Is Determinism with regard to the Spheres of Law or Nature Consistent?

Probably the most important problem for lawyers is the relationship between cases that confront them and the rules of the legal order that they have to apply. Lawyers want to know whether a certain case falls under a certain rule or, more generally, to which set of cases a certain rule has to be applied. If they are able to answer this question, then those lawyers can tell you fairly precisely what the content of a certain rule is

Parallel Peeling Algorithms

The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k are removed until there are no vertices of degree less than k left. The remaining hypergraph is known as the k-core. In this paper, we analyze parallel peeling processes, where in each round, all vertices of degree less than k are removed. It is known that, below a specific edge density threshold, the k-core is empty with high probability. We show that, with high probability, below this threshold, only (log log n)/log(k-1)(r-1) + O(1) rounds of peeling are needed to obtain the empty k-core for r-uniform hypergraphs. Interestingly, we show that above this threshold, Omega(log n) rounds of peeling are required to find the non-empty k-core. Since most algorithms and data structures aim to peel to an empty k-core, this asymmetry appears fortunate. We verify the theoretical results both with simulation and with a parallel implementation using graphics processing units (GPUs). Our implementation provides insights into how to structure parallel peeling algorithms for efficiency in practice.Comment: Appears in SPAA 2014. Minor typo corrections relative to previous versio

The Fake News Effect: Experimentally Identifying Motivated Reasoning Using Trust in News

Motivated reasoning posits that people distort how they process new information in the direction of beliefs they find more attractive. This paper introduces a novel experimental paradigm that is able to portably identify motivated reasoning from Bayesian updating across a variety of factual questions; the paradigm analyzes how subjects assess the veracity of information sources that tell them the median of their belief distribution is too high or too low. A Bayesian would infer nothing about the source veracity from this message, but motivated reasoners would infer that the source were more truthful if it reported the direction that they find more attractive. I find novel evidence for politically-motivated reasoning about immigration, income mobility, crime, racial discrimination, gender, climate change, gun laws, and the performance of other subjects. Motivated reasoning from messages on these topics leads people's beliefs to become more polarized, even though the messages are uninformative

Do People Engage in Motivated Reasoning to Think the World Is a Good Place for Others?

Motivated reasoning is a bias in inference in which people distort their updating process in the direction of more attractive beliefs. Prior work has shown how motivated reasoning leads people to form overly "positive" beliefs that also serve to bolster one's self-image in domains such as intelligence, prosociality, and politics. In this paper, I study whether positivity-motivated reasoning persists in domains where self-image does not play a role. In particular, I analyze whether individuals motivatedly reason to think that the world is a better place for others. Building off of the design from Thaler (2020), I conduct a large online experiment to test for positivity-motivated reasoning on issues such as cancer survival rates, others' happiness, and infant mortality. I find no systematic evidence for positivity-motivated or negativity-motivated reasoning, and can rule out modest effects. Positivity is not a sufficient condition for motivated reasoning

Continuous Time Channels with Interference

Khanna and Sudan \cite{KS11} studied a natural model of continuous time channels where signals are corrupted by the effects of both noise and delay, and showed that, surprisingly, in some cases both are not enough to prevent such channels from achieving unbounded capacity. Inspired by their work, we consider channels that model continuous time communication with adversarial delay errors. The sender is allowed to subdivide time into an arbitrarily large number $M$ of micro-units in which binary symbols may be sent, but the symbols are subject to unpredictable delays and may interfere with each other. We model interference by having symbols that land in the same micro-unit of time be summed, and we study $k$-interference channels, which allow receivers to distinguish sums up to the value $k$. We consider both a channel adversary that has a limit on the maximum number of steps it can delay each symbol, and a more powerful adversary that only has a bound on the average delay. We give precise characterizations of the threshold between finite and infinite capacity depending on the interference behavior and on the type of channel adversary: for max-bounded delay, the threshold is at D_{\text{max}}=\ThetaM \log\min{k, M})), and for average bounded delay the threshold is at $D_{\text{avg}} = \Theta(\sqrt{M \cdot \min\{k, M\}})$.Comment: 7 pages. To appear in ISIT 201