OR Pioneer Balinski Delivers Messenger Lectures on Representing, Electing and Ranking
Michel Balinski, Professor Emeritus, École Polytechnique and CNRS, Paris, presented three lectures discussing the mathematics of fairness, including apportioning seats (and kidneys), ranking candidates (and wines), and eliminating gerrymandering. Professor Balinski was introduced by Professor Louis Billera, a member of the Mathematics Department and the Field of Operations Research, who has posted abstracts, video and slides of the lectures. At Cornell Professor Robert Bland's course, ORIE 436, A Mathematical Examination of Fair Representation, covers several of the topics discussed by Professor Balinski.
|Professor Balinski, seen here with the original Gerrymander.|
Professor Balinski, a U.S. citizen, has been involved in seminal work in optimization and discrete mathematics beginning with his 1959 doctoral thesis. He is the founder of the Mathematical Programming Journal, won OR's Lanchester Prize in 1965, and has served as a mathematical consultant for major corporations. His work on the mechanisms discussed in the Messenger lectures began in the 1970's and continues unabated today.
In 1924, Hiram Messenger established a Cornell fund "to provide a course of lectures on the Evolution of Civilization for the special purpose of raising the moral standard of our political, business, and social life." Previous Messenger Lecturers include astronomer Sir Arthur Eddington, historian Carl Becker, physicist J. Robert Oppenheimer, philosopher Paul Tillich, statistician Jerzy Neyman, computer scientist Marvin Minsky, mathematician Roger Penrose, and poetry critic Helen Vendler.
The first lecture discussed proposals for apportioning representatives to the states in according to their respective numbers, a requirement of the U.S. Constitution. A fully proportional allocation of a fixed number of seats almost inevitably entails fractional representatives, so the problem is how to deal fairly with the fractions. Solutions were proposed by the likes of John Quincy Adams, Alexander Hamilton, Thomas Jefferson, Daniel Webster and others. Balinski defined fairness and discussed whether each of various methods is fair, concluding that the current method, due to Joseph Hill, does not pass the test. Moreover, the choice of allocation mechanism can impact the outcome: the 1876 presidential election, in which Tilden won the popular vote but Hayes became president by the electoral vote based on the apportionment mechanism of the day, would have come out differently had Webster's method, the only unbiased and fair method, been used.
In the second lecture, Professor Balinski turned to the problem of how to elect one among several candidates. In 2000 the popular vote in Florida determined the outcome in the electoral college. The presence of an 'irrelevant' candidate with too little support to hope for election influenced the outcome of the popular vote in Florida and hence the election. Voting schemes are usually predicated on the idea that voters have implictly ranked candidates in a preference list. Professor Balinski pointed out that when they have such 'lists of preference' Arrow's Social Choice Impossibility Theorem (for which Arrow won the Nobel Prize in economics) tells us that no voting mechanism exists that avoids the possibility that an irrelevant candidate can sway the outcome. Balinski proposed instead a mechanism by which voters assign a grade of a common language to each candidate: for example, "excellent", "very good", "good", "acceptable", "poor", "reject." The median grade across all voters determines the grade of each candidate; the candidate with the highest grade (subject to a tie-breaking mechanism) wins. The method has been used to evaluate wines in a French competition and was successfully tested in an experiment carried out in parallel with the 2007 French presidential election. According to Balinski it avoids the problem of the 'irrelevant candidates,' respects majority opinion, and avoids the possibility of voters impacting the outcome through strategic voting ("gaming" the system).
|Ithaca's voting district resembles a relative of the gerrymander, a 'Gerryphant', perhaps.|
The third lecture dealt with the practice known, since it was employed early in the 19th century by Governor Elbridge Gerry, as "gerrymandering". The name derives from the salamander-like creature cartoonist Elkanah Tisdale used to portray a resulting district of Massachusetts, seen behind Professor Balinski in the photo above.
Interactive computer programs now permit extremely fine tuning of district boundaries. Balinski showed that gerrymandering is inevitable despite the courts’ insistence that there be an equality of populations in each district, pointing out that the courts have rejected arguments based on other criteria. As a result, a majority in the House of Representatives can be determined by a minority of voters. Building on the concept of “coherence” introduced in the first lecture, he proposed a new mechanism, Fair Majority Voting. This approach entails allocating votes in proportion to the party votes in each state and then rescaling the candidate votes to determine which candidate should be seated in each district. The proposed procedure, which is now being used in the city and canton of Zürich, eliminates the rationale for gerrymandering by making every vote count.
The lectures provided a rich background in the history of the problems they dealt with, showing roots in the Talmud, the works of Aristotle, and Supreme Court decisions.