All answers must be indicated on the MARK SHEET.
Read the following magazine article about mapping the districts used in the election of public
officials, and answer the questions below.
Paragraph１ Gerrymandering — the drawing of electoral boundaries to benefit a particular political party — is currently a hot political topic in the US, where the Supreme Court is considering a landmark case on the practice. But can electoral maps ever be drawn fairly? And what exactly does fairness mean? To answer these questions, we need to put mathematics at the heart of politics.
Paragraph２ Underpinning the democratic process is the idea that all votes should count equally: if it takes a thousand voters to elect a representative in one district, for example, it shouldn't take only two in another. This is an admirable goal, and one reason why regular population censuses form an important part of democratic life. But even within electoral districts of similar size, a single vote doesn't always carry the same weight. The value of a few votes in finely balanced districts is exaggerated under the winner-takes all system. This is the system typically used for representative elections across the US, the major exception being the election of the president. Under this system, a party can win millions of votes and still secure no representation.
Paragraph３ In other countries using a winner-takes-all system, politicians generally don't get to decide the electoral maps: in the UK, for example, these are drawn by independent boundary commissions. But in the US, those in power across most of the country have almost total freedom to redesign the maps. And redesign them they do. Republicans and Democrats are both guilty of gerrymandering, despite both sides agreeing that it's wrong. The classic technique to hijack an election is called “packing and cracking": a gerrymanderer tries to create a small number of districts packed with their opponent's voters, and draws other seats to spread the remaining vote so there isn't quite enough for a majority. This results in their opponent winning a few seats with large majorities, while narrowly losing many more. But spotting the practice is tricky, and proving it even trickier.
Paragraph４ However, despite the threat to the democratic process, when political bias has determined the drawing of electoral boundaries, American courts have up to now been largely toothless. The result is that voters don't choose their elected officials; instead, elected officials choose their voters. The case now being considered by the US Supreme Court has its origins in a redrawing of the electoral map of Wisconsin by Republican legislators in ２０１１. The benefit to their party was obvious, as a year later they won ６０ per cent of the seats in the Wisconsin State Assembly with less than half the overall vote. When they repeated this feat at the ２０１４ elections, a group of Democrat voters sued. Nearly every similar lawsuit had failed, but surprisingly this group won. In November ２０１６, the state's federal court in Madison concluded that the maps were so biased that they violated the constitutional rights of Democrat voters.
Paragraph５ But how should we define fairness? For most people, a natural definition is found in proportional representation, where the percentage of votes won by a party aligns with its share of seats. But that is far from the intent of winner-takes-all systems, where non-proportional results are typical. Somewhere like Massachusetts, for example, has a solid Democrat majority spread evenly across the state — so all nine members returned to the US House of Representatives are Democrats. “Even if you tried to gerrymander Massachusetts in favor of Republicans, it would be extremely hard,” says Mira Bernstein, a mathematician at Tufts University, near Boston. The Supreme Court has previously ruled that proportional representation is not guaranteed by the constitution, thus excluding it as a way of defining "fair" boundaries.
Paragraph６ One test will be obvious to anybody who has ever seen a gerrymandered district: it looks funny. This is hinted at by the word "gerrymander” itself, coined after the １８１２ redistricting plan of Massachusetts governor Elbridge Gerry, whose redrawn maps included one notorious district bizarrely shaped like the creature known as a salamander. Ever since, mathematicians have tried to craft some measure that would reveal when a district was too strangely shaped to be anything but the product of a party-political agenda, The trouble starts when you try to quantify what it is that makes one shape more bizarre than another. One simple test measures convexity, or how closely the district's area matches that created by placing a giant elastic band around it. Squares and rectangles are very convex, while crescent moons and star shapes are not. Tests like convexity are a step in the right direction, but ultimately they fail a key test: sometimes, districts just need to be a funny shape. Highways, rivers, mountain ranges and city boundaries all impose real limitations on map-makers, and, for reasons that are perfectly justifiable, this can result in shapes no less strange than Gerry's salamander.
