February 26, Ms. Akasemi Newsome, Program Director Russell Sage Foundation 112 East 64th Street New York, NY 10021

Transcription

1 February 26, 2007 Ms. Akasemi Newsome, Program Director Russell Sage Foundation 112 East 64th Street New York, NY Dear Ms. Newsome: We would like to submit a proposal to the Russell Sage Foundation regarding our project, A Scientific Approach to Redistricting Analysis. Our project fits within the Request for Proposals from the Sage Foundation s Social Inequality Program to examine the politics of inequality. We discuss issues in redistricting that result in social inequality. Our aim is to create and provide a free and widely accessible tool to facilitate redistricting analysis and the creation of fair and competitive electoral districts. Our computational and mathematical tool will be transformative for democracy and redistricting. The key personnel are three full-time faculty members at the University of Illinois at Urbana- Champaign. We compose a broad multidisciplinary team composed of a political scientist and statistician, a computer scientist, and a theoretical mathematician, with unique strengths as individuals and as a team. Our resumes are enclosed along with our proposal. Please let me know if you have any questions. I am the lead principal investigator and can be reached via at wendycho@uiuc.edu. My other contact information is listed below. Thank you. Sincerely, Wendy K. Tam Cho Professor of Political Science and Statistics Senior Research Scientist National Center for Supercomputing Applications University of Illinois at Urbana-Champaign

2 RSF PROJECT AWARD APPLICATION Cover Sheet Principal Investigator(s) Name(s):! Institutional Affiliation(s): Address: Telephone: University to serve as the project s Fiscal Agent: Project Title: Amount Requested: Requested Project Start Date:!! Project End Date: What is the relevant RSF research program area for your project? Please list previous and current RSF-funded research: (Attach additional page, if necessary) Brief Project Abstract:! Please list the names of co-pis and their institutional affiliations on the title page of your proposal.!! Project period begins with the date of the first expected expenditure and ends with the completion of the project s final product.

3 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL A SCIENTIFIC APPROACH TO REDISTRICTING ANALYSIS Although it is not difficult to see the manifestations of social inequality in the United States, it is difficult to pinpoint the origins of social inequality. At the same time, the link to political institutions is not hard to establish. Even if social inequality is not created directly by political institutions, if these inequalities persist over time, they are certainly perpetuated by political institutions. In the United States, these political institutions are intertwined with our attempts to implement a system of democratic governance. The rising social inequality of the past three decades, however, must give us pause and resolve to examine the performance of the U.S. political system in achieving a truly democratic form of governance. One obvious starting point is redistricting reform. Currently, electoral district lines are highly manipulable within the constraints of the law. Consider the hypothetical districts in Figure 1. The first map depicts a hypothetical state partitioned into 12 areas, which either tend toward the Republicans or toward the Democrats. As we can see, 6 of the areas lean Republican while 6 of the areas lean Democratic, perhaps suggesting that half the state s representatives should belong to one party and half to the other. In the second map, 4 districts are drawn. In 3 of these districts, Democrats comprise 2/3 of the voters, so that the outcome is virtually predestined to be 3 elected Democrats and 1 elected Republican. The third map shows a different configuration of 4 districts. In this case, the virtually predestined outcome is the election of 3 Republicans and only 1 Democrat. The last map may appear to be most fair from the point of view that half the districts will almost certainly elect a Democrat while the other half will almost certainly elect a Republican. As this simple illustration demonstrates, the key to determining who will hold power lies in the redistricting, and district lines are highly manipulable to yield a desired pre-determined outcome. Drawing districts lines to favor a specific outcome is generally called gerrymandering. 1 In a gerrymandered district, politicians essentially hand-pick their voters. It is not, as we have come to assume in a democracy, the voters choosing their representative. Gerrymanders are not looked upon favorably, and the practice of gerrymandering is obviously controversial, but regulating the practice is quite challenging. There are so many ways to draw gerrymanders within the legal constraints that the phenomenon continues scarcely impeded by regulation. We approach redistricting reform from a different perspective. Rather than discussing regulations that are intended to constrain the possible set of maps, we propose the development of tools that will both illuminate and open up the process of redistricting. By making it easier to do the needed research, these tools will broaden the range of scholars, students, policy analysts, citizen advocacy groups, and individuals who are able to participate in the process. The 1990 redistricting was the first redistricting that relied heavily on politicians using computers and software to redistrict, though the idea of using computers for redistricting was advocated many years ago (Vickrey, 1961; Nagel, 1965; Weaver and Hess, 1963). The 1960s even saw the advent of early computer programs for this purpose (Nagel, 1965; Harris, 1964; Thoreson and Liittschwager, 1967). However, it was the 1990s that saw this dream come to fruition as computing power caught up with desire. The ability to explore and obsess over myriad possibilities altered the process (Monmonier, 2001). Both the computing techniques and computing power a decade earlier in the 1980s 1 The term traces its origins back to the Democratic-Republican party in Massachusetts in In that year, Governor Elbridge Gerry signed a bill to construct new senatorial districts that consolidated the Federalist vote. One of these districts resembled a salamander. The Boston Weekly Messenger brought the term gerrymander into common usage with an editorial cartoon depicting the district in question with heads, arms, and a tail. 1

