Truthful approximations to range voting

We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare maximization in this setting. With m being the number of alternatives, we exhibit a randomized truthful-in-expectation ordinal mechanism implementing an outcome whose expected social welfare is at least an Omega(m^{-3/4}) fraction of the social welfare of the socially optimal alternative. On the other hand, we show that for sufficiently many agents and any truthful-in-expectation ordinal mechanism, there is a valuation profile where the mechanism achieves at most an O(m^{-{2/3}) fraction of the optimal social welfare in expectation. We get tighter bounds for the natural special case of m = 3, and in that case furthermore obtain separation results concerning the approximation ratios achievable by natural restricted classes of truthful-in-expectation mechanisms. In particular, we show that for m = 3 and a sufficiently large number of agents, the best mechanism that is ordinal as well as mixed-unilateral has an approximation ratio between 0.610 and 0.611, the best ordinal mechanism has an approximation ratio between 0.616 and 0.641, while the best mixed-unilateral mechanism has an approximation ratio bigger than 0.660. In particular, the best mixed-unilateral non-ordinal (i.e., cardinal) mechanism strictly outperforms all ordinal ones, even the non-mixed-unilateral ordinal ones

R&D Investments with Competitive Interactions

In this article we develop a model to analyze patent-protected R&D investment projects when there is (imperfect) competition in the development and marketing of the resulting product. The competitive interactions that occur substantially complicate the solution of the problem since the decision maker has to take into account not only the factors that affect her/his own decisions, but also the factors that affect the decisions of the other investors. The real options framework utilized to deal with investments under uncertainty is extended to incorporate the game theoretic concepts required to deal with these interactions. Implementation of the model shows that competition in R&D, in general, not only increases production and reduces prices, but also shortens the time of developing the product and increases the probability of a successful development. These benefits to society are countered by increased total investment costs in R&D and lower aggregate value of the R&D investment projects.

Nounself pronouns: 3rd person personal pronouns as identity expression

This paper is an examination of and attempt at a preliminary definition of nounself pronouns, which are a large number of newly invented English 3rd person personal pronouns that have not been previously studied. The pronouns are created and used primarily by a virtual community on the blogging platform tumblr.com, with the first occurrence of a nounself pronoun in late 2013. The study is based on data from 134 responses to a questionnaire written by the author, distributed through tumblr.com, as well as on email-based interviews with three respondents who volunteered to be interviewed.  Analysis of the data suggests that the pronouns are used to express, explore, and negotiate the identities of the respondents, in particular in relation to gender identities

On Data Structures and Asymmetric Communication Complexity

In this paper we consider two party communication complexity when the input sizes of the two players differ significantly, the ``asymmetric'' case. Most of previous work on communication complexity only considers the total number of bits sent, but we study tradeoffs between the number of bits the first player sends and the number of bits the second sends. These types of questions are closely related to the complexity of static data structure problems in the cell probe model. We derive two generally applicable methods of proving lower bounds, and obtain several applications. These applications include new lower bounds for data structures in the cell probe model. Of particular interest is our ``round elimination'' lemma, which is interesting also for the usual symmetric communication case. This lemma generalizes and abstracts in a very clean form the ``round reduction'' techniques used in many previous lower bound proofs

Circuit Depth Relative to a Random Oracle

The study of separation of complexity classes with respect to random oracles was initiated by Bennett and Gill and continued by many other authors. Wilson defined relativized circuit depth and constructed various oracles A for which   P^A ¬ NC^A NC^A_k ¬ NC^A_k+varepsilon, AC^A_k ¬ AC^A_k+varepsilon, AC^A_k ¬ subset= AC^A_k+1-varepsilon, and NC^A_k not subset= AC^A_ k-varepsilon,for all positive rational k and varepsilon, thus separating those classes for which no trivial argument shows inclusion. In this note we show that as a consequence of a single lemma, these separations (or improvements of them) hold with respect to a random oracle A

On-Line Reevaluation of Functions

Given a finite set S and a function f : S^n -> S^m, we consider the problem of making a data structure which maintains a value of x in S^n and allows us to efficiently change an arbitrary coordinate of x and efficiently evaluate f_i(x) for arbitrary i. We both examine the problem for specific choices of f and relate the possibility of an efficient solution to general properties of f: expressibility as a formula, space complexity and time complexity