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“O h, my,” said Alice, “is it really true that there are elections in Wonderland?”

“Of course, you foolish girl,” the Queen of Hearts replied. “This is a constitutional monarchy. The Single Member of the Congress of Wonderland is elected by democratic means. Come, I shall introduce you to the electorate.”

Alice followed the Queen to a field, in the middle of which was a table where the Mad Hatter and three of his friends were feasting. “The Mad Hatter’s Party, with its four members, is one of the three political parties here in Wonderland,” the Queen told Alice. “The other two parties, Tweedledum’s Party and Tweedledee’s Party, have three members apiece.” Sure enough, Tweedledum and Tweedledee stood nearby, each with two followers.

“The electoral system of Wonderland,” the Queen continued, “is based on the method of Plurality Voting by Single-Member Districts, sometimes known as Winner Takes All. You understand how that works, of course.”

“No,” said Alice sorrowfully, “I am afraid I do not.”

The Queen shouted, “Off with her head!”

“Please,” Alice begged, “I’ll do my best to learn about the electoral system of Wonderland, if only you will explain it.”

“Very well,” the Queen said. “But I must warn you, the more I explain about Plurality Voting, the less you will understand it. For example, the most important part of our system of Plurality Voting by Single-Member Districts is the shape of the district.”

“I cannot imagine why,” Alice said.

The Queen was shocked. “Have you never heard of the Gerrymander?” At the mention of its name, the Gerrymander—a large and rather fearsome creature somewhat like a cross between a salamander and a Jabberwock—shambled forth. “Go on,” the Queen ordered the beast, “draw the Single-Member District for the forthcoming congressional election.”

Alice watched as the Gerrymander, dipping its brush in the pot of red paint hanging from its neck, began to outline a square in the grass. Soon the square’s borders included the three members of the Tweedledum Party and the three members of the Tweedledee Party. But when it came to the four supporters of the Mad Hatter’s Party, the Gerrymander painted a red stripe right down the middle of their banquet table.

“There,” the Queen said with satisfaction. “Thanks to the Gerrymander, we now have a Single-Member District with two large parties—those of Tweedledum and Tweedledee—with three voters apiece, and one small party, the Mad Hatter’s Party, with only two voters.”

“But that isn’t right!” cried Alice. She rushed to the Mad Hatter. “Aren’t you going to do something?”

“Why on earth should I?” he asked.

“You have the biggest party,” Alice replied. “Your party has four members, and the other two parties have only three voters apiece.”

“Oh, you silly girl,” said the Mad Hatter, pointing to the red stripe bisecting the table. “Can’t you see that my party has only two voters eligible to vote in the Single-Member District?”

Alice noticed Tweedledum and Tweedledee handing purses full of coins to the Gerrymander. “Don’t you see what they’ve done to you? They’ve drawn the Single-Member District to minimize the power of your voters!”

“Of course they have,” the Mad Hatter chuckled. “We’d have done the same to them, if we could afford to pay the Gerrymander.”

“But it isn’t fair to your party! Why don’t you protest?”

“Protest!” All four members of his party—the two inside the Single-Member District and the two outside—burst into laughter. “Protest? Why, our elections have always been held this way. To protest would be unpatriotic and vulgar.” At this, the Mad Hatter and his friends resumed their banquet.

Alice was thinking very deeply. At length she said, “I have devised a strategy by which your party can maximize its influence—even though the Gerrymander has turned you into a minority party.”

The Mad Hatter looked up from the table in annoyance. “Are you still here?”

Alice explained her plan. “The Queen of Hearts said that Wonderland has a Plurality Voting System. Therefore—it is all very puzzling, I admit—the winner needs either a simple majority in a two-party race or less than a majority—a mere plurality—in a three-party race. In a plurality election, the greater the number of parties, the smaller the plurality that is necessary to win.”

“Yes, yes, yes,” the Mad Hatter said, drumming his fingers on the table. “Is there a point to this tedious lesson in political science?”

“Who can get that plurality is very, very important,” Alice insisted. “Your two-person party is too small to win. Therefore you must decide which of the other two parties you prefer.”

“Oh, that is easy,” replied the Mad Hatter. “The positions of the Tweedledee Party are nearest our own positions, whereas we find the Tweedledum platform positively hateful.”

“Well, then,” Alice responded, “you must vote for the Tweedledee Party—not for your own.”

“Not vote for our own party!” the Mad Hatter exclaimed.

Alice explained: “If you vote for the Tweedledee Party, then it will defeat the Tweedledum Party, by five votes to three. But if you vote for your own party, then you increase the chances that the Tweedledum Party will win. It’s only rational.”

“It may be rational, but this is Wonderland, and I’ll have none of it!” the Mad Hatter declared.

There was no time for further argument, for at that very moment the Queen ordered, “Let the ballasting begin!”

A large balloon appeared above the treetops and drifted over the field. The balloonist shouted down to the Mad Hatter’s Party: “How do you want your ballast cast?”