4 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL Figure 1: Redistricting as a Determinant of Power were insufficient. The 1980 redistricting relied heavily on large maps hung on walls to illuminate the geographical landscape and the possible districting schemes. Politicians spent long hours musing in front of these maps, slowing trying out various possibilities. Technologically, the world has undergone an unmistakable and immense transformation. In the future, we must take advantage of these technological advances to facilitate societal tasks. We are at the threshold of being able to use statistical and mathematical modeling and computing technology in the redistricting process in an unprecedented manner. Instead of merely tinkering with endless possibilities, we will be able to develop computationally intensive models that can generate and evaluate alternative redistricting schemes and compare them to each other on various notions of fairness. 1 Racial Gerrymandering Every ten years following the census, districts are redrawn. Almost inevitably after the districts are drawn, lawsuits are filed. The majority of these lawsuits are based on the Voting Rights Act that guarantees the right of minorities to elect a representative of their choice. In these lawsuits, the plaintiffs and the defendants enlist expert witnesses to testify. Often the plaintiff is a group like the National Association for the Advancement of Colored People (NAACP) or the Mexican American Legal Defense and Education Fund (MALDEF). These groups (and their expert witnesses) argue that the districts need to be redrawn because minorities are not able to elect the representative of their choice. The expert witness for the defense, on the other hand, argues the direct opposite that the current configuration of districts does allow minorities to elect the representatives of their choice. How do these expert witnesses arrive at contradictory conclusions? How does one assess whether a particular redistricting plan is fair? The 1990s round of redistricting resulted in the Supreme Court issuing new standards for how redistricting or Voting Rights cases would be decided by the courts. The notable decisions began with Shaw v. Reno (509 U.S. 630 (1993)) when the Court ruled for the first time that minority districts may violate the Equal Protection clause in the Constitution. The district in question was North Carolina s 12th Congressional district, which is depicted in Figure 2. The district appears thin because it stretches approximately 160 miles along Interstate 85 from Durham to Greensboro to Charlotte to Gastonia. For much of its length, the district is no wider than the I-85 corridor, branching out at various locales to include minority residents. Miller v. Johnson (515 U.S. 900 (1995)) built on the Shaw decision. In Miller, the Court struck down a black district that stretched 6,784 square miles from Atlanta to the Atlantic Ocean, declaring it a 2

5 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL Figure 2: Shaw v. Reno Figure 3: Other 1990 Redistricting Cases geographic monstrosity and unconstitutional under the Equal Protection Clause according to the interpretation in Shaw. The Court declared that when race is the predominant factor in a redistricting plan, strict scrutiny the most demanding level of judicial review must be applied. Strict scrutiny means that the law must address a compelling governmental interest (the Court has already deemed minority representation to be a compelling governmental interest), be narrowly tailored to achieve that interest, and be the least restrictive means for achieving that interest. The Court did not delineate how one might determine whether race was the predominant factor or merely one of the factors in crafting a redistricting plan, how to narrowly tailor districts, or how to craft the least restrictive redistricting plan in accordance with a compelling governmental interest. It merely set forth general criteria. The Shaw and Miller decisions resonated throughout the country in a round of racial redistricting cases highlighting the nation s most bizarrely-shaped districts. Several of these are shown in Figure 3. In Louisiana, the 1990 redistricting included the strangely shaped 4th congressional district. This district began in Shreveport at the upper left, wound through all or part of 28 parishes, and ended up in Lafayette at the bottom-most tip. This district was used in the 1992 elections, but redrawn on a federal district court order for subsequent elections. Florida s redistricting included its 3rd congressional 3

