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FLYING WITH PAMBO
I read with interest your article about Pam Melroy (“Mission Control,” September/October 2008). I was fortunate to have firsthand experience of Pam’s leadership style and effectiveness as a crew member on that mission aboard Discovery. Pambo (as we call her in the astronaut office) is a great commander, and it’s true–our crew chemistry was fantastic, with plenty of laughing and having a great time. Pambo set the tone for the crew by making sure that our families came first. By emphasizing the human and personal aspect of our lives and careers, we were able to fully focus on our mission objectives when necessary.

I was the only member of the Discovery crew scheduled to stay at the International Space Station for four months. One of the worst moments of the flight for me was when we closed the hatch and I had to say good-bye to Pambo and the rest of the crew. We had so much fun in our year and a half of training, joking, and laughing together that I knew I would miss my “on-orbit family” dearly. I consider my time training and flying with Pambo one of the best–and most enjoyable–periods of my career.

Daniel Tani ‘84, SM ‘88
Houston, TX

APPROVAL VOTING WORTH CONSIDERING
I was pleased to see “Scoring the Candidates” (September/October 2008), which points out mathematical flaws in the current U.S. system of voting (for example, that a candidate preferred by the majority of voters can be “squeezed out” by more extreme candidates) and describes a better method known as range voting.

Range voting is indeed one better way. Another well-analyzed and simple alternative is approval voting, in which voters cast votes for all candidates they approve of, and the candidate with the most votes wins. (Steven J. Brams ‘62 discusses approval voting at alum.mit.edu/news/WhatMatters/Archive/200211.)

Approval voting can be thought of as a version of range voting, where the range is restricted to 0 or 1. But is it clear that a larger range–say, 0 to 100–is better?

From a game theory standpoint, there is no difference between approval voting and range voting for “rational” voters, who maximize their vote’s count toward a desirable outcome. A single vote in a range from 0 to 100 can also be thought of as 100 votes of 0 or 1. But if the optimum choice is to vote “1” on one of the 100 votes, why not vote “1” on the other 99? So the hypothetical rational voter would rank all the candidates 0 or 100. (Obviously, not all voters would be rational, and some would aim to express an opinion rather than maximize an outcome.)

Since the two systems are functionally equivalent, every advocate of approval voting should be equally in favor of range voting.

Geoffrey A. Landis ‘77
Berea, OH

WOULDN’T BORDA BE BETTER?
The authors of “Scoring the Candidates” are quite correct that plurality voting is a poor method when there are more than two candidates. However, they seem to be unaware that in the 1990s, mathematicians analyzed voting systems and found that Arrow’s theorem does not mean there are no good voting methods; rather, the hypotheses of Arrow’s theorem are not as reasonable as they at first appear. We also now know that the best voting system is not range voting but a version of rank-order voting known as the Borda count (this system is often used to rank college football teams by polling coaches). If we are going to change our voting system (as we should), let’s change it to the best system.

For more information on voting systems, I recommend Donald G. Saari’s website: www.math.uci.edu/~dsaari/.

David J. Marcus, PhD ‘83
Somerville, MA

Authors Alan T. Sherman, PhD ‘87, Warren D. Smith ‘84, and Richard T. Carback III reply:
Marcus advocates the Borda count election method, citing work by Donald Saari. But Saari’s notions of “best” are not based on utility, and Saari only shows that Borda is “best” among weighted positional methods, a small subclass of rank-order systems excluding range voting. Experiments show that range voting outperforms Borda, using utility-based yardsticks, for honest and especially for strategic voters. This is unsurprising given that range voting becomes Borda voting when strength-of-preference information in range votes is erased. When voters attempt to act strategically, the Borda method often yields wildly unreasonable results (for example, all front-runners can lose). What’s more, Borda is more complicated than range voting and can’t handle write-ins. To learn more, go to rangevoting.org/BordaExec.html and rangevoting.org/DonSaari.html.

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Credit: Courtesy of Daniel Tani

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