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Communicating Quantitative Information

Communicating Quantitative Information. Wire tapping Electoral districts: exercises Homework: Postings. Start thinking about topic for presentation/paper. Diagrams. ????. General wire tapping. Screen all (many?) Phone calls Emails ?

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Communicating Quantitative Information

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  1. Communicating Quantitative Information Wire tapping Electoral districts: exercises Homework: Postings. Start thinking about topic for presentation/paper

  2. Diagrams • ????

  3. General wire tapping • Screen all (many?) • Phone calls • Emails • ? • Recall HIV screening with large number of false positives in generally HIV free population.

  4. Wire tapping • What is the population of the United States? • What are the number of conversations & emails & searches? • What would be an estimate of the number of terrorists? • What are the number of conversations & emails & searches? • How accurate would a data mining program be? • sensitivity: correctly identifying a terrorist hint: sensitive to condition • identifying terrorist conversation/email/search • specificity: correctly identifying a non-terrorist hint: specific enough to NOT label those without condition • identifying (clearing) an innocent conversation…

  5. Analysis Focus on people, not conversations. For conversations the numbers are even bigger • About 300,000,000 people • Assume about 300 terrorists • 299,999,700 • Assume detection is 99% sensitive AND specific • Then detection will find correctly point to 297 of the 300 but also will point to (about) 3,000,000 (this is taking 1% of 299,999,700 and rounding) • This produces about 3,000,000 (2,999,997+297) people for follow-up investigation!!! • For conversations, more and more are produced every day…

  6. "Both Ilegal and Ineffective" • John Allen Paulos (mathematician at Temple University) • http://abcnews.go.com/Technology/WhosCounting/story?id=1560771

  7. Trade-off • Sensitivity (identifying the cases with the condition) versus Specificity (correctly clearing the cases without the condition) • Even assuming just one measurement involved, there can be overlap

  8. Math is not just numbers, but • graphs • networks • patterns • geometry

  9. Flu shot story • Policy being proposed by some scientists is to aim to vaccinate school children to cut down on amount of disease and, consequently, reduce risk to elderly and [more] vulnerable. • Proposed as more effective than vaccinating only the vulnerable populations. • Networking/graph theory/probability • Herd immunity

  10. NUMB3RS • TV show (police procedural, two brothers, mathematician) • Application of math—fair to questionable • networking, 'patient 1' • Compstat: actual system in use. Used in old show: The District. Now featured in Bluebloods. • locate crimes • focus attention by all agencies • (use to ask better questions to people arrested)

  11. Graphs • Nodes and edges (here directed edges) • May have added qualities: length, strength, duration,…

  12. Election districts • Geography + population • sometimes just or mostly geography: • 2 senators to each state • minimum one representative • Georgia once had County Unit System: each county treated the same. Limited the political power of Atlanta

  13. Electoral votes State: number of senators + representatives. Washington, D.C. gets 3 votes 538 (100 + 435 + 3) total Advantage to smaller states? Defend your answer?

  14. Show by example • Look at electoral voting power of… Wyoming (and other small states) • 3 electoral votes. Population: 495,304 • pop/ev = 165101 California (and other large population states) • 55 electoral votes. Population 33,930,798 • pop/ev = 616924 http://www.electoral-vote.com/info/states.xls

  15. http://www-personal.umich.edu/~mejn/election/ • 2004 election maps • red and blue states • modified to population • modified to electoral votes • counties

  16. How to define election district • How to break up state into regions of equal population • Other considerations besides equal population? • compactness • 'natural' boundaries • historic boundaries • affirmative action • reconsidered

  17. http://www.fraudfactor.com/ffgerrymander.html#actualredistrictingmapshttp://www.fraudfactor.com/ffgerrymander.html#actualredistrictingmaps From the site: Although the Democratic-Republican party was in power in Massachusetts in 1812, it had little hope of retaining its control in the approaching elections. To save something for the party Governor Elbridge Gerry signed a reapportionment bill to construct new senatorial election districts that consolidated the Federalist vote. An exasperated editor hung a map showing one of these districts. Gilbert Stuart, the painter, added head, wings, and claws to the outline, noting, "That will do for a salamander." "Better say Gerrymander," the editor responded.

  18. Recent example

  19. New York State

  20. Compactness formula • B = length of boundary • A = area • CM = B/square_root(A) • Helps, but there can still be problems!

  21. Examine compactness formula • Gives same value for all squares: Square of side s produces (4*s)/sqrt(s2) • unit-less, pure number • grows when boundaries added without much area

  22. Exercise (from Michael Robbins, www.fraudfactor.com site)Divide into 3-block contiguous regions

  23. Challenge: create 3 safe Democratic and 2 safe Republican districts

  24. Consequences • Creating one type of district can create extremely safe other types of districts. • Recent court cases have questioned the creation of minority districts that take potential Democratic votes out of neighboring districts.

  25. Puzzle • Consider the following series • triangle, square, pentagon, hexagon, … Suppose this series continues on infinitely. Eventually, the figures will most resemble A=Octagon B=Circle C=Block D=Dot E=It is impossible to tell.

  26. Project I • Pick story/topic. Two options: • Write (re-write) news story on topic involving quantitative information (about 1000 words) • grammar and spelling count! Papers that have not been proofread will be returned, ungraded. Marks off for lateness! • Include appropriate table(s), diagram(s), graph(s) • Include sources (in text, but with enough information for me to find) • Prepare and make formal (short) presentation • Include appropriate table(s), diagram(s), graph(s) • Include 1 page abstract, sources, optional: diagram, graph • Posting of proposal due October 20. • Paper & Presentation due Nov. 6.

  27. Posting possibility • Anything on existing congressional districts • Research your own. Find out history. • Research predictions on how many are competitive in this year’s elections. • ‘Emerging’ races

  28. Homework • Postings (original and replies) • you cannot catch up the last few weeks. Do some postings before Spring break. • Project I • Topic due October 20 • Paper due November 6 • Midterm: October 23 (guide posted)

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