In McLean and Postlewaite (Econometrica 56, 1992, p. 2421), we analyzed pure exchange economies with asymmetrically informed agents. We defined a notion of informational size and showed that, when the aggregate information of all agents resolves nearly all the uncertainty regarding the state of nature, the conflict between incentive compatibility and (ex post) efficiency can be made small if ag...

In chapter 9 of Knowledge and its Limits, Timothy Williamson argues for the thesis that the evidence that a subject has is constituted by propositions known by the subject (a thesis that he summarizes in the equation E=K). Moreover, Williamson also argues that whatever justifies a subject in believing a proposition is part of that subject’s evidence, and thus that only propositions that a subje...

In contrast to a focus on efficiency, we advocate aggressive usage of available resources. This view is embodied in what we call the Buffet principle: continue using more resources as long as the marginal cost can be driven lower than the marginal benefit. We illustrate through several examples how this seemingly obvious principle is not adhered to by many common designs and how its application...

Uncertainty is a state of lack of certainty, where having incomplete knowledge can make it impossible to describe the outcome. There are many challenges that occur due to uncertainty. Uncertainty in events can cause losses of data, providing inaccurate data, noisy output. Thus the need to handle uncertainty is essential. This paper represents an outline of various methods through which the unce...

For cancers with more than one risk factor, the sum of probabilistic estimates of the number of cancers attributable to each individual factor may exceed the total number of cases observed when uncertainties about exposure and dose-response for some factors is high. In this study we outline a method to bound the fraction of lung cancer fatalities not attributed to specific wellstudied causes in...

We establish an uncertainty principle over arbitrary finite groups, generalizing those of Donoho, Stark and Meshulam. Specifically, we show that if Π is a projection operator on the group algebra C[G] that commutes with projection onto each group element, and Π̂ is a projection operator that commutes with the right G-action on C[G], then ‖Π Π̂‖2 ≤ rk Π× rk Π̂/|G|.

The revelation principle asserts that every outcome brought by a mechanism is realized by a truthful direct mechanism. The present paper investigates the regularity conditions of these two mechanisms in the continuous space of the agent’s type. It questions what regularity condition a general mechanism confers upon a direct mechanism through the revelation principle. By so doing, we elucidate t...

Wormholes have been advanced as both a method for circumventing the limitations of the speed of light as well as a means for building a time machine (to travel to the past). Thus it is argued that General Relativity may allow both of these possibilities. In this note I argue that traversable wormholes connecting otherwise causally disconnected regions, violate two of the most fundamental princi...