Vorlesung Analysis 2, 38. Stunde (Gastvortrag von Jerome Goldstein)

Description Vorlesung im SoSe 2015; Dienstag, 30. Juni 2015
Creator Rainer Nagel (author); Jerome Arthur Goldstein (author); Frank Loose (author)
Contributor ZDV Universität Tübingen (producer)
Publisher ZDV Universität Tübingen
Creation Date 2015-06-30
Subjects Mathematik, Vorlesung, apportionment problem, house of representatives, mathematics of apportionment, Alexander Hamilton, largest remainder method, taxicab geometry, divisor method, Thomas Jefferson, Daniel Webster, Samuel Vinton, Alabama paradox, equal proportions method, Edward Huntington, axiomatic study of apportionment problem, Michel Balinski, Peyton Young
Rights Rechtshinweise


00:00:00 introduction of Jerome Goldstein by Rainer Nagel
00:01:00 mathematics is everywhere
00:02:46 mathematical conference 1974 at Texas Tech, connection between mathematics and founding of the country
00:05:45 apportionment problem for the US house of representatives
00:06:45 each state shall have number of representatives according to their respective numbers (US constitution)
00:09:04 mathematics of apportionment, introduction and terminology
00:12:22 how can one achieve the best apportionment?
00:14:53 apportionment method by Alexander Hamilton (largest remainder method)
00:17:55 mathematical analysis of Hamiltons method
00:19:47 taxicab geometry
00:21:30 minimizing taxicab metric yields best apportionment, this is Hamiltons method (did not become law)
00:22:45 divisor method by Thomas Jefferson (was law from 1790 to 1830)
00:24:15 controversy leads to method by Daniel Webster, law from 1830 to 1850
00:26:43 apportionment method by Samuel Vinton (equals Hamiltons method, law from 1850 to 1930)
00:27:31 the Alabama paradox (increase in house size reduced fair share)
00:32:06 equal proportions method by Edward Huntington
00:33:54 equal proportions method, process to minimize relative inequity (law since 1930)
00:36:39 axiomatic study of apportionment problem (by Michel Balinski and Peyton Young)
00:37:05 Axiom 1: house monotonicity (i.e. avoid Alabama paradox!)
00:38:22 Axiom 2: quota rule, number of representatives should be integers closest to fair share (constitutional requirement)
00:39:20 axiomatic study of apportionment problem, results
00:41:22 Axiom 3: binary consistency
00:42:06 equal proportions method by Balinski and Young (satisfies all three Axioms)
00:44:52 Balinski and Young method was attacked by Garrett Birkhoff
00:46:11 new Axiom 3: individual state monotonicity
00:47:54 these three Axioms are contradictory (Balinski and Young)