6 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL Figure 4: Bush v. Vera TX-18 TX-29 TX-30 district that began in Gainesville at the western tip, winding upward before landing downstate in Orlando. The district was intended to be a black majority district but the court found that blacks were not sufficiently compact to warrant this race-based remedy. Illinois s redistricting included the 4th congressional district, affectionately named the ear muff district in honor of its shape. The intent was to create a Latino district without disturbing the neighboring black majority districts. This district appears thin in parts like the 12th district in North Carolina because it makes it way through cemeteries, forest preserves, and railroad tracks in order to exclude non-minority populations, branching out primarily to include Latino populations. Although the district court allowed this district, the Supreme Court vacated the judgment and remanded the district court to reconsider based on the new criteria set forth by the Court. In 1996, the Supreme Court continued its review of racial redistricting cases in Bush v. Vera when it considered three districts in the state of Texas: the 18th, the 29th, and the 30th congressional districts (shown in Figure 4). District 18 was a reconfigured black district. District 29 was a new majority Hispanic district in Harris County. District 30 was a new majority black district in Dallas County. The Supreme Court ruled that these districts were subject to strict scrutiny and were not narrowly tailored to serve a compelling state interest. Rather than laying out a clear framework for how to judge redistricting cases, the Bush v. Vera case introduced yet more questions about the role of race in redistricting. Texas officials had acknowledged that race played a role in the creation of these districts but additionally claimed that the odd shapes resulted not from considering race but other more traditional and legally acceptable criteria. Justice O Connor acknowledged that race often coincides with other factors. She wrote, [d]espite the strong correlation between race and political affiliation, the maps reveal that political considerations were subordinated to racial classification in the drawing of many of the most extreme and bizarre district lines. The implication is that when race is the predominant factor for abandoning compact district lines, redistricting crosses the line and becomes an unconstitutional racial gerrymander. The new standards set forth by the Court in the 1990 round of redistricting introduced a set of criteria that were, at best, fuzzy and not well-defined. While the Court expressly stated that race could not be the predominant factor, the Court did not expound on how to determine whether race is the predominant factor rather than just one of many factors. Commonly, line drawers begin with 4

7 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL the notion that a safe minority district should be 65% minority to account for lower rates of minority turnout and to allow for more than a slight edge in the event of a competitive opponent (Swain, 1995). At the same time, districts must be narrowly tailored to achieve a compelling state interest, but narrow tailoring is not easily achieved given the large number of possible redistricting schemes. How intricate or contorted the district lines must be is a different matter from how intricate the lines can be. Clearly, what is needed here is a method that can rank redistricting plans and so identify the plan that is most narrowly tailored to achieve some specified level of minority representation. However, given the very large number of possible redistricting plans, ranking possible redistricting schemes is far from trivial and requires enormous computing power. Indeed, the new criteria set forth by the Court highlight the unmistakable value to be gained by adapting the process to a computational format. 2 Partisan Gerrymandering Partisan gerrymanders are routinely practiced and widely credited for creating safe U.S. House districts. The 2000 round of redistricting resulted in the safest House districts in our nation s history. Since 1998, U.S. House members have been re-elected more than 98% of the time. The 2006 midterm elections were tumultuous in comparison due to short-term factors, but the long-term trends show that the 2002 House elections, the first following the 2000 redistricting, were less competitive than typical elections in recent times and were less competitive than elections after the three preceding congressional redistrictings, 1992, 1982, and 1972 (Issacharoff, Neuborne and Pildes, 2006). Moreover, this trend toward non-competitive seats has been ongoing for some time. In 1974, Mayhew noted that the number of competitive House seats was less than half of what it was in 1956 (Mayhew, 1974). The increasing safeness of House seats has some groups clamoring for change, citing that democracy is not being served. In particular, citizen advocacy groups like Common Cause strongly hold to the position that redistricting should be removed from the purview of partisan legislators and put into the hands of nonpartisan independent redistricting commissions who will create districts that are both more representative of the population and more competitive than current districts. Citizens in a democracy are shortchanged, they say, when elections are not competitive. Indeed, many citizen advocacy groups, individuals, legal scholars, and political scientists alike place great value on competitive elections (Issacharoff, 2002; Lowenstein and Steinberg, 1985; Pildes, 1999; Key, 1949, 1956; McDonald and Samples, 2006). The argument is intuitively appealing, and there are many reasons why most individuals would likely favor more competitive elections. First, competition fosters accountability in representation. If elections are not competitive, legislators grow complacent. At the same time, voters are unable to replace complacent legislators who reside in safe, non-competitive districts (Jacobson, 2006; Wittman, 1997; Bernstein, 1989). Second, competitive elections garner much more interest among those in the electorate (Gimpel, Lay and Schuknecht, 2003). Voters who are more interested are generally better informed, a desirable aspect of a democracy. Third, competitive elections command far greater media exposure than one-sided contests, which in turn, produces a larger base of information for voters (Iyengar and Simon, 2000). Fourth, competitive elections increase voter turnout (Grofman, Collet and Griffin, 1998; Gray, 1976). In short, competitive elections, it is argued, are more likely to produce healthy democracies with informed and interested voters who feel efficacious. Interestingly, even some clearly partisan interests have emerged lately waving the banner of competitive districts. Democrats, who were out of power for more than a decade, have recently have begun extolling the 5

