The drift-diffusion model (DDM) is a model of sequential sampling with diffusion signals, where the decision maker accumulates evidence until the process hits either an upper or lower stopping boundary and then stops and chooses the alternative that corresponds to that boundary. In perceptual tasks, the drift of the process is related to which choice is objectively correct, whereas in consumption tasks, the drift is related to the relative appeal of the alternatives. The simplest version of the DDM assumes that the stopping boundaries are constant over time. More recently, a number of papers have used nonconstant boundaries to better fit the data. This paper provides a statistical test for DDMs with general, nonconstant boundaries. As a by-product, we show that the drift and the boundary are uniquely identified. We use our condition to nonparametrically estimate the drift and the boundary and construct a test statistic based on finite samples.
We analyze how to optimally engage in social distancing in order to minimize the spread of an infectious disease. We identify conditions under which any optimal policy is single-peaked, i.e., first engages in increasingly more social distancing and subsequently decreases its intensity. We show that an optimal policy might delay measures that decrease the transmission rate substantially to create herd-immunity and that engaging in social distancing sub-optimally early can increase the number of fatalities. Finally, we find that optimal social distancing can be an effective measure and can substantially reduce the death rate of a disease.
We analyze how to optimally engage in social distancing (SD) in order to minimize the spread of an infectious disease. We identify conditions under which the optimal policy is single-peaked, i.e., first engages in increasingly more social distancing and subsequently decreases its intensity. We show that the optimal policy might delay measures that decrease the transmission rate substantially to create “herd-immunity” and that engaging in social distancing sub-optimally early can increase the number of fatalities. Finally, we find that optimal social distancing can be an effective measure in substantially reducing the death rate of a disease.
A key part of decentralized consensus protocols is a procedure for random selection, which is the source of the majority of miners cost and wasteful energy consumption in Bitcoin. We provide a simple economic model for random selection mechanism and show that any PoW protocol with natural desirable properties is outcome equivalent to the random selection mechanism used in Bitcoin.
Bitcoin’s main innovation lies in allowing a decentralized system that relies on anonymous, profit driven miners who can freely join the system. We formalize these properties in three axioms: anonymity of miners, no incentives for miners to consolidate, and no incentive to assuming multiple fake identities. This novel axiomatic formalization allows us to characterize which other protocols are feasible: Every protocol with these properties must have the same reward scheme as Bitcoin. This implies an impossibility result for risk-averse miners: no protocol satisfies the aforementioned constraints simultaneously without giving miners a strict incentive to merge. Furthermore, any protocol either gives up on some degree of decentralization or its reward scheme is equivalent to Bitcoin’s.
We explore conclusions a person draws from observing society when he allows for the possibility that individuals' outcomes are affected by group-level discrimination. Injecting a single non-classical assumption, that the agent is overconfident about himself, we explain key observed patterns in social beliefs, and make a number of additional predictions. First, the agent believes in discrimination against any group he is in more than an outsider does, capturing widely observed self-centered views of discrimination. Second, the more group memberships the agent shares with an individual, the more positively he evaluates the individual. This explains one of the most basic facts about social judgments, in-group bias, as well as "legitimizing myths" that justify an arbitrary social hierarchy through the perceived superiority of the privileged group. Third, biases are sensitive to how the agent divides society into groups when evaluating outcomes. This provides a reason why some ethnically charged questions should not be asked, as well as a potential channel for why nation-building policies might be effective. Fourth, giving the agent more accurate information about himself increases all his biases. Fifth, the agent is prone to substitute biases, implying that the introduction of a new outsider group to focus on creates biases against the new group but lowers biases vis a vis other groups. Sixth, there is a tendency for the agent to agree more with those in the same groups. As a microfoundation for our model, we provide an explanation for why an overconfident agent might allow for potential discrimination in evaluating outcomes, even when he initially did not conceive of this possibility.