The Future of Partisan Symmetry as a Judicial Test for Partisan Gerrymandering after

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II. Conceptualizing and Measuring Partisan Fairness

We now explain the concept of partisan symmetry as a standard for partisan fairness, and then the measurement of how redistricting plans may deviate from this fairness standard. We also discuss whether measures of partisan fairness should be imposed prospectively, before an election is held under a redistricting plan, or retrospectively, and finally we clarify some common misunderstandings about partisan symmetry.


As we wrote in King et al., “The symmetry standard requires that the electoral system treat similarly-situated parties equally, so that each receives the same fraction of legislative seats for a particular vote percentage as the other party would receive if it had received the same percentage [of the vote].”27 Social scientists have long recognized partisan symmetry as the appropriate way to define partisan fairness in the American system of plurality-based elections,28 and for many years such a view has been virtually a consensus position of the scholarly community. We are aware of no published disagreement or even clear misunderstanding in the scholarly community about partisan symmetry as a standard for partisan fairness in plurality-based American elections since the clarification and measures introduced in Gary King and Robert X. Browning in Democratic Representation and Partisan Bias in Congressional Elections.29 This level of consensus is explicitly acknowledged by Justice Stevens, who writes in his opinion in LULAC that “this standard is widely accepted by scholars as providing a measure of partisan fairness in electoral systems.”30 Indeed, as Justice Stevens pointed out, “the symmetry standard was not simply proposed by an amicus to the Court [in LULAC], it was also used by the expert for plaintiffs and the expert for the state in assessing the degree of partisan bias in Plans 1151C [the 2001 Balderas court-drawn plan] and Plan 1374C [the 2003 plan under challenge].31 Moreover, neutral officials such as courts and non-partisan members of redistricting commissions have also regularly made use of it.32

The concept of partisan symmetry is broadly applicable, in that it applies not only to two-party legislative elections, but also to multiparty systems,33 and even non-legislative elections.34 For simplicity of exposition, however, we focus here only on the simple and important case of two-party (Democratic and Republican) contests in single-member, plurality winner legislative districts.

For the purpose of this article, we define an electoral system as a set of specific legal rules that govern an election – such as winning by plurality, who has the franchise, where the voting machines are located, etc. – as well as the legislative districting plan.35 The key to the symmetry definition of fairness is that it evaluates the electoral system as a whole by evaluating how voter preferences statewide are translated into the division of legislative seats between the parties. It is also a simple and direct generalization of the symmetry standard universally applied to candidates in winner-take-all plurality elections in individual single-member legislative districts. We explain the definition of fairness in this simple single-district context first and then discuss the generalization that works for collections of districts in evaluating entire state electoral systems in the context of redistricting.

The electoral rule in the simple context of a single member legislative district is that whichever candidate receives a plurality of the votes wins the legislative seat. It is important to recognize that this obvious definition of fairness requires no knowledge of the vote outcome or who actually will win the election; rather it evaluates fairness by setting rules for allocating all possible vote outcomes to seat outcomes, and refers to candidates only by their vote totals and not by their names or attributes. In particular, the reason it is considered fair for one candidate to win the seat if he or she wins a plurality of the votes is not because of what happened in the election, but rather because of what would happen under the symmetric but opposite hypothetical outcome: if the other candidate had received a plurality of votes instead, he or she would win the seat. An unfair system would be one where we know the opposite hypothetical would not occur.

Thus, the symmetry standard in this case merely involves the comparison of one hypothetical outcome to another. Fairness is defined in this context by each party’s candidate being treated equally under the law by rules that provide an equal opportunity to compete for the seat. Symmetry is thus a way of ensuring “anonymity,” the fairness criterion that prevents electoral system rules from referring to political parties by name rather than in terms of how many votes they receive in the election. Anonymity is ensured by partisan symmetry since if we take an electoral result and switch the names of the parties that received the particular vote outcomes, the seat outcomes would also switch.

This basic symmetry definition given above is applicable to each individual district in all single-member, plurality winner, district-based legislative election contests in the U.S. Any electoral rule that would require one candidate in a district to garner more votes to win than another candidate, or which refers to the names or attributes of the candidates in deciding the winner would obviously not last long in any U.S. court with appropriate jurisdiction. The rule is also a clear reflection of fundamental tenets of American representative democracy and culture.

