Communicating Quantitative Information

Wire tappingElectoral districts: exercises

Homework: Postings. Start thinking about topic for presentation/paper

Diagrams

• ????

General wire tapping

• Screen all (many?)– Phone calls– Emails– ?

• Recall HIV screening with large number of false positives in generally HIV free population.

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…

AnalysisFocus 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…

"Both Ilegal and Ineffective"

• John Allen Paulos (mathematician at Temple University)– http://abcnews.go.com/Technology/WhosCou

nting/story?id=1560771

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

Math is

not just numbers, but

• graphs

• networks

• patterns

• geometry

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

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)

Graphs

• Nodes and edges (here directed edges)

• May have added qualities: length, strength, duration,…

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

Electoral votes

State: number of senators + representatives.Washington, D.C. gets 3 votes538 (100 + 435 + 3) total

Advantage to smaller states?

Defend your answer?

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

http://www-personal.umich.edu/~mejn/election/• 2004 election maps

• red and blue states

• modified to population

• modified to electoral votes

• counties

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

http://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.

Recent example

New York State

Compactness formula

• B = length of boundary

• A = area

• CM = B/square_root(A)

– Helps, but there can still be problems!

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

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

R R R R

R R D D

D D D D

R R R R R

R R R R R

R R R R R

R D D D D

D D D D D

Challenge: create 3 safe Democratic and 2 safe Republican districts

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.

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.

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.

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

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)