Which matters most when determining the popularity of a particular day for early voting: the total number of votes cast that day, or the average number of votes cast per hour?

Who cares, you ask? The N.C. State Board of Elections. That much was apparent Thursday as the board debated the merits of mandating Sunday voting for one eastern N.C. county.

The debate ought to remind us that misleading statistics can skew political discussion.

The story starts with an early-voting plan for Craven County’s general election this fall. Craven had offered 548 total hours of early voting for the last presidential election in 2012. All three members of the county’s Board of Elections agreed this year that the number of early-voting sites and early-voting hours should increase.

The board’s two Republicans submitted a plan that added three voting sites and 15 total hours of early voting, a 2.7 percent increase. That included an extension of weekday hours to 7 p.m. during the closing days of early voting.

But, in contrast to 2012, Craven County’s plan featured no Sunday voting. That didn’t sit well with Democratic elections board member Zeda Trice. She voted against the GOP plan and submitted an alternative with four hours of early voting at a single site on consecutive Sundays.

In weighing the merits of Trice’s proposal, Democratic state elections board member Joshua Malcolm latched onto the statistic of voters per hour. In 2012, more than 400 Craven County voters cast ballots on the first Sunday of early voting. Roughly 370 voters headed to the polls one week later. Those totals corresponded to averages of 100 voters per hour on the first Sunday, and 93 voters per hour on the second.

Those averages were among the highest for Craven County’s 2012 early-voting turnout, and that fact convinced Malcolm and Democratic colleague Maja Kricker that Craven should trade one day of Saturday voting for Trice’s proposal for two days of Sunday voting.

Their logic failed to convince the state board’s Republicans. “The low days are the two Sundays in 2012, are they not?” asked board member James Baker. “You have 407 people and 374 on this chart who voted in 2012, and some days you had well over 2,000 voters. … Clearly, voting is much more on the weekdays.”

When Trice responded that the 2012 election record included just four hours of voting on each Sunday, Baker reminded her that her 2016 plan would employ the same standard.

“When you’re trying to compute the number of voters per hour, if you only have that site open for a few hours, and you only have one site open, of course you’re going to have a high number of voters per hour because they’re all crammed into a short period of time,” Baker explained. “You’re going to have a lower number of voters per hour when you’ve got many sites open for 13 hours a day, certainly.”

Malcolm rejected Baker’s reasoning. “You could take that argument and turn it on its head and say, ‘Well, hell, that tells you that instead of being open for four hours, you need to be open 12 [hours on Sunday] because they’ll come.”

“Or 24 [hours]. Or 17 days. Or 30 days,” Baker retorted. “The idea, though, that there’s such a great need for the voting on Sunday, I’m not seeing it historically in Craven County. I’m seeing a great need maybe for longer hours on other days when you’ve got 2,000 or 2,500 people trying to vote.”

Eventually the state board rejected the Democrats’ plan, then voted 3-2 along party lines to add four hours of voting on a single Sunday.

Did that decision shortchange potential Sunday voters? Citing his voter-per-hour standard, Malcolm suggested the answer was yes.

But notably absent from the debate were key statistics that no one would have been able to provide. How many more people would have voted on Sundays in 2012 had additional hours been available those days? Of those, how many were voters who ended up casting ballots on other days?

How many more people would have voted in 2012 had Craven extended early voting hours on different days or added polling sites, as Republican county board members recommended for this year? Would some of the people who voted on Sundays four years ago used one of those other options had they been available?

Elections officials would be mistaken to assume that voter-per-hour figures would remain constant as hours are added. It’s just as plausible that a voter who cast a ballot at 4:45 on a Sunday afternoon might cast a ballot at 5:15 the same day if he knew that his deadline had been extended from 5 p.m. to 6 p.m. Or he might choose to cast a ballot at a more convenient location or at a more convenient time on another day if those options are available.

Academic research suggests that this latter scenario is likely. Studies of early voting tend to show little impact on overall turnout, with one 2014 report suggesting a negative link between expanded early-voting options and overall turnout.

So the potential impact of this year’s early-voting expansion remains unclear. What is clear is this: First, the local Craven County elections board agreed unanimously to expand both sites and hours of early voting in 2016 compared to 2012. Second, the entire State Board of Elections agreed at least some Sunday voting seemed reasonable for a county that used that option four years ago.

Third, Democrats who voted against the enacted plan relied on a voter-per-hour statistic with limited value.

Mitch Kokai is an associate editor of Carolina Journal.