How Democracy Resolves Conflict in Difficult Games
Steven Brams '62, SB '62, Professor of Politics, New York University
Description: Using game theory, and with some help from the Bible, Steven Bramsargues that voting can resolve certain kinds of conflicts.
He explores in detail the classic game Prisoner's Dilemma. In his version, players must choose whether or not to contribute to the renovation of a public park. In a two"person variation of the game, in which Brams posits a rich person as one player, and the public as the other, "each person has an incentive to a free ride." The dominant strategy for each, he says, is not to contribute, and let the other pay for the public good. Then Brams reframes this game,with the addition of voting. With two persons, a majority means both must vote to finance the park for the renovation to happen. One vote for financing the park won't cut it. "You go from non"cooperative to cooperative as a dominant strategy, by allowing voting to determine the outcome," says Brams.
To illustrate a multiple, or N"person version of Prisoner's Dilemma, Brams turns to the Old Testament story of Moses after Mount Sinai. Upon Moses' return with the Ten Commandments, the Israelites are worshiping idols, and God threatens to destroy them. Moses asks the Israelites to choose between idolatry and the one God. Those who do not commit to the God of Israel are killed. In Brams' view, Moses took a gamble in a kind of referendum that the majority would vote his way, and "to prevent defections from the outcome, Moses deemed it necessary that those who chose (idolatry) be decimated." Says Brams, "This is a gruesome way to achieve consensus but hardly unknown in recent times."
When games become voting games, cooperative outcomes take on a new status, says Brams. "The idea is, if you don't have a sufficient number, nobody pays, and everybody suffers. If you have a sufficient number, everybody paysand you get the cooperative outcome. There aren't in"between outcomes where some pay and some don't, and the ones that don't pay make out like bandits. That's what voting does -- it prevents that banditry."
In countries like the U.S., when a government can "credibly commit to providing a public good that a majority supports, the solution that democracy provides is compelling." But in situations where crime or corruption is the rule -- say, in some developing nations -- there must be assurances that the cooperative outcome the majority supports will really be implemented, says Brams.
About the Speaker(s): Steven Brams' most recent book is Mathematics and Democracy: Designing Better Voting and Fair"Division Procedures (Princeton University Press, 2008). He has also written The Win"Win Solution: Guaranteeing Fair Shares to Everybody, with Alan D. Taylor; Fair Division: From Cake"Cutting to Dispute Resolution, with Alan D. Taylor; and Theory of Moves.
Bram has been teaching at NYU since 1969. Previously, he was an assistant professor at Syracuse University, a research associate for the Institute for Defense Analyses, and an executive trainee with the Office of the Secretary of Defense.Bram received his Ph.D. from Northwestern University in 1966.
Host(s): School of Engineering, Materials Processing Center
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