8 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL value of more competitive districts (Jacobson, 2006; Oppenheimer, 2005). There are others, however, who are not entirely convinced that competitive elections are the panacea for democracy s ills (Persily, 2002). This alternative camp argues that that competitive elections create a situation where incumbents are overly concerned with campaigning and fundraising rather than the tasks of policymaking and representation. Whether partisan gerrymanders or competitive districts are inherently good or bad for democracy is a policy question that we do not broach. The impact of partisan gerrymanders on democratic rule is not well understood, but we take no sides on the societal consequences of the practice of redistricting. Instead, we recognize that these questions are important and need to be analyzed with the proper tools and a unified theoretical framework. In the debate about competitive elections, clearly, the analyst needs to have a sense of what alternative scenarios are possible. Undoubtedly, much of the uncertainty about how to judge particular redistricting plans revolves around the inability to evaluate alternative redistricting plans. What do competitive districts look like? How biased is a proposed plan for one party or the other? One may assume or know the plan is biased, but without an ability to quantify the bias, it is difficult to assess the fairness of any particular plan, and whatever assessment is made is ultimately subjective. 3 Redistricting Analysis: A Computational Approach We address the fundamental question of how to evaluate the bias (racial, partisan, or otherwise) in a districting plan. Our approach is computationally intensive but is a theoretically attractive method of judging particular maps and is based on considering the space of all possible redistricting maps. We proceed as follows. First, we define the problem and describe its computational magnitude. Second, we demonstrate how the problem is a standard, albeit very large, constrained optimization problem. Third, we propose that the method of simulated annealing is an appropriate and especially suitable optimization technique for analyzing redistricting plans. 3.1 Possible Districting Maps Drawing electoral maps amounts to arranging a finite number of indivisible geographic units (census blocks, precincts, counties, etc.) into a smaller number of larger areas. For simplicity, call the former units and the latter districts. An immediate constraint is that every unit must belong to exactly one district. A map is thus a partition of the set of all units into a pre-established number of non-empty districts. With no other constraints imposed, the total number of possible maps when drawing k districts using n units is a Stirling number of the second kind, S(n, k) (Keane, 1975). The Stirling number of the second kind is defined, combinatorially, as the number of partitions of an n- element set into k blocks, which is why it equals the number of partitions of n units into k districts. The Stirling number of the second kind can be computed recursively as S(n, k) = k S(n 1, k)+s(n 1, k 1), which is valid when n 1 and 1 k n. Table 1 shows S(n, k) for a selection of small values of n and k, to provide a sense of magnitude. With a modest number of units, the scale of the unconstrained map-making problem is awesome. The final column, for n = 55, shows the number of possible electoral maps if one wanted to create k districts from 55 units. If one wanted to divide 55 units into 6 districts, the number of possibilities is , a formidable number of possibilities even for the high-end computers that exist today. 6

9 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL Table 1. Selected Values of S(n, k), Stirling Numbers of the Second Kind n k , , ,375, , ,355, , ,766, , ,693, ,662, , This number is larger than the number of microseconds that would have passed if, in every second since the universe began, the number of microseconds was equal to the number of seconds that have passed since the universe began. There have been fewer than seconds since the beginning of the universe. A simplifying consideration, however, is contiguity. It is required that electoral districts consist only of units that are contiguous. Many of the partitions counted by S(n, k) violate the contiguity constraint. One aspect of making the problem computationally feasible is finding a way to restrict our attention to the maps satisfying this constraint. Another consideration that reduces the number of maps to be considered is the requirement that districts be roughly equipopulous, but still the number of maps remains enormous. In actual redistricting problems when census blocks are the units, a typical n is on the order of thousands while k is typically a double digit number. Hence, the number of possibilities in actual redistricting problems is far larger than the very large numbers that appear in Table 1, creating a prohibitively large computational problem. Let us lay aside for the moment the formidable combinatorial problem we have introduced. Once a map has been defined, it is simple to determine various characteristics of the districts such as their median income, education level, and age as well as vote histories, partisan registration, and turnout propensities. In fact, we have this information not only for the district as a whole but for each of the thousands of component parts that were aggregated to form the district. If one seeks a map that maximizes competitiveness, one can rank alternative maps on a scale that measures this, such as balance in partisan registration. Each map lies somewhere on the scale, distinguishing highly competitive maps from those that are not competitive at all. Indeed, maps can be scored on many criteria. If one seeks a district likely to elect a minority candidate, one can also evaluate on other 7

