Fair Division :: Essays Papers

Fair Division The problem of how resources can be fairly distributed has remained at the forefront of political, academic, and social life for centuries. According to political scientist Steven J. Brams (1996) and mathematician Alan D. Taylor (1996), the issue of fair division can be traced back to the Hebrew Bible, with King Solomon’s proposal to divide a baby in two in order to appease the claims of two mothers. Within the last century, questions regarding the fair division and allocation of property have arisen throughout various spheres—divorce claims, estate settlements, assessments of taxes—and attempts to solve these dilemmas have increased as well (Brams & Taylor 1996). It is my intention with this essay to better understand this issue of fair division by looking at two permutations of the fair division problem. I would like to look at two existing methods—Divider-Chooser and the Method of Sealed Bids—and criteria—cooperation, rationality , privacy, symmetry—in order to examine the ways in which people have used mathematical devices to guarantee a fair share. However, it is also my intention with this essay to a introduce a new criteria—manipulation—to see how it coexists with the existing criteria, and how well it works in accordance with the two methods. One historical problem concerning a fair share has been the selection of a new king from a list of several candidates, such that each candidate receives a fair share at the chance to become king. According to Theodore P. Hill (2000), there exist many legends explaining attempts to solve this problem—Darius became king when his horse was the first to neigh at the city walls, and O’Neill became king under the rule that â€Å"he who first touches Irish soil will be monarch,† by chopping off his left hand and tossing it ashore ahead of his competitors. The problem with these methods was that they lacked a central organizing premise, such that each participant would be satisfied that they received a fair shot. Imagine that little Hank and little Johnny have just mowed the backyard for their parents. As a reward for their efforts, Hank and Johnny’s parents give them a box of pastries from the local bakery. There are muffins, à ©clairs, cookies, and even a few Russian teacakes. Fair Division :: Essays Papers Fair Division The problem of how resources can be fairly distributed has remained at the forefront of political, academic, and social life for centuries. According to political scientist Steven J. Brams (1996) and mathematician Alan D. Taylor (1996), the issue of fair division can be traced back to the Hebrew Bible, with King Solomon’s proposal to divide a baby in two in order to appease the claims of two mothers. Within the last century, questions regarding the fair division and allocation of property have arisen throughout various spheres—divorce claims, estate settlements, assessments of taxes—and attempts to solve these dilemmas have increased as well (Brams & Taylor 1996). It is my intention with this essay to better understand this issue of fair division by looking at two permutations of the fair division problem. I would like to look at two existing methods—Divider-Chooser and the Method of Sealed Bids—and criteria—cooperation, rationality , privacy, symmetry—in order to examine the ways in which people have used mathematical devices to guarantee a fair share. However, it is also my intention with this essay to a introduce a new criteria—manipulation—to see how it coexists with the existing criteria, and how well it works in accordance with the two methods. One historical problem concerning a fair share has been the selection of a new king from a list of several candidates, such that each candidate receives a fair share at the chance to become king. According to Theodore P. Hill (2000), there exist many legends explaining attempts to solve this problem—Darius became king when his horse was the first to neigh at the city walls, and O’Neill became king under the rule that â€Å"he who first touches Irish soil will be monarch,† by chopping off his left hand and tossing it ashore ahead of his competitors. The problem with these methods was that they lacked a central organizing premise, such that each participant would be satisfied that they received a fair shot. Imagine that little Hank and little Johnny have just mowed the backyard for their parents. As a reward for their efforts, Hank and Johnny’s parents give them a box of pastries from the local bakery. There are muffins, à ©clairs, cookies, and even a few Russian teacakes.