CS 100 M Lecture 26 - 26. Models, Data, Simulation...

Info iconThis preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
26. Models, Data, Simulation Congressional Apportionment Google PageRank Sensitivity Analysis
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Quantifying Fairness How do you 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? Quite possibly one of the greatest division problems of all time!
Background image of page 2
Quantifying Importance How do you rank web pages for importance given that you know the link structure of the Web, i.e., the in-links and out-links for each web page. Quite possibly one of the greatest ranking problems of all time!
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Related Questions How “close” is a state to losing a Congressional district because of population changes? How to do new or deleted links that involve a web page affect its PageRank?
Background image of page 4
Reasoning About Change Sensitivity analysis: How does the “answer” change if the input data changes or if the assumptions that underlie the computation change? VERY IMPORTANT IN SCIENCE & ENGINEERING
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
An Earlier Example MyPi = 3.14; R = 3961.12345; EarthArea = 4*MyPi*R*R Math error in MyPi, measurement error in R, model error in spherical model, rounding error in arithmetic.
Background image of page 6
Subtext These examples provide distinct opportunities to review 100M programming techniques.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Apportionment Problem
Background image of page 8
Notation Number of states: n State populations: p(1),…,p(n) Total Population : P State delegation size: d(1),…,d(n) Number of seats: D
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 = = =
Background image of page 10
29.376 435 281424177 19004973 ) ( = = NewYork d D P p(i) i d ) ( = i.e., And so for NY in 2000. . But delegation size must be a whole number!!!
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
More Realistic… 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
Background image of page 12
An Apportionment Method determines delegation sizes d(1),…,d(n) that are whole numbers so that representation is approximately equal: ) ( ) ( ... ) 1 ( ) 1 ( n d n p d p Definition
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Decide on a ``common ratio’’, the ideal number of constituents per district. In 1790:
Background image of page 14
Image of page 15
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/23/2008 for the course CS 100 taught by Professor Fan/vanloan during the Spring '07 term at Cornell University (Engineering School).

Page1 / 59

CS 100 M Lecture 26 - 26. Models, Data, Simulation...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online