis of the 27 separate chi-square statistics revealed no particular patterns. I was left to conclude that the election results were consistent with random voting (even though, in reality, voting was certainly not random—for example, married couples are likely to vote at the same time, and the sorts of people who vote in the middle of the day will differ from those who cast their ballots in the early morning or evening). I regretfully told my correspondent that he had no case. In this example, we cannot interpret a nonsignificant result as a claim that the null hypothesis was true or even as a claimed probability of its truth. Rather, nonsignificance revealed the data to be compatible with the null hypothesis; thus, my correspondent could not argue that the data indicated fraud. A P Value that Was Reasonable but Unnecessary It is common for a research project to culminate in the estimation of one or two parameters, with publication turning on a P value being less than a conventional level of significance. For example, in our study of the effects of redistricting in state legislatures (Gelman and King),7 the key parameters were interactions in regression models for partisan bias and electoral responsiveness. Although we did not actually report P values, we could have: what made our article complete was that our findings of interest were more than two standard errors from zero, thus reaching the P < 0.05 level. Had our significance level been much greater (eg, estimates that were four or more standard errors from zero), we would doubtless have broken up our analysis (eg, studying Democrats and Republicans separately) to broaden the set of claims that we could confidently assert. Conversely, had our regressions not reached statistical significance at the conventional level, we would have performed some sort of pooling or constraining of our model to arrive at some weaker assertion that reached the 5% level. (Just to be clear: we are not saying that we would have performed data dredging, fishing for significance; rather, we accept that sample size dictates how much we can learn with confidence; when data are weaker, it can be possible to find reliable patterns by averaging.) In any case, my point is that in this example it would have been just fine to summarize our results in this example via P values even though we did not happen to use that formulation. A Misleading P Value Finally, in many scenarios P values can distract or even mislead, either a nonsignificant result wrongly interpreted as a confidence statement in support of the null hypothesis or a significant P value that is taken as proof of an effect. A notorious example of the latter is the recent article by Bem,8 which reported statistically significant results from several experiments on extrasensory perception (ESP). At brief glance, it seems impressive to see multiple independent findings that are statistically significant (and combining the P values using classical rules would yield an even stronger result), but with enough effort it is possible to find statistical significance anywhere (see the report by Simmons et al9). The focus on P values seems to have both weakened that study (by encouraging the researcher to present only some of his data so as to draw attention away from nonsignificant results) and to have led reviewers to inappropriately view a low P value (indicating a misfit of the null hypothesis to data) as strong evidence in favor of a specific alternative hypothesis (ESP) rather than other, perhaps more scientifically plausible, alternatives such as measurement error and selection bias. PRIORS, POSTERIORS, AND P VALUES Now that I have established my credentials as a pragmatist who finds P values useful in some settings but not others, I want to discuss Greenland and Poole’s proposal to either interpret one-sided P values as probability statements under uniform priors (an idea they trace back to Gossett)10 or else to use one-sided P values as bounds on posterior probabilities (a result they trace back to Casella and Berger).11 The general problem I have with noninformatively derived Bayesian probabilities is that they tend to be too strong. At first, this may sound paradoxical, that a noninformative or weakly informative prior yields posteriors that are too forceful—and let me deepen the paradox by stating that a stronger, more informative prior will tend to yield weaker, more plausible posterior statements. How can it be that adding prior information weakens the posterior? It has to do with the sort of probability statements we are often interested in making. Here is an example from Gelman and Weakliem.12 A sociologist examining a publicly available survey discovered a pattern relating attractiveness of parents to the sexes of their children. He found that 56% of the children of the most attractive parents were girls, when compared with 48% of the children of the other parents, and the difference was statistically significant at P < 0.02. The assessments of attractiveness had been performed many years before these people had children, so the researcher felt he had support for a claim of an underlying biological connection between attractiveness and sex ratio. The original analysis by Kanazawa13 had multiple-comparisons issues, and after performing a regression analysis rather than selecting the most significant comparison, we get a P value closer to 0.2 rather than the stated 0.02. For the purposes of our present discussion, though, in which we are evaluating the connection between P values and posterior probabilities, it will not matter much which number we use. We shall go with P = 0.2 because it seems like a more reasonable analysis given the data. Let θ be the true (population) difference in sex ratios of attractive and less attractive parents. Then the data under discussion (with a two-sided P value of 0.2), combined with a uniform prior on θ, yield a 90% posterior probability that θ is positive. Do I believe this? No. Do I even consider this a reasonable data summary? No again. We can derive these “No” responses in three different ways: first, by looking directly at the evidence; second, by considering the prior; and third, by considering the implications for statistical practice if this sort of probability statement were computed routinely. First, a claimed 90% probability that θ > 0 seems too strong. Given that the P value (adjusted for multiple comparisons) was only 0.2—that is, a result that strong would occur a full 20% of the time just by chance alone, even with no true difference—it seems absurd to assign a 90% belief to the conclusion. I am not prepared to offer 9-to-1 odds on the basis of a pattern someone happened to see that could plausibly have occurred by chance alone, nor for that matter would I offer 99-to-1 odds based on the original claim of the 2% significance level. Second, the prior uniform distribution on θ seems much too weak. There is a large literature on sex ratios, with factors such as ethnicity, maternal age, and season of birth corresponding to difference in probability of girl birth of <0.5 percentage points. It is a priori implausible that sex-ratio differences corresponding to attractiveness are larger than for these other factors. Assigning an informative prior centered on zero shrinks the posterior toward zero, and the resulting posterior probability that θ > 0 moves to a more plausible value in the range of 60%, corresponding to the idea that the result is suggestive but not close to convincing. Third, consider what would happen if we routinely interpreted one-sided P values as posterior probabilities. In that case, an experimental result that is 1 standard error from zero—that is, exactly what one might expect from chance alone—would imply an 83% posterior probability that the true effect in the population has the same direction as the observed pattern in the data at hand. It does not make sense to me to claim 83% certainty—5-to-1 odds—based on data that not only could occur by chance alone but in fact represent an expected level of discrepancy. This system-level analysis accords with my criticism of the flat prior: as Greenland and Poole1 note in their article, the effects being studied in epidemiology are typically range from −1 to 1 on the logit scale; hence, analyses assuming broader priors will systematically overstate the probabilities of very large effects and will overstate the probability that an estimate from a small sample will agree in sign with the corresponding population quantity. Rather than relying on noninformative priors, I prefer the suggestion of Greenland and Poole1 to bound posterior probabilities using real prior information. I would prefer to perform my Bayesian inferences directly without using P values as in intermediate step, but given the ubiquity of P values in much applied work, I can see that it can be helpful for researchers to understand their connection to posterior probabilities under informative priors. SUMMARY Like many Bayesians, I have often represented classical confidence intervals as posterior probability intervals and interpreted one-sided P values as the posterior probability of a positive effect. These are valid conditional on the assumed noninformative prior but typically do not make sense as unconditional probability statements. As Sander Greenland has discussed in much of his work over the years, epidemiologists and applied scientists in general have knowledge of the sizes of plausible effects and biases. I believe that a direct interpretation of P values as posterior probabilities can be a useful start—if we recognize that such summaries systematically overestimate the strength of claims from any particular dataset. In this way, I am in agreement with Greenland and Poole’s interpretation of the one-sided P value as a lower bound of a posterior probability, although I am less convinced of the practical utility of this bound, given that the closeness of the bound depends on a combination of sample size and prior distribution. The default conclusion from a noninformative prior analysis will almost invariably put too much probability on extreme values. A vague prior distribution assigns much of its probability on values that are never going to be plausible, and this disturbs the posterior probabilities more than we tend to expect—something that we probably do not think about enough in our routine applications of standard statistical methods. Greenland and Poole1 perform a valuable service by opening up these calculations and placing them in an applied context.