10 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL criteria to find the map that satisfies this criterion in the most narrowly tailored way, satisfying the Supreme Court directive. If a map scores highly on other criteria, then we would have evidence that racial considerations were not the predominant factor in its creation. If the problem were not so large, then one would generate and evaluate all maps satisfying the constraints. 2 However, the size of the problem makes this approach intractable in the foreseeable computing environment (Altman, 1997). Our goal, therefore, is to explore the space of possible maps more intelligently, producing a near-optimal map with very high probability. A useful approach here is to view the redistricting problem as a standard optimization problem. The problem is to maximize the score on various measures subject to constraints such as contiguity, equipopulation, compactness, etc. The measures and the constraints are flexible and can be defined in many ways. Together, they produce a constrained optimization problem. The main complicating factor in solving this constrained optimization problem is its sheer size. The limitations imposed by the size of the problem have perhaps steered practitioners away from our approach despite its theoretically-appealing and objective nature. We contend that the time is ripe to revisit the computational approach to the redistricting problem because of the enormous computing power that is available today and several additional attractive features. The first feature is that our approach is objective, not subject to the biases of expert witnesses or the interests that employ those expert witnesses. Another attractive property is that given the enormous number of possibilities, a computer is plainly much more efficient, accurate, and capable of solving this optimization problem than a human being. Lastly, this approach makes it feasible to consider simultaneously many different criteria. 3.2 Simulated Annealing What is needed is an optimization technique that is suited for large-scale problems. One possibility is to pursue techniques that have been used to solve large combinatorial optimization problems such as the Traveling Salesman Problem. A picture of a Traveling Salesman Problem is shown in Figure 5 (Press et al., 1988). Here, there are 100 cities. The traveling salesman must visit each of the cities. The problem is to find the shortest itinerary for the traveling salesman. He may start at any city, and from that initial city can travel to any other city, and then to any other unvisited city after that until all cities have been visited. The number of possible paths among which one must find the shortest path grows extremely quickly with the number of cities. In addition, other constraints may be added, such as creating a river running perpendicular to the x-axis at x = 50 and adding a penalty each time the river is crossed. This constraint changes how the cost for each path is calculated, but it does not change the basic optimization problem. The method of simulated annealing (Eglese, 1990; Fleischer, 1995) has solved the Traveling Salesman Problem in the sense that simulated annealing can reasonably quickly produce solutions that are approximately optimal. The success in solving the Traveling Salesman Problem has highlighted the method of simulated annealing for large-scale optimization problems, such as the redistricting problem we are considering here. The term simulated annealing has its origins in the process of annealing in metallurgy. In short, annealing involves heating metal at high temperatures and then allowing the metal to cool slowly in order to remove internal stresses, toughen the metal, and become 2 This approach has been used (Garfinkel and Nemhauser, 1970; Gudgin and Taylor, 1979; Papayanopoulos, 1973; Shepherd and Jenkins, 1970), though only for applications of very small redistricting problems. The implemented methods are not generalizable and are infeasible for any problem of practical size. 8

11 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL Figure 5: Traveling Salesman Problem a pure crystal. If the liquid metal is not cooled slowly, it does not reach this state but rather ends up in a polycrystalline or amorphous state. So slow cooling is essential to the process of annealing a liquid into a solid. In the simulated annealing approach to an optimization problem, a parameter plays the role of temperature. When the parameter modeling the temperature is high, we accept larger changes from our current partition in search of an optimal redistricting configuration. As the algorithm progresses, the temperature parameter is gradually reduced, mimicking the slow cooling process of annealing. The idea of adapting the method of simulated annealing to the redistricting problem (though without specific detail) has been suggested by others (Browdy, 1990) as well as implemented in various forms for specific problems such as police districts (D Amico et al., 2002) and electrical power districts (Bergey, Ragsdale and Moskote, 2003). The idea of applying simulated annealing (Zissimopoulos, Paschos and Pekergin, 1991) and genetic algorithms (Chandrasekharam, Subhramanian and Chaudhury, 1993) to set or graph partitioning problems has also been explored. However, adapting the method of simulated annealing to the redistricting problem remains challenging and not entirely straightforward, since there are many choices in how to design the components of a simulated annealing algorithm and the evaluation criteria it uses. Once these evaluation functions are defined for an application of a simulated annealing algorithm, several considerations must be weighed. First, simulated annealing begins with a random start. That is, while the algorithm traverses the space of possible redistricting maps, it must begin from a particular configuration, and this initial configuration will influence how the space is traversed. Some previous attempts at drawing district configurations have begun from the current districting plan with some further testing at other randomly generated starts (D Amico et al., 2002; Bergey, Ragsdale and Moskote, 2003). One immediate consideration, then, is how to generate random map configurations. This is not obvious, and we will explore various algorithms for generating random starts. For example, this can be done by randomly selecting an initial unit for each district and then grow- 9