Paragraph７ In ２０１４, Nicholas Stephanopoulos of the University of Chicago Law School helped to develop an alternative test. Called the "efficiency gap," it's a simple way to hunt for signs of packing and cracking, and has accompanied the Wisconsin case all the way to the Supreme Court. The efficiency gap is based around counting "wasted” votes for all political parties, a wasted vote being defined as one that doesn't contribute to electing a representative. Every system will have wasted votes, but if one party is wasting substantially fewer than another, it's likely to be a symptom of gerrymandering. In Wisconsin, the efficiency gap was １３ per cent in favor of the Republicans, three times the average across the country. The lawyers in the original court case argued that anything over ８ per cent should be considered unconstitutional, and are hoping the Supreme Court approves their logic. But for some, the efficiency gap fails because it again assumes that there has to be a fit between vote share and representation. "There is absolutely no reason to think that this is required by the constitution," emphasizes Bernstein,
Paragraph８ Arguably, the best mathematical test for gerrymandering may be to use the ability of computer simulation to generate thousands of different maps. A team led by Jonathan Mattingly at Duke University, North Carolina, recently used an algorithm to randomly draw ２０,０００ possible electoral maps for Wisconsin that satisfied all of the criteria required in US law. In most of these, the Republicans won a majority, making it seem like the Democrats were simply at a natural disadvantage. But in most of the maps, Republicans secured a narrow advantage, while their ２０１４ margin of victory was reproduced only in a very small number. This means that the current Wisconsin electoral map is clearly an exceptional case and therefore is likely to have been gerrymandered. For mathematicians like Bernstein who worked on the algorithm, this statistical analysis is vitally important yet has been largely ignored in favor of the efficiency gap.
Paragraph９ "If the court rules the Wisconsin map unconstitutional under a particular test," says Joshua Douglas at the University of Kentucky, "then that will place an outer limit on the worst forms of gerrymandering. The ruling would ultimately produce fairer maps, which also will likely give average Americans more confidence in the election process." But, while a strict mathematical test for gerrymandering would help level the playing field, it is unlikely to help the US overcome its party-political divides. Those with strong political views tend to vote with their feet, moving to live near those who hold similar opinions. Democrats cluster in cities, while Republicans dominate surrounding districts. At the end of the day, the problems pulling American society apart arise when people start gerrymandering themselves.
Timothy Revell. Wrong division How math can save democracy from gerrymandering. 2017.
(１) Choose the best way to complete each of these sentences about Paragraphs (１) to (９).
A discusses how computer simulation can be used to generate large numbers of potential electoral
maps, thus providing indications of gerrymandering.
B discusses how gerrymandering is much less likely to occur in Wisconsin than in Massachusetts.
C discusses the pros and cons of a new method for measuring the fairness of electoral mapping based on the proportion of votes wasted for each of the parties involved.
D discusses the role of American courts in regulating the practice of gerrymandering, mentioning an important case decided in a state federal court several years ago.
E explains a flawed method of testing whether gerrymandering has taken place based on the shape of the resulting electoral districts.
F explains that, even if the upcoming Supreme Court decision recognizes a mathematical method for judging gerrymandering, this will not eliminate the party-based divisions in America today.
G explains why gerrymandering is particularly likely to occur in the United States and how it is most typically done.
H explains why it is extremely unlikely that the Supreme Court will come to a decision that will reduce the occurrence of gerrymandering in American elections.
I introduces the concept of proportional representation and explains why it cannot serve as a measure of fair electoral mapping in the American context.
J introduces the concept of the efficiency gap based on geometric forms, explaining why it has been largely ignored because of the attention given to computer simulation.
K introduces the principle that each elector's vote should have equal value and explains why it is difficult to maintain under particular electoral systems.
L introduces the term gerrymandering, briefly explaining its meaning and that it is now a controversial topic.
(２) From the box below, select the most appropriate way to complete each of the following sentences concerning people referred to in the article.
１ The academic who is quoted as arguing that creating fairer electoral maps is likely to increase public confidence in American democracy is
２ The federal court judge in Madison, Wisconsin, who initially heard the suit brought by Democrat voters against the Republican legislators responsible for redrawing the electoral districts of the
３ The head of the team which used computing to generate twenty thousand potential maps of Wisconsin electoral districts is
４ The legal expert who contributed to the creation of the efficiency gap test used in support of the Wisconsin State Assembly law suit is
５ The mathematician who argues that the ideological assumptions underlying the efficiency gap test have no constitutional basis is
６ The statesman who created an electoral district with a particularly bizarre shape is
F none of the above.
(３) Choose the best way to complete each of these sentences, which refer to the underlined words in the passage.
１ Here hijack suggests that an election has been won
C narrowly. D unfairly
２ Here toothless indicates that regulation by the courts has been
３ Here feat refers to a
４ Here aligns with means
５ Here bizarrely means
６ Here ultimately means
A from the start.
B in the end.
E without doubt.
７ Here symptom means
８ Here help level the playing field suggests that the election of representatives would be made
A less biased.
B less complex.
C more controversial.
(４) Choose the best way to complete the following sentence concerning the position of the author of the passage, Timothy Revell.
Revell tends to agree with Mira Bernstein that the most effective way to prove that gerrymandering has taken place is through the use of
A computer simulation.
B convexity measurements.
C efficiency gap testing.
D proportional representation,
E regular population censuses.