Column by Marcelo Viana in Folha: Making decisions is difficult.
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The documentary "Edifício Master," directed by Eduardo Coutinho and released in 2002, portrays the daily life of a building in Copacabana, Rio de Janeiro. With 12 floors and 500 residents in 276 adjoining apartments (23 per floor!), the Master is a microcosm of the "Little Princess of the Sea," with its glories and miseries. The crew lived in the building for three weeks, filming and interviewing residents. Some testimonies are hilarious, others dramatic. All are profoundly human.
One of the interviews is with the building manager, who rescued the building from a long period of disrepair. When asked how he manages all the problems, he replies with a slight smile: "I use Piaget a lot. When that doesn't work, I resort to Pinochet." These are references to the Swiss psychologist Jean Piaget (1896-1980), a pioneer in the study of child development, and to the Chilean dictator Augusto Pinochet (1915-2006), responsible for the worst period of human rights repression in his country.
I keep imagining what the Master condominium meetings will be like, and how math could help. Let's suppose the following situation, which doesn't seem very complicated. The condominium needs to elect a committee of three people to draft the new bylaws. There are exactly three candidates, which simplifies things. But the list needs to be ordered, because the first will be the committee chairman – very prestigious! –, the second will be a mere vice-chairman, and the third will be the secretary – who will have all the work.
This is a type of problem that occurs in many other situations, of course. For example, at IMPA (Institute of Pure and Applied Mathematics) we have to deal with situations like this when hiring researchers or deciding on awards or scholarships for students.
The Master building manager suggests that each of the 276 residents vote, indicating their order of preference among the three candidates, and so it is done. Now it is necessary to transform the 276 rankings proposed by the residents into a collective ranking, representative of the entire building. If everyone had indicated the same preference, it would be very easy: unanimous decision and everyone goes home early. But when does a condominium meeting ever have unanimity?!?
In this difficult time, our dynamic building manager does what any enlightened administrator would do: he calls in a mathematician for help, of course. The task is to define a fair, impartial, and impersonal rule to find the preference of the entire condominium based on those expressed by the residents. The mathematician immediately proposes that the following principles be adopted.
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