12 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL ing these units into districts by absorbing neighboring units until all units are allocated. The growth can be guided by adhering to the equipopulation requirement and maintaining good characteristics such as geographic compactness or population homogeneity. We will also consider the opportunities provided by beginning with the alternative plans proposed by interest groups and individuals. Exploring these various options will also help us assess the robustness of the eventual algorithm. A second important consideration is how the algorithm will locate the next map to consider. In a redistricting problem, some obvious options are to perturb the map at the edges of the districts. One might swap census blocks at the edges of existing districts to create new districts. This could be done two at a time or k at a time where k > 2 while maintaining the contiguity requirement. In addition, k could also be regulated by the temperature of the annealing program so that k could be relatively large when the temperature is high at the beginning of the algorithm and would be closer to 2 as the temperature cools. Third, in simulated annealing, if the new map has a better score on the scales being used for evaluation (e.g. competitiveness score or likelihood of electing a minority candidate), then the new configuration is retained as the current plan. If the plan is not better, then it may still be retained, with some probability depending on the temperature parameter. As the search for new configurations progresses, the temperature decreases gradually so that the probability of stepping temporarily to a lower-rated plan declines. This probabilistic acceptance allows the algorithm to search a greater proportion of the overall space in a random fashion and avoids getting stuck at solutions that are only locally optimal. In short, there are several important criteria that determine how a simulated annealing algorithm will proceed for the redistricting problem. It is not obvious a priori how to specify these various items. Accordingly, much of our efforts will focus on fine-tuning the methods for regulation of temperature, generation of random starts, and generation of random moves to new configurations. We are not rigid in our conception of these items, but are seeking to test and explore how best to specify the problem within an optimization framework. Thus, we may ultimately implement a specialized heuristic that resembles simulated annealing but has modified features adapted specifically for our problem. 4 Measurement of Goodness A simulated annealing process uses evaluation functions to compare the goodness of alternative configurations. Such functions aim to measure abstract concepts such as competitiveness, compactness, socioeconomic homogeneity, propensity to elect minority representatives, etc. Part of our agenda is to develop a variety of these evaluation functions. As before, we are not wedded to certain specifications and we intend for our final product to be as flexible as possible in allowing the user to choose various combinations of evaluation functions. There have been quite a few suggestions for how to measure compactness (Niemi et al., 1990; Young, 1988). For instance, one option is to compute the ratio of the district s area to its circumference. Another option is to divide a district s area by the area of a circle with a circumference equal in length to the district s perimeter. Yet another idea is to use a count of how many times the district makes a right or left turn on the perimeter. Indeed, there are many options. Since we intend to provide as much flexibility in the program as possible, we will include a variety of reasonable measures from which the user can select. Since practitioners are often interested in ranking redistricting plans on more than one 10

13 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL measure, we will also allow users to combine multiple measures by specifying a linear combination of the available measures. Two arguments against implementing a method such as simulated annealing is that one is not assured that the solution ultimately arrived upon is the true global optimal map (Altman, 1997) and that any process embodying political values is inherently not objective (Dixon, 1968; Anderson and Dahlstrom, 1990). We concur that redistricting is a political process and that there is discretion in how one implements the measurements of goodness and in devising the parameters that define how the simulated annealing algorithm will proceed. However, we note that we are not requiring the acceptance of the final plan as the globally optimal plan. We are, instead, providing a tool embodying optimization techniques, which have been shown to be highly successful in combinatorial optimization problems, to open up the process and allow a far greater number of participants. Enlarging the base of researchers, in itself, provides a check on the process and on the proposed optimal plan. Our tool, moreover, will be as transparent as possible. All measures and all parameters will be defined explicitly and known. We also note that these criticisms were made before recent advances in the development of performance measures to assess the effectiveness of generalized hill climbing algorithms such as simulated annealing (Jacobson and Yücesan, 2004). These performance measures are helpful both in assessing the likelihood of the algorithm terminating at the globally optimal solution and in choosing the parameters that define the specific algorithm. 5 Formalization of the Redistricting Problem There are many ways to specify our redistricting problem depending on the objective function one wishes to optimize and the constraints one wishes to impose. One specific formulation of the problem might be as follows. There is a set of N units, u 1, u 2,..., u N, and a set of J districts, d 1, d 2,..., d J. Let C be the N N augmented adjacency matrix with entries c ij defined for 1 i N and 1 j N by { 1 if unit i and unit j are adjacent or i = j c ij = 0 otherwise. The convention that c ij = 1 for i = j is adopted to simplify the checking of connectedness of districts. The populations of the N units, respectively, are denoted by p 1, p 2,..., p N. If the districts were equipopulous, then the total population in each district would be the average population, P, given by P = 1 N p i. J i=1 11

14 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL Let X be an N J matrix with elements x ij denoting our decision variables. To specify a map, these variables are chosen for 1 i N and 1 j J so that x ij = The population in district j is then { We have constraints of three types. 1 if unit u i is assigned to district d j 0 otherwise. P j = N x ij p i for j = 1, 2,..., J. i=1 1. Each unit must be assigned to exactly one district, N x ij = 1 for j = 1, 2,..., J. i=1 2. The maximum deviation in population across all J districts is no greater than a specified value PD. That is, for 1 j 1 J and 1 j 2 J, -PD P j1 P j2 PD. 3. In each district, the units must form a connected set, meaning that each unit is accessible from any other in the set via transitions encoded in the adjacency matrix C. It is an elementary result of graph theory (found in many introductory texts) that position (i, j) in the kth power of C is nonzero if and only if some walk of length at most k joins u i to u j. It is then immediate that an n-element subset S of the set of units forms a connected set if and only if the nth power of the corresponding n n submatrix of C is nonzero in every position. 3 Subject to the constraints above, we seek to optimize a specified objective function. The objective function may incorporate many criteria to measure qualities such as compactness, competitiveness, and homogeneity of districts, among others. For example, a measure of competitiveness could be as follows. Let D j be the Democratic share of the Presidential vote in the last election in district j and R j be the Republican share of the Presidential vote in the last election in district j. (Alternatively, D j and R j could be averages over several elections, or the percentages of partisan registration, etc.) A district is deemed most competitive when D j = R j. An overall measure of noncompetitiveness in a map could be the expression below; we would seek to minimize this. z = J (D j R j ) 2. j=1 3 Because the arrangement of units in the plane imposes a linear bound on the number of adjacencies, there are faster algorithms than this for testing connectedness. We merely mention this conceptually simple method to observe that testing connectedness is easy. 12

