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13. Packing and Cracking:

The Gerrymander Paradox


The Question:

(///Check before publication: SCOTUS’s decision on Gill v. Whitford///)

In an election for parliament, each political party obtains more or less the number of representatives that reflects its share in the population. If, for example, Party A has the support of 60 percent of the population, then that party’s delegation will be just about 60 percent of parliament.


The Paradox:

Sometimes. And sometimes not.

In the 2016 elections for the United States House of Representatives, 1,859,426 citizens in the State of Virginia cast their votes for Democrats, 1,843,010 for Republicans. Nevertheless, the minority of Republicans sent 7 representatives to Washington DC while the majority of Democrats sent only 4. In Ohio, Republicans scored 58 percent of the vote but obtained 75 percent of the seats, while Democrats, with 42 percent of the vote, got 25 percent of the seats

Overall, the Republican Party obtained 63,173,815 votes (50.56%), the Democratic Party 61,776,554 (49.44%). Had the 435 seats in the House been allocated strictly in proportion to the parties’ strengths, Republicans should have received 220 seats, Democrats 215. In fact, Republicans won 241 seats, 21 more than their fair share, Democrats 194, 21 less than their fair share.



It takes many kinds of people to make up a nation. Young and old, rich and poor, straights and gays, urbanites and suburbanites, religious and secular, whites, black, Latinos, conservatives and liberals, hipsters and cranks, folks who love the sun and folks who enjoy the snow. To a certain degree, neighborhoods are homogenous and people who live in close vicinity usually have similar interests and worries. To represent the objectives and aspirations of these citizens, keeping in mind their characteristics and particularities, representative democracies divide the nation into districts, each of which sends one representative to parliament.

The United States, for example, are divided into 435 congressional districts. These districts are supposed to comprise approximately the same number of citizens – on average about 710,000 people – and be compact and contiguous, unless there are natural obstacles in the way. In that manner, the interests of groups of citizens, with all their idiosyncrasies and special interests, are represented by the 435 congresspeople.

Political parties try to push the maximum number of their own party’s representatives into parliamente. And there’s the rub. Usually, the party in power gets to design the congressional districts. In the USA, they must abide by the requirement that the districts comprise about 710,000 citizens. But in designing the contours of the district, the ruling party has some flexibility. And they often use this freedom to draw the contours in such a manner as to maximize the chances of their party’s candidates getting elected.

One of the early such manipulations occurred in 1812 when election districts were redrawn in Massachussetts. Leading the effort was Governor Elbridge Gerry. When a cartoonist depicted one of the strangely shaped districts as a salamander, a new term was born: Gerry’s salamander became Gerrymander, both as a noun, as in ‘a gerrymander’, and as a verb, as in ‘to gerrymander’.



As we saw above, the Republican party managed to do so in 2016. But how? By packing and cracking, that’s how. Pack the other party’s adherents into few districts and crack one’s own electorate into many districts.

Figure 1 illustrates what can happen when 50 citizens vote for five representatives. With 60 votes overall for Party Blue and 40 for Party Red, the fair allocation would be three seats for Blue and two for Red. By judiciously packing and cracking, districts can be designed so that there will be five seats for Blue and none for Red, or two for Blue and three for Red.

When the party in power designs congressional districts, each encompassing about 710,000 citizens, they allow them to snake through the nation, grabbing as many voters of the opposing party as possible along the way (and wasting few of one’s own), thus packing them into a single district. A blatant historical example is Congressional District 12 in North Carolina of 1992.(See Figure 2.)


Technical supplement:

As one may expect, whenever a party believes that it has lost seats because of gerrymandering it files a lawsuit. The claim usually is that the ‘one person one vote’ maxim is violated because the packed votes are wasted and the cracked votes carry more weight than they should. Most suits were unsuccessful, mainly because of the plaintiffs’ inability to quantify the extent by which the district boundaries have been manipulated. After all, what does compact mean in this context. The most compact region, mathematically, is a circle, but there may be lakes, rivers or mountain ranges which serve as natural boundaries to a district. Furthermore, it is mathematically impossible to cover a nation with circular districts without leaving interstices between them. Judges in general are at a loss.

Recently, a law professor and a political scientist proposed a measure that does measure the degree of gerrymandering.[1]  The authors proposed a so-called ‘efficiency gap’ which takes account of wasted votes. There are two kinds of wasted votes: those for a losing candidate and those for a winning candidate that go beyond what is necessary for victory 

To illustrate, let us assume five districts with 100 voters in each. Party A wins districts 1 to 4, by 53 to 47 votes. District number 5 is won by Party B with 85 votes to 15. Thus, Party A garnered four sets, against one seat for Party B, even though according to the proportion of votes (227 to to 273) Party A should have obtained fewer seats than Party B.

The efficiency gap is computed thus: Party A had 8 superfluous votes (in each the four districts it obtained 53 votes instead of the bare majority needed of 51), and another 15 votes in district 5. So it wasted 23 votes. Party B, on the other hand, wasted 34 votes in district 5 (85 votes instead of the bare majority of 51), and all its votes in the other four districts (4 times 47). Altogether Party B wasted 222 votes. The efficiency gap is defined as the difference of wasted votes for each party, as a proportion of total votes cast: (222-23)/500, i.e., 40 percent.

The efficiency gap is a measure of the undeserved share of seats. In the above example: had the election been fair, Party A should have received only 2 seats: (227/500) x 5 = 2.27 seats, rounded to 2. In fact, it received 2 additional seats.


Figure 1:


Figure 2: Congressional District 12 in North Carolina, 1992.


[1] Stephanopoulos, Nicholas O. and McGhee, Eric M. (2015) "Partisan Gerrymandering and the Efficiency Gap," University of Chicago Law Review: Vol. 82, 2. 

Comments, corrections, observations:    

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