The reaction of Professors Alvarez, Ansolabehere, and Stewart to my study of the voting technologies in the states of Pennsylvania and Wyoming was instructive in pointing out how differing perspectives, both among researchers and among state election administrators, make the task of understanding the dynamics of our electoral system a complex and difficult one. Fortunately, we have access to vehicles that allow us to share the knowledge that we gain along our paths of research. Therefore, I appreciate the opportunity to take advantage of their comments in an effort to add greater depth and detail to the portrait of the electoral system in the United States that we, jointly as researchers, are attempting to build.

Professors Alvarez et al. point to a concern that they have with the small N available for research purposes when studying the electoral phenomena within particular states such as those of Pennsylvania and Wyoming, the ones that I chose to study. They argue that" at least 1500 observations are needed to measure the sorts of effects involved using simple means and correlations." Formulae for calculating sample size indicate this to be the number necessary to gauge a level of precision that they have predetermined acceptable. Normally, a confidence level of 95% is determined to be a comfortable one. However, most national pollsters usually rely on well less than 1,500 observations as their baseline sample size, although most of us would agree that 1,500 or so may be preferable. All of this being said, however, a sample size of less than 1,500 is not readily achievable when studying intrastate variations and may well be a price worth paying for achieving full control of a variable that might be quite confounding in larger sample sizes more readily achievable in cross-state studies of counties. The same formulae for calculating sample size can be used to obtain a 95% confidence level, or a 95% certainty that you are correct in your estimation of the results. In the case of Pennsylvania, that number is 57 counties based on a population of 67 counties.(1) I used 58 counties, as correctly pointed out by the CalTech/MIT team. In the case of Wyoming, use of the sample size calculation formula is not necessary since the entire population is being studied.