Focusing on the last election, the researchers varied the state's congressional districts to calculate what the outcome of the 2012 U.S. House of Representatives elections might have been had the state's districts been drawn to emphasize nonpartisan boundaries. The team re-ran the election 100 times -- using the same votes as in 2012 and tweaking the voting map with only the legal requirements of a redistricting plan in mind. Not once did they get the split of Democratic and Republican seats seen in the actual election.

The researchers hope the study will bolster calls for redistricting reform in the 2016 election season.

During the 2012 elections in North Carolina, Republicans took nine of the state's 13 U.S. House seats although 51 percent of the two-party vote went to Democratic candidates.

The gerrymandering that led to these results isn't unique to North Carolina or any specific party. Both Democrats and Republicans have used it for political advantage over the years. However, new technology makes it possible to draw partisan districts with increasing precision.

"North Carolina's 12th and 4th congressional districts in particular look a little crazy," said study co-author and Duke senior Christy Vaughn, who is originally from Taylorsville, N.C.

Vaughn and Duke math professor Jonathan Mattingly attempted to quantify how gerrymandering actually affects recent election outcomes.

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They used a statistical algorithm to randomly redraw the boundaries of North Carolina's 13 congressional districts. The model produced thousands of versions of the redrawn map. All of them were based only on the legal requirements of redistricting, ensuring the districts represented roughly equal numbers of voters and were as geographically compact as possible, without accounting for race or political affiliation.

Next the researchers re-ran the 2012 U.S. House election on a computer and calculated what the outcome would have been for each new version of the map.

"If someone voted for a particular candidate in the 2012 election and one of our redrawn maps assigned where they live to a new congressional district, we assumed that they would still vote for the same political party," Vaughn said.

After re-running the election 100 times, with a randomly drawn nonpartisan map each time, the average simulated election result was 7 or 8 U.S. House seats for the Democrats and 5 or 6 for Republicans. The maximum number of Republican seats that emerged from any of the simulations was eight. The actual outcome of the election -- four Democratic representatives and nine Republicans -- did not occur in any of the simulations.

"We used the exact same votes as the 2012 election, and by only tweaking the district boundaries we got drastically different results," Mattingly said. "The outcome of the election varies according to how you draw the district boundaries."

The model isn't meant as a tool for creating new voting districts, the researchers say. "Our districts aren't perfect," Vaughn said.

But the methods they used can identify when a particular set of district boundaries may misrepresent the will of the people, and quantify the potential effects on an election. "This gives us a way to judge how reasonable a proposed redistricting is and what we should expect under a given set of boundaries," Mattingly said.

The researchers hope the study will bolster calls for redistricting reform in the 2016 election season in North Carolina and other states. Any changes in the districting process would most likely go into effect after the next national Census in 2020, when states again redraw the boundaries of their congressional maps to reflect changes in their population.

The study appears online this week on the preprint server arXiv. The work was supported by Duke.