15 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL Similar measures can be devised for measuring homogeneity with respect to racial or economic criteria, and earlier we described several possible measures of geographic compactness. The overall objective function may be any combination of a large number of such measures. Educational Component An important component of this project is educational outreach, which spans from K 12 to graduate education. For the educational realm in particular, we plan to build a cyberenvironment for redistricting, one that will illuminate the foundations of democracy for all students. The cyberenvironment will be such that the data are stored at a data repository, but the users will be able to use the data through a web interface and utilize the tools we develop to design various redistricting plans and to form a basic understanding of the redistricting landscape. For those students studying the components of democracy, we provide a way to link ideas and collaborate with a broad spectrum of students that transcends geography. This project will aid in preparing tomorrow s social science students to conceptualize social science ideas in a computational way as well as aid in helping today s social science researchers to adopt more computational approaches to the study of social science. In this way, we aim to influence graduate education in the social sciences by helping to carve the frontier of this type of research. Our cyberenvironment will facilitate also research. It will increase the number of researchers in the field and make it easier for them to We will build a tool to be used by anyone. We argue that this research framework is more ideal than the current one where a few politicians sit behind closed doors with propriety software and access to data to determine the political districts that profoundly affect all of us and determine the direction of public policy. We intend this project to transform the way redistricting is done into the indefinite future. Personnel: Cross-Disciplinary Team We bring a broad cross-disciplinary team to this project. Cho, a political scientist, has worked extensively in the area of voting rights and redistricting issues. West, a mathematician, specializes in graph theory and extremal combinatorial problems. Jacobson, a computer scientist, does research in the area of operation research with a specialization in discrete optimization heuristics. He is Director of the Simulation and Optimization Laboratory at the University of Illinois, a teaching and research facility containing software and hardware devoted to computation in simulation and optimization. Our team is broad in that it represents many different fields of study that have not traditionally or commonly worked together. Even more pointedly, however, our team is unique in its ability to communicate with each other and across fields of study, which are often barriers to developing effective broad multidisciplinary research teams. Jacobson and West have effectively advised common graduate students, and Cho has an undergraduate degree in Applied Mathematics with Computer Science as her applied field. As the lead PI, Cho will oversee all aspects of this project. The team will work together in algorithm development. Cho and Jacobson will work together with a graduate student researcher in algorithm implementation. Budget and Work Plan We anticipate our project to run 3 years in duration. The first year will be devoted to developing the optimization heuristic to be implemented. The second year will be devoted to programming and implementation. The third year will concentrate on testing a beta version with users, streamlining the final product, and adding requested features. The budget covers cover 1 month summer salary for Cho and West and 1/2 month summer salary to Jacobson to devote to the project, a full-time graduate 13

16 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL research assistant from the Department of Computer Science, travel to conferences and workshops to discuss and present research related to this proposal, materials and supplies related to the research project including costs for publication and dissemination of findings, and a computer service rate (a standard fee assessed by the Computer Science department to support infrastructure costs) The 3-year budget should be in the range of $290,000, which includes an overhead of 15 percent of direct costs as allowed by the Russell Sage Foundation. Significant additional resources outside this grant proposal for this research project will be donated through Jacobson s Simulation and Optimization Laboratory and Cho s affiliation with the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign. 14

