Telescope Time Without Tears: A Distributed Approach to Peer Review

The procedure that is currently employed to allocate time on telescopes is horribly onerous on those unfortunate astronomers who serve on the committees that administer the process, and is in danger of complete collapse as the number of applications steadily increases. Here, an alternative is presented, whereby the task is distributed around the astronomical community, with a suitable mechanism design established to steer the outcome toward awarding this precious resource to those projects where there is a consensus across the community that the science is most exciting and innovative.Comment: 9 pages, accepted for publication in Astronomy & Geophysic

Symmetry of Nonparametric Statistical Tests on Three Samples

Problem statement: Many different nonparametric statistical procedures can be used to analyze ranked data. Inconsistencies among the outcomes of such procedures can occur when analyzing the same ranked data set. Understanding why these peculiarities can occur is imperative to providing an accurate analysis of the ranking data. In this context, this study addressed why inconsistent outcomes can occur and which types of data structures cause the different procedures to yield different outcomes. Approach: Appropriate properties were identified and developed to explain why different methods can define different rankings of three samples with the same data. The approach identifies certain symmetry structures that are implicitly contained within the data and analyzes how the procedures utilize these structures to produce an outcome. Results: We proved that all possible differences among the nonparametric rules are caused because different rules place different levels of emphasis on the specified symmetry configurations of data. Our findings explain and characterize why different procedures can output different results using the same data set. Conclusion: This study therefore served as crucial step in deciding which nonparametric procedure to use when analyzing ranked data. In addition, it serves as the building block to defining new techniques to analyze rankings. Because different procedures use different aspects of the data in different ways, then one may determine the choice of analysis procedure based on what parts of the data one deems important

Sufficient Statistics

It is shown how bordered hessians, sufficient statistics, and integrability conditions from utility theory are closely related to the characterization theorems for mechanism design. Then, new results are outlined about a theory for implicitly defined objective functions, about how to incorporate different kinds of information sets modeling, say, externalities into the theory, and about the actual construction of economic mechanisms.

Connecting and Resolving Sen's and Arrow's Theorems

As shown, the source of Sen's and Arrow's impossibility theorems is that Sen's Liberal condition and Arrow's IIA counter the critical assumption that voters' have transitive preferences. As this allows transitive and certain cyclic preferences to become indistinguishable, the Pareto condition forces cycles. Once the common cause of these perplexing conclusions is understood, resolutions are immediate.

Symmetry Extensions of 'Neutrality' I: Advantage to the Condorcet Loser

This is the first of three papers introducing a theory for positional voting methods that determines all possible election rankings and relationships that ever could occur with a profile over all possible subsets of candidates for any specified choices of positional voting methods. As such, these results extend to all positional voting systems what was previously possible only for the Borda Count and the plurality voting systems. In this first part certain mathematical symmetries based on neutrality are used 1) to generalize the basic properties that cause the desired features of the Borda Count and 2) to describe classes of positional voting methods with new types of election relationships among the election outcomes. Some of these relationships generalize the well-known results about the positioning of a Condorcet winner/loser within a Borda ranking, but now it is possible for the Condorcet loser, rather than the winner, to have the advantage to win certain positional elections. Included among the results are axiomatic characterizations of many positional voting methods.