Floris Heukelom

To understand the relationship between experimental and behavioral economics, we need to go back to the late 1970s and early 1980s. In the 1970s, psychologists began conducting new kinds of experiments, the results of which seemed to falsify the assumption of rational individual behavior. This compelled experimental economists to stake out a position for the economics discipline regarding the results. Much to their surprise, their experiments corroborated the results of the psychologists. This led them to completely discard preference theory but at the same time to emphasize the role of the market as the mechanism that rationalizes individual behavior. An initially diverse and unorganized group of financial and other economists drew very different conclusions from these same experimental results. They saw them as proof of observed anomalies in financial markets and hailed Daniel Kahneman and Amos Tversky's prospect theory as the most important candidate for replacing the traditional microeconomic model of human behavior.

Johanna Etner, Meglena Jeleva, Pierre‐André Jouvet

This article study the impact of risk perception on environmental policy. The environmental quality is uncertain and can be improved by voluntary contributions. We introduce then an heterogeneity in individuals' risk perceptions. In this context, the social optimum can be decentralized by tax financed government subsidies to private provision. We distinguish the case of a government who represents perfectly agents' preferences from the case of a government with its own risk preferences. In the two cases, we show that neutrality still holds

Geoffrey B. Sprinkle

This paper reports the results of an experiment that examines how incentive-based compensation contracts compare to flat-wage compensation contracts in motivating individual learning and performance. I use a multiperiod cognitive task where the accounting system generates information (feedback) that has both a contracting role and a belief-revision role. The results suggest that incentives enhance performance and the rate of improvement in performance by increasing both: (1) the amount of time participants devoted to the task, and (2) participants' analysis and use of information. Further, I find evidence that incentives improve performance only after considerable feedback and experience, which may help explain why many prior one-shot decision-making experiments show no incentive effects. Collectively, the results suggest that incentives induce individuals to work longer and smarter, thereby increasing the likelihood that they will develop and use the innovative strategies frequently required to perform well in complex judgment tasks and learning situations.

Włodek Rabinowicz

No abstract is available for this record.