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# L27post - Previous Lecture Recursion Efficiency Todays...

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Previous Lecture: Recursion Efficiency Today’s Lecture: Models Quantifying fairness Quantifying importance Simulation—Google “Page Rank”

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December 3, 2009 Lecture 27 3 Announcements P7 due today at 11pm Final exam: 12/14 (Mon) 7pm at Barton (indoor field) West Please fill out course evaluation on-line (Engineering will email about it, see “Exercise15”) Regular office (consulting) hours end tomorrow (today). “Study Break” hours start next week. Review Session: 12/13 Sun 4:30-6pm, Location TBA Pick up any paper from consultants (prelim, regrade results) during consulting hours next week. Everything will be shredded afterwards. Read announcements on course website!
December 3, 2009 Lecture 27 4 Proportional representation in the spirit of “one person, one vote” Article I Section 2 of the US Constitution: Representatives… shall be apportioned among the several States, which may be included within this Union, according to their respective numbers…” How do you quantify fairness? There are different models of fairness. (Were some models advanced for political reasons?)

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December 3, 2009 Lecture 27 5 The ratio of population to delegation size as a measurement of fairness Distribute 435 Congressional seats among the 50 states so that the ratio of population to delegation size is roughly the same from state to state. Sounds specific, but even with this “definition” of fairness there’re different models that can be used as demonstrated throughout history… and in this lecture.
December 3, 2009 Lecture 27 6 Related questions How “close” is a state to losing a Congressional district because of population changes? If Puerto Rico and/or Washington DC become states and the number of Congressional seats remain the same, which states would lose a seat? •Reasoning about change is very important! •How does the “answer” change if the data change or if the assumptions that underlie the computation change? Æ Sensitivity analysis

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December 3, 2009 Lecture 27 12 The apportionment problem Number of states: n State populations: p(1),…,p(n) Total population: P State delegation size: d(1),…,d(n) Number of seats: D Distribute 435 Congressional seats among the 50 states so that the ratio of population to delegation size is roughly the same from state to state.
December 3, 2009 Lecture 27 13 Ideal: Equal Representation Number of states: n State populations: p(1),…,p(n) Total population: P State delegation size: d(1),…,d(n) Number of seats: D ) ( ) ( ... ) 1 ( ) 1 ( n d n p d p D P = = =

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December 3, 2009 Lecture 27 15 Realistic situation Number of states: n State populations: p(1),…,p(n) Total population: P State delegation size: d(1),…,d(n) Number of seats: D ) ( ) ( ... ) 1 ( ) 1 ( n d n p d p D P
December 3, 2009 Lecture 27 16 An Apportionment Method determines delegation sizes d(1),…,d(n) that are whole numbers so that representation is approximately equal: ) ( ) ( ...

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L27post - Previous Lecture Recursion Efficiency Todays...

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