## Shaping Public Policy

Tasks and problems intended to illustrate the way mathematics arises in life and work.

Budget Comparison. Between 1990 and 1995 inflation totaled 25.3%, the population of college-age students declined 3.5%, and the average cost of a year in college climbed 38%. During these same years the funds appropriated by Congress for student loans increased from 1.2 billion to 1.7 billion. Some believe that during this period student loan funds increased, whereas others argue that it decreased. Who's right?

Tax Policy. Talk of tax reform produces many graphs: of nominal rates, of marginal rates, of actual percentage paid, of proposed tax cut, and of total taxes collected, each as a function of individual or family income. Use such graphs to interpret the effects of specific proposals such as a flat tax, or an increased deduction for children. Who benefits most, and who least, from the proposed changes? Who pays the most taxes in total, and who least? Under what circumstances can reduced tax rates result in increased tax revenue?

Understanding Taxes. Tax policy is constantly in the news, with debates about flat tax systems, capital gains tax rates, FICA (social security) taxes, mortgage deductions, etc. To participate intelligently in debates about tax policy, citizens need to understand the difference between marginal and average tax rates. To manage their own resources most effectively, individuals need to understand the behavior of marginal tax rates that jump from one bracket to another. Graphs showing national patterns as a function of income can be very revealing.

Inflation Analysis. Given data on annual inflation rates in the United States from 1975 through 1995, use a spread sheet to figure out what the average annual inflation rate was during this period. What salary in 1975 would correspond to a salary of \$20,000 in 1995? Compare the 1975 and 1995 salary figures with (a) the average cost of a new car and (b) the average cost of a year in college for 1975 and 1995. Which of these two items--cars, college costs--increased at more than inflation?

Drawing District Lines. Describe criteria and procedures to add fairly a congressional district to a state in a way that will minimize disruption of current districts while creating new districts that are relatively compact (non-gerrymandered) and of nearly equal size.

Fair Apportionment. Examine the impact of the census on reapportionment of the House of Representatives, looking at how numbers of representatives might change if the original census data were altered to reflect known patterns of undercounting.

Voting Theory. Explore various options for voting (e.g., runoff ballots vs. approval voting) among three choices (propositions or candidates) in which the electorate has non-transitive preference rankings.

National Debt. Examine the growth of the national debt on a per person basis, or based on income, or in comparison with the gross domestic product.

Comparing Income. Using data and graphs on the median income of men and women for the last two decades, show how these graphs can be used to justify two apparently conflicting conclusions--that women's wages are catching up, and that they are not.

Cost of Education. Examine data on cost of education and SAT scores over the past 30 years in relation to (a) inflation and (b) changes in the percentage of the population that takes the SAT exam.

High School Graduation. Data on high-school graduation rates by state and region, for consecutive years, disaggregated by ethnic and economic indicators, offer many challenges to summarize and present conclusions.

SAT Scores. Draw conclusions from a table of SAT scores by state and ethnic category, together with information on the fraction of each state's population that takes the test. Can you find a fair or sensible way to compare SAT scores between one state and another?

School Funding. Examine data relating school funding to school achievement in relation to socio-economic data such as average family income and infant mortality rates.

Community Growth. A City Council is trying to decide if it should annex a plot of land to provide room for additional housing, an industrial park, and a new school. An important point of contention concerns projections of population growth for the next twenty years. Advocates of annexation project rapid growth, whereas opponents foresee more modest increases. Both reason from the same population data, from which some infer exponential growth while others see only linear growth. As a reporter for the daily newspaper, explain the reasoning behind each argument to your readers.

Detecting Bias. Given data on applicants and on new hires for summer jobs at a local office supply store, see whether there is any evidence of bias in favor of any particular group (boys or girls, Hispanics or Asians, tall or short).

Timing Traffic Lights. A four-mile stretch of a suburban road lined with shopping plazas carries heavy commuter traffic northbound in the mornings and southbound in the evenings. The road has 15 traffic signals, unevenly spaced, where cross streets and mall entrances intersect. Figure out how to time the lights to maximize the flow of commuter traffic.