Win or Lose

http://www.newyorker.com/arts/critics/books/2010/07/26/100726crbo_books_gottlieb?currentPage=all

Approval voting, as used in the last round of old Venetian elections, is a rating system with just two grades: approved and not approved. In the late thirteenth century, cardinals began to use it to elect Popes, too, though they stopped in 1621, perhaps because combining it with the Holy Ghost’s two-thirds rule complicated matters. Approval voting was revived in the nineteen-seventies, when several American mathematicians and political scientists independently began to study it. (It is explored and defended by the N.Y.U. game theorist Steven Brams in his 2008 study “Mathematics and Democracy.”) Campaigns to introduce approval voting for public elections have so far failed, but many mathematicians seem to like the way it works. The American Mathematical Society and the Mathematical Association of America, among others, use it for internal elections, though the larger Institute of Electrical and Electronics Engineers, which also adopted it, came to have second thoughts.

Range and approval voting deal neatly with the problem of vote-splitting: if a voter likes Nader best, and would rather have Gore than Bush, he or she can approve Nader and Gore but not Bush. Above all, their advocates say, both schemes give voters more options, and would elect the candidate with the most over-all support, rather than the one preferred by the largest minority. Both can be modified to deliver forms of proportional representation.