Single-Elimination Brackets Fail to Approximate Copeland Winner

Single-elimination (SE) brackets appear commonly in both sports tournaments and the voting theory literature. In certain tournament models, they have been shown to select the unambiguously-strongest competitor with optimum probability. By contrast, we reevaluate SE brackets through the lens of approximation, where the goal is to select a winner who would beat the most other competitors in a round robin (i.e., maximize the Copeland score), and find them lacking. Our primary result establishes the approximation ratio of a randomly-seeded SE bracket is 2^{- Theta(sqrt{log n})}; this is underwhelming considering a 1/2 ratio is achieved by choosing a winner uniformly at random. We also establish that a generalized version of the SE bracket performs nearly as poorly, with an approximation ratio of 2^{- Omega(sqrt[4]{log n})}, addressing a decade-old open question in the voting tree literature

Growth and emigration of white shimp, Litopenaeus vannamei, in the Mar Muerto Lagoon, Southern Mexico

Microcohorts of white shrimp, Litopenaeus vannamei, were sampled with a cast net at fortnightly intervals in the Mar Muerto Lagoon, Southern Mexico. Shrimp recruited to the lagoon throughout the sampling period (January to August 1993). Mean growth rates of microcohorts ranged from 0.21 to 1.21 mm total length (TL) per day. Juvenile shrimp mainly between the sizes of 70 to 80 mm TL emigrated from the lagoon. Growth and the onset of emigration appeared to be related to water salinity