“Two for the Mad Hatter’s Party!”

The balloonist tossed down two bags of ballast, which crashed in the midst of the table. Following the instructions of the other parties’ voters, he cast three bags of ballast at the feet of Tweedledum and three at the feet of Tweedledee.

“The ballasting is complete,” the Queen announced, as the balloon, deprived of ballast, drifted up into the sky and disappeared, taking the panicked balloonist with it.

“The election is a tie,” Alice observed. “Tweedledum and Tweedledee each have three votes.”

“No matter,” said the Queen. “Under our Single-Member District Plurality Voting System, the outcome in a close race is often decided by the way the Swing Vote breaks.”

“Who casts the Swing Vote?” Alice asked.

“Why, you do, little girl. Guards!”

Two guards appeared and forced poor Alice to climb up a tree containing an old, rotten, and very unsafe swing. With a great deal of anxiety, Alice sat in the swing and hung on for dear life as the guards gave it a push.

Back and forth Alice swung. As she passed overhead, first the Tweedledum Party and then the Tweedledee Party reached up, promising concessions in return for her support. Finally, on the third pass, the Swing Vote broke. Screaming, Alice was hurtled into the arms of Tweedledum.

“I got the Swing Vote!” Tweedledum exclaimed. “I won the election! I won the election!”

“But that isn’t fair!” Alice cried. “It isn’t fair three ways! It isn’t fair the first way because the district was Gerrymandered, so the biggest party, the Mad Hatter’s, was turned into a minority. And it isn’t fair the second way because the plurality method of voting ensured that either the Tweedledum Party or the Tweedledee Party would win—even though a majority of the voters in the district voted against each party. And it isn’t fair the third way because the election was so close that its outcome was settled by a Swing Voter—me—whose views may have nothing in common with what all of the other voters in the district want. It isn’t fair at all! It’s a travesty of democracy, which means nothing if it does not mean majority rule!”

The Queen gasped. “Little girl, what does democracy have to do with majority rule? In Wonderland, democracy means the Rule of the Largest Minority, helped out by a minuscule Swing Vote, in a Gerrymandered Single-Member District. Majority rule, indeed! Off with her head!”

T he electoral system of Wonderland, as described above (with apologies to Lewis Carroll), is—as Alice rightly insists—unjust and perverse. Unfortunately, that electoral system is our own. (Coincidentally, it is one that Carroll himself would not have approved of. A mathematician by training, he was fascinated by voting systems and produced important work on voting theory—including developing elaborate alternative voting procedures that would eliminate bizarre distortions like those in Wonderland—that went completely unnoticed until the 1950s. He used to pass out pamphlets explaining his obscure theories to his Oxford colleagues, none of whom had an inkling as to what he was talking about.)

Plurality voting by single-member districts is how we elect the House, state legislatures, city councils, and other legislative bodies. Our method produces the same undemocratic effects identified by Alice, but they are somewhat less humorous when we tally their political consequences:

GERRYMANDERING Under the Constitution, state legislatures are permitted to redraw the lines of U.S. House districts every 10 years, following the census. If the Republicans gain control of the statehouses in the midterm elections next November (32 states currently have Republican governors; 18 have GOP-controlled legislatures), this could spell disaster for the Democrats. As Republican National Chairman Jim Nicholson predicts: “The winners are going to determine the political landscape in at least the first decade of the next millennium, because they are the people who are going to preside over the process of reapportionment and redistricting of their respective states as a result of the 2000 census.” Because the party of the president usually loses seats in midterm elections, this is an ominous prospect. And Democrats have good reasons to fear a Republican gerrymander: The current 15-seat Republican majority in the House is largely due to cynical GOP efforts during the last round of redistricting in 1991 to forge what some Democrats have called an “unholy alliance” with black and Hispanic Democrats to carve up racially mixed liberal districts into “safe” black and Hispanic seats and equally “safe” Republican seats. The GOP even went so far as to make expensive redistricting software available to minority activist groups as part of its plan to split up the white liberal vote and ghettoize the nonwhite liberal vote. As a result, there are only four white Democrats in the House from South Carolina, Georgia, Alabama, Mississippi, and Louisiana combined. In Newt Gingrich’s Georgia, before racial gerrymandering, there were nine Democrats (eight white and one black) and only one Republican. Today the Georgia delegation numbers eight Republicans—all white—and three Democrats—all black.

SWING VOTE A relatively modest swing vote breaking rightward has helped make the South a solidly Republican stronghold. A shift of only a few percentage points can move divided districts from the Democratic to the Republican camp. Where the districts themselves are swing districts, holding the balance of power between the two parties in Congress, the votes of a tiny minority of swing voters in a few districts can create a revolution in national politics. Morton Kondracke, a columnist for Roll Call, estimates that less than 12,000 voters nationwide—or six-hundredths of 1 percent of the eligible voting population—swung the vote to the House Republicans in 1996.