17 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL References Altman, Micah Is Automation the Answer? The Computational Complexity of Automated Redistricting. Rutgers Computer and Technology Law Journal 23(1): Anderson, A. J. and W. S. Dahlstrom Technological Gerrymandering: How Computers Can Be Used in the Redistricting Process to Comply with Judicial Criteria. The Urban Lawyer 22: Bergey, P. K., C. T. Ragsdale and M. Moskote A Simulated Annealing Genetic Algorithm for the Electric Power Districting Problem. Annals of Operations Research 121: Bernstein, Robert A Elections, Representation, and Congressional Voting Behavior: The Myth of Constitutency Control. Prentice Hall. Browdy, Michelle H Simulated Annealing: An Improved Computer Model for Political Redistricting. Yale Law and Policy Review 8: Chandrasekharam, R., S. Subhramanian and S. Chaudhury Genetic Algorithm for Node Partitioning Problem and Application in VLSI Design. Computers and Digital Techniques, IEE Proceedings 140(5): D Amico, S.J., S.J. Wang, R. Batta and C.M. Rump A Simulated Annealing Approach to Police District Design. Computers and Operations Research 29: Dixon, Robert Democratic Representation: Reapportionment in Law and Politics. New York: Oxford University Press. Eglese, R. W Simulated Annealing: A Tool for Operational Research. European Journal of Operational Research 46: Fleischer, M.A Simulated Annealing: Past, Present, and Future. Proceedings of the 27th Winter Simulation Conference 00: Garfinkel, R. S. and G. L. Nemhauser Optimal Political Districting by Implicit Enumeration Techniques. Management Science 16(8):B 495 B 508. Gimpel, James G., J. Celeste Lay and Jason E. Schuknecht Cultivating Democracy: Civic Environments and Political Socialization in America. Brookings. Gray, Virginia A Note on Competition and Turnout in the American States. Journal of Politics 38(1): Grofman, Bernard, Christian Collet and Robert Griffin Analyzing the Turnout-Competition Link with Aggregate Cross-Sectional Data. Public Choice 95(3 4): Gudgin, G. and P. J. Taylor Seats, Votes and the Spatial Organization of Elections. London: Pion. Harris, Curtis A Scientific Method of Districting. Behavioral Science 9: Issacharoff, Samuel Gerrymandering and Political Cartels. Harvard Law Review 116(593):

18 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL Issacharoff, Samuel, Burt Neuborne and Richard H. Pildes Brief as Amici Cuiae for Appellants, League of United Latin American Citizens v. Rick Perry et al. Technical report United States Supreme Court. Iyengar, Shanto and Adam F. Simon New Perspectives and Evidence on Political Communication and Campaign Effects. Annual Review of Psychology 51: Jacobson, Gary C Competition in U.S. Congressional Elections. In The Marketplace of Democracy, ed. Michael P. McDonald and John Samples. Brookings pp Jacobson, S.H. and E. Yücesan Analyzing the Performance of Generalized Hill Climbing Algorithms. Journal of Heuristics 10(4): Keane, M The Size of the Region-Building Problem. Environment & Planning A 7: Key, V.O Southern Politics in State and Nation. New York: Knopf. Key, V.O American State Politics: An Introduction. New York: Knopf. Lowenstein, Daniel H. and Jonathan Steinberg The Quest for Legislative Districting in the Public Interest: Elusive or Illusory. UCLA Law Review 33(1): Mayhew, David Congressional Elections: The Case of the Vanishing Marginals. Polity 6: McDonald, Michael P. and John Samples The Marketplace of Democracy. Brookings. Monmonier, Mark Bushmanders & Bullwinkles. Chicago: University of Chicago Press. Nagel, Stuart S Simplified Bipartisan Computer Redistricting. Stanford Law Review 17(5): Niemi, Richard G., Bernard Grofman, Carl Carlucci and Thomas Hofeller Measuring Compactness and the Role of a Compactness Standard in a Test for Partisan and Racial Gerrymandering. Journal of Politics 52(4): Oppenheimer Deep Red and Blue Congressional Districts. In Congress Reconsidered, 8th edition, ed. Lawrence Dodd and Bruce Oppenheimer. CQ Press pp Papayanopoulos, L Quantitative Principles Underlying Apportionment Methods. Annals of the New York Academy of Sciences 219:3 4. Persily, Nathaniel In Defense of Foxes Guarding Henhouses. Harvard Law Review 116: Pildes, Richard H The Theory of Political Competition. Virginia Law Review 85: Press, William H., Brian P. Flannery, Saul A. Teukolsky and William T. Vetterling Numerical Recipes in C: The Art of Scientific Computing. Cambridge: Cambridge University Press. Shepherd, J. W. and M. A. Jenkins Decentralizing High School Administration in Detroit: A Computer Evaluation of Alternative Strategies of Political Control. Economic Geography 48(1):

19 CHO, JACOBSON, WEST REDISTRICTING PROPOSAL Swain, Carol Strategies for Increasing Black Representation in Congress. In The Politics of Race: African Americans and the Political System, ed. Theodore Rueter. Armond, N.Y.: Sharpe. Thoreson, James and John Liittschwager Computers in Behavioral Science: Legislative Districting by Computer Simulation. Behavioral Science 12: Vickrey, William S On the Prevention of Gerrymandering. Political Science Quarterly 76: Weaver, J. B. and S. W. Hess A Procedure for Nonpartisan Districting: Development of Computer Techniques. Yale Law Journal 72: Wittman, Donald A The Myth of Democratic Failure: Why Political Institutions are Efficient. Chicago: University of Chicago Press. Young, H. Peyton Quarterly 13: Measuring the Compactness of Legislative Districts. Legislative Studies Zissimopoulos, V., V. T. Paschos and F. Pekergin On the Approximation of NP-Complete Problems by Using a Boltzmann Machine Method: The Cases of Some Covering and Packing Problems. IEEE Transactions on Computers 40(12):