Calabi-Yau threefolds with large h^{2, 1}

We carry out a systematic analysis of Calabi-Yau threefolds that are elliptically fibered with section ("EFS") and have a large Hodge number h^{2, 1}. EFS Calabi-Yau threefolds live in a single connected space, with regions of moduli space associated with different topologies connected through transitions that can be understood in terms of singular Weierstrass models. We determine the complete set of such threefolds that have h^{2, 1} >= 350 by tuning coefficients in Weierstrass models over Hirzebruch surfaces. The resulting set of Hodge numbers includes those of all known Calabi-Yau threefolds with h^{2, 1} >= 350, as well as three apparently new Calabi-Yau threefolds. We speculate that there are no other Calabi-Yau threefolds (elliptically fibered or not) with Hodge numbers that exceed this bound. We summarize the theoretical and practical obstacles to a complete enumeration of all possible EFS Calabi-Yau threefolds and fourfolds, including those with small Hodge numbers, using this approach.Comment: 44 pages, 5 tables, 5 figures; v2: minor corrections; v3: minor corrections, moved figure; v4: typo in Table 2 correcte

A first step toward higher order chain rules in abelian functor calculus

One of the fundamental tools of undergraduate calculus is the chain rule. The notion of higher order directional derivatives was developed by Huang, Marcantognini, and Young, along with a corresponding higher order chain rule. When Johnson and McCarthy established abelian functor calculus, they proved a chain rule for functors that is analogous to the directional derivative chain rule when $n = 1$. In joint work with Bauer, Johnson, and Riehl, we defined an analogue of the iterated directional derivative and provided an inductive proof of the analogue to the chain rule of Huang et al. This paper consists of the initial investigation of the chain rule found in Bauer et al., which involves a concrete computation of the case when $n=2$. We describe how to obtain the second higher order directional derivative chain rule for abelian functors. This proof is fundamentally different in spirit from the proof given in Bauer et al. as it relies only on properties of cross effects and the linearization of functors

Principles of karmic accounting: How our intuitive moral sense balances rights and wrongs

We are all saints and sinners: Some of our actions benefit other people, while other actions harm people. How do people balance moral rights against moral wrongs when evaluating others’ actions? Across 9 studies, we contrast the predictions of three conceptions of intuitive morality—outcome- based (utilitarian), act-based (deontologist), and person-based (virtue ethics) approaches. Although good acts can partly offset bad acts—consistent with utilitarianism—they do so incompletely and in a manner relatively insensitive to magnitude, but sensitive to temporal order and the match between who is helped and harmed. Inferences about personal moral character best predicted blame judgments, explaining variance across items and across participants. However, there was modest evidence for both deontological and utilitarian processes too. These findings contribute to conversations about moral psychology and person perception, and may have policy implications

Belief digitization in economic prediction

Economic choices depend on our predictions of the future. Yet, at times predictions are not based on all relevant information, but instead on the single most likely possibility, which is treated as though certainly the case— that is, digitally. Two sets of studies test whether this digitization bias would occur in higher-stakes economic contexts. When making predictions about the future asset prices, participants ignored conditional probability information given relatively unlikely events and relied entirely on conditional probabilities given the more likely events. This effect was found for both financial aggregates and individual stocks, for binary predictions about the direction and continuous predictions about expected values, and even when the “unlikely” event explicitly had a probability as high as 30%; further, it was not moderated by investing experience. Implications for behavioral finance are discussed

Optimality bias in moral judgment

We often make decisions with incomplete knowledge of their consequences. Might people nonetheless expect others to make optimal choices, despite this ignorance? Here, we show that people are sensitive to moral op- timality: that people hold moral agents accountable depending on whether they make optimal choices, even when there is no way that the agent could know which choice was optimal. This result held up whether the outcome was positive, negative, inevitable, or unknown, and across within-subjects and between-subjects de- signs. Participants consistently distinguished between optimal and suboptimal choices, but not between sub- optimal choices of varying quality — a signature pattern of the Efficiency Principle found in other areas of cognition. A mediation analysis revealed that the optimality effect occurs because people find suboptimal choices more difficult to explain and assign harsher blame accordingly, while moderation analyses found that the effect does not depend on tacit inferences about the agent's knowledge or negligence. We argue that this moral optimality bias operates largely out of awareness, reflects broader tendencies in how humans understand one another's behavior, and has real-world implications

Optimality bias in moral judgment

We often make decisions with incomplete knowledge of their consequences. Might people nonetheless expect others to make optimal choices, despite this ignorance? Here, we show that people are sensitive to moral op- timality: that people hold moral agents accountable depending on whether they make optimal choices, even when there is no way that the agent could know which choice was optimal. This result held up whether the outcome was positive, negative, inevitable, or unknown, and across within-subjects and between-subjects de- signs. Participants consistently distinguished between optimal and suboptimal choices, but not between sub- optimal choices of varying quality — a signature pattern of the Efficiency Principle found in other areas of cognition. A mediation analysis revealed that the optimality effect occurs because people find suboptimal choices more difficult to explain and assign harsher blame accordingly, while moderation analyses found that the effect does not depend on tacit inferences about the agent's knowledge or negligence. We argue that this moral optimality bias operates largely out of awareness, reflects broader tendencies in how humans understand one another's behavior, and has real-world implications

Good decisions, good causes: Optimality as a constraint on attribution of causal responsibility

How do we assign causal responsibility for others’ decisions? The present experiments examine the possibility that an optimality constraint is used in these attributions, with agents considered less responsible for outcomes when the decisions that led to those outcomes were suboptimal. Our first two experiments investigate scenarios in which agents are choosing among multiple options, varying the efficacy of the forsaken alternatives to examine the role of optimality in attributing responsibility. Experiment 3 tests whether optimality considerations also play a role in attribution of causality more generally. Taken together, these studies indicate that optimality constraints are used in lay decision theory and in causal judgment

Behaviorist thinking in judgments of wrongness, punishment, and blame

Moral judgment depends upon inferences about agents’ beliefs, desires, and intentions. Here, we argue that in addition to these factors, people take into account the moral optimality of an action. Three experiments show that even agents who are ignorant about the nature of their moral decisions are held accountable for the quality of their decision—a kind of behaviorist thinking, in that such reasoning bypasses the agent’s mental states. In particular, whereas optimal choices are seen as more praiseworthy than suboptimal choices, decision quality has no further effect on moral judgments—a highly suboptimal choice is seen as no worse than a marginally suboptimal choice. These effects held up for judgments of wrongness and punishment (Experiment 1), positive and negative outcomes (Experiment 2), and agents with positive and negative intentions (Experiment 3). We argue that these results reflect a broader tendency to irresistibly apply the Efficiency Principle when explaining behavior