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Doing so dismisses crucial information about voters' preferences; reinserting the lost information into the system leads to Borda's method. Szpiro also adopts the unfortunate but standard approach whereby after uncovering a negative property for a method, it is continually used to discredit, rather than judge, the rule.

This regrettable misuse of perfection becomes an enemy of progress. To underscore the reality that all rules have many strengths and weaknesses, I jokingly offer: "Tell me which voting system to trash and which one to promote; for a price, I will create properties that support your objectives. With the above caveats and a warning that Szpiro often uses "majority" rather than "plurality", I recommend the book as an interesting, selective introduction into the complexities of voting reform.

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Please login or register to read this article. Register to continue Get a month's unlimited access to THE content online. Once registered you can read a total of 3 articles each month, plus: Sign up for the editor's highlights Receive World University Rankings news first Get job alerts, shortlist jobs and save job searches Participate in reader discussions and post comments Register. In time, the infighting over the apportionment methods spread form the Congress to the academia. After the Census, the Congress failed to choose between two methods on the table: Webster's of equal major fractions and Hill's of equal proportions.

Their proponents became divided between the "Cornell" and "Harvard" schools. Wilcox was a Cornell professor of social sciences and statistics, while E. Huntington was a professor mathematics and mechanics at Harvard. Szpiro narrates the story of the often acrimonious argumentation in succulent detail showing his humorous side where humor is called for. As became obvious by early , the feuding politicians and their academic counterparts were unable to reach an agreement. The method was eventually adopted but political consideration did not let the matter rest. In , another NAS committee has been formed led by Luther Eisenhart member of the previous study group.

Risk-limiting Audits for Nonplurality Elections

The committee included two other Princeton mathematicians Marston Morse and the illustrous John von Neumann. The committee stuck with the HH method. The twelfth chapter of the book is devoted essentially to the result of Michel L.

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Balinski and H. Peyton Young. Balinski and Young proved that the only apportionment methods that avoid paradoxes are the so called divisor methods. Among the methods mentioned in this review, the Jefferson, WW, and its bitter rival HH all fall into this category. They also looked into the matter of fair representation: "a state should receive no more and no less than its fair share of seats. Hamilton's method does, but it also leads to various paradoxes.

Their third result concerns the possible tendency of a method to produce apportionment that consistently favors either small or large states. What they found was that "From among all methods that use divisors, the Webster-Wilcox method is the only one that is practically unbiased. Stay informed and spot emerging risks and opportunities with independent global reporting, expert commentary and analysis you can trust.

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