Thanks to a Carolina Journal reader, I have learned of a computational error I made in putting together recent columns about the efficiency-gap analysis. That’s the tool that has attracted national attention this week because of the U.S. Supreme Court case of Gill v. Whitford.

Opponents of partisan gerrymandering in electoral redistricting tout the efficiency gap as an effective tool to help courts decide whether an election map is “too partisan.” The high court could decide in Gill whether efficiency-gap analysis provides a basis for throwing out election maps in Wisconsin. The impact would have ripple effects in North Carolina and across the country.

The Aug. 25 Carolina Journal Online column “Exposing gaps in the ‘efficiency gap’” featured my attempt to perform efficiency-gap analysis for a single election conducted under one election map. I chose the 2008 N.C. Senate election.

My mathematical computations were correct, but I made an error in determining what constituted a “wasted vote.”

Efficiency-gap analysis assumes every vote cast for a losing candidate is “wasted. ” So far, so good.

The analysis also assumes that every vote cast for a winning candidate is wasted, in excess of the number of votes the candidate needed to win the election. I assumed initially that this meant every vote the winning candidate earned in excess of the number of votes the losing candidate earned. In other words, if Smith beat Jones, 40,000 to 25,000 votes, then 14,999 of Smith’s votes would have been “wasted.” He needed only 25,001 votes to beat Jones.

That is the wrong reading of efficiency-gap analysis. Under that analysis, Smith actually needed 32,501 votes to beat Jones. That’s because 32,501 votes represents one vote more than 50 percent of the 65,000 total votes cast. Rather than 14,999 wasted votes, winning candidate Smith had 7,999 wasted votes. (Technically, Smith’s party had those wasted votes, since efficiency-gap analysis assumes that parties control votes that are deployed across the state.)

This means I overcounted the number of wasted votes for winning 2008 Senate candidates across North Carolina.

Did the error render the rest of my analysis useless? No.

A corrected district-by-district analysis suggests that Republicans “wasted” more than 1.3 million (76 percent) of their votes, while Democrats wasted fewer than 1.1 million (55 percent) of their votes. Republicans “wasted” 275,000 more votes than Democrats. That yielded an efficiency gap of 7.4 percent. Discount third-party votes, and the gap widens to 316,000 votes, a gap of 8.6 percent. This is because the 17th District featured a race between a Republican and a Libertarian. Remove the Libertarian from the equation, and the wasted Republican vote total jumps up by more than 46,000.

The original column suggested a smaller efficiency gap of 4 percent and outlined scenarios that would have increased that gap to the 8 percent dubbed “presumptively unconstitutional” under some efficiency-gap literature. With the larger efficiency gap detected in the corrected numbers, the alternate scenarios set out as possible ways to surpass 8 percent become even more plausible.

Two other items are worth mentioning here. First. the original column addressed the issue of uncontested races but made no attempt to adjust for them. Since 10 Democrats and 10 Republicans ran uncontested races in 2008, they roughly canceled each other out. The 17th District offered the only two-party race between a major-party candidate and a Libertarian. We’ve seen how those numbers impact the overall efficiency gap. My next column gave credit to the efficiency gap’s authors for recognizing that their theory didn’t do a great job accounting for uncontested races. They offered suggestions for adjustments that would help address the problem. It’s unfortunate for efficiency-gap proponents that those adjustments move the analysis further away from the mathematical precision that it promises to provide and further into the realm of educated guesswork.

Second, recalculating efficiency-gap numbers highlighted a problem for a theory that assumes that every election contest will pit only two major-party candidates. Take the case of the 2008 N.C. Senate race in District 8. A Democrat beat a Republican, 47,905 votes to 45,093. But a Libertarian also collected 5,454 votes. How should efficiency-gap analysis account for this result? In my original calculation, I assigned 45,093 wasted votes to Republicans and 2,811 to Democrats — using the assumption that the Democrat needed 45,094 votes to win. The Libertarian didn’t enter into the equation. But the correct efficiency-gap analysis assumes that a winning candidate needs 50 percent plus one vote to win. In this case, that’s 49,227 votes. The Democrat fell 1,322 short of that mark. Should we subtract that number from the Democrats’ wasted-vote total? Should we assume zero wasted votes for the Democrat? Should we eliminate the Libertarian votes and assign the Democrats 1,405 wasted votes by considering the two-party vote totals alone? I suspect efficiency-gap experts have cooked up an answer to that question. But it involves adjustments that stray from actual vote totals. Once again, the illusion of mathematical precision disappears.

The bottom line is that the calculation errors in the original column do not blunt its central message about the efficiency gap’s unreliability as a tool for determining whether an election map should be presumed constitutional.