The definition of partisan symmetry in the context of redistricting takes this same venerable principle and slightly generalizes it to apply to the relevant group of districts, such as an entire state legislature or all the congressional districts within a state. For this group of districts, the symmetry standard requires that the number of seats one party would receive if it garnered a particular percentage of the vote be identical to the number of seats the other party would receive if it had received the same percentage of the vote, or in other words that outcomes not depend upon party names. For example, suppose the Democratic Party receives an average of 55% of the vote totals in a state’s legislative district elections and, because of the way the district lines were drawn, it wins 70% of the legislative seats in that state. Is that fair? That question cannot be answered based on this one piece of evidence alone. It depends on a comparison with the opposite hypothetical outcome: It would be fair only if the Republican Party would also have received 70% of the seats in an election where it had received an average of 55% of the vote totals in district elections. This electoral system would be biased against the Republican Party if it would garner fewer than 70% of the seats and biased against the Democratic Party if the Republicans would garner more than 70%. In other words, partisan symmetry requires that “each political group in a State has the same chance to elect representatives of its choice as any other political group.”36

The key idea is that candidates of each political party should have equal opportunity in translating voter support into the division of legislative seats between the parties: as we noted previously, symmetry requires that the electoral system treat similarly-situated political parties equally. Partisan symmetry says nothing about which candidates should be elected, and it is not conditioned on any particular vote division: it only says that if a party is able to muster a certain fraction of votes, then it should get the same number of seats as the other party would if that party had received the same voter support. Symmetry thus evaluates partisan gerrymandering only by its consequences.

Other features of the electoral system that have sometimes been used as proxies for partisan gerrymandering are only relevant to this definition insofar as they affect the partisan symmetry of the electoral system. These other factors – such as who drew the district lines, whether there was proper citizen input, or whether the districts are compact, split local political subdivisions, or maintain communities of interest – may in fact be of interest to courts or to the legislature for other reasons, or as values in and of themselves, but in terms of fairness to political parties, they are only relevant under this standard if they have an effect on making the electoral system deviate from partisan symmetry. (Of course, the Court may also wish to require some of these other criteria to hold as well.)

Measuring symmetry and partisan bias does not require “proportional representation” (where each party receives the same proportion of seats as it receives in votes). Of course, an electoral system that is proportional, like any electoral system, may treat the parties symmetrically and thus fairly.37 Yet symmetry can exist (or not exist) in all types of electoral systems. Because most electoral systems in the United States are single-member districts that are winner-take-all, in practice they normally give a “bonus” of varying sizes (above proportionality) in seats to the party that wins a majority of the votes across a state. So long as this bonus is awarded based on whoever wins the majority, rather than to a specific party by name, it would be fair under the partisan symmetry standard despite giving non-proportional results.

The range of electoral systems that are symmetric can be ordered by the degree of electoral responsiveness. Electoral responsiveness – also referred to as the “bonus” for the majority party, the “swing ratio,” or the “degree of representation” – quantifies this idea by asking how much the seat division between the parties change as the vote proportions change. A purely proportional system is one in which a one percent increase in the votes for a party leads to a one percent increase in seats for that party. Statistical models of plurality-based elections have demonstrated that plurality-based elections are only rarely proportional, i.e., they exhibit an electoral responsiveness that is different from one. If, for example, the electoral responsiveness were 2, and there were only two political parties, this would mean that, on average, for every one percentage point gain in vote share above but near 50% a party could expect to gain an additional 2 percentage points of seat share in the legislature, e.g., for a vote share of 60 percent, a party could expect to control roughly 70 percent of the seats in the legislature. This common pattern violates proportional representation but does not violate symmetry, so long as whatever party wins a majority of the votes gets the bonus. Under symmetry, there is nothing necessarily unfair about one party winning a greater proportion of seats than the other, so long as that “one party” is not any particular party. An electoral system may have any degree of partisan bias, no matter what level of responsiveness happens to exist.

Electoral responsiveness is often regarded as a normatively good feature of elections. Certainly elections in which the seat division between the parties did not respond at all to changes in voter preferences would not be democratic. Low levels of responsiveness can be produced by a legislative redistricting plan, or by other features of elections, such as high levels of incumbency advantage, many uncontested elections, weak candidates, or a politically polarized electorate. Most scholars therefore regard electoral systems with higher levels of electoral responsiveness as better,38 and this is one of the reasons many favor the American system of district-based elections, since it tends to produce a higher level of responsiveness than other systems. A few state constitutions favor what we think is properly conceptualized as high levels of electoral responsiveness, i.e., a preference for competitive seats, but it is not clear that the Supreme Court has addressed this issue other than to explain that in making partisan gerrymandering justiciable, they were not favoring proportional representation. That makes a great deal of sense in this context, because requiring proportional representation in the American context of single member district plurality-based elections is effectively synonymous with requiring low levels of electoral responsiveness, something that few favor and something that has little basis in American law.

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