Nicole Kirby looks over results during a statewide presidential election recount on Thursday in Milwaukee. (Morry Gash/AP)

Thanks to the efforts of Green Party presidential candidate Jill Stein, a recount is underway in Wisconsin. It is highly unlikely to change the outcome — as Hillary Clinton’s campaign has stated — but it is much more likely to overturn some conventional wisdom about counting votes. In particular, we may learn, yet again, that computers are better than humans at counting ballots.

Wisconsin’s most recent experience with a statewide recount provides some useful background for the current recount. In 2011, David Prosser ran against JoAnne Kloppenburg for a seat on the state supreme court. After the initial count, Prosser was 7,316 votes ahead of Kloppenburg, out of 1.5 million votes cast. Kloppenburg demanded and received a recount. The recount added votes to both candidate’s total, although more to Kloppenburg’s. Ultimately, Prosser won by 7,004 votes. This is a tiny change.

Another way to think about it is to take the absolute difference between the number of votes for a candidate in the original count and in the recount. The absolute difference means it didn’t matter whether the candidate gained or lost votes in the recount. For instance, if Candidate Smith received 100 votes in the original count and 102 votes in the recount, the discrepancy would be 2 percent. It would also be 2 percent if the candidate had 98 votes in the recount.

Based on that calculation, the discrepancy between the initial count and the recount in the 2011 race was 0.18 percent. It would take a much larger discrepancy — at least 0.80 percent in Clinton’s favor, and more likely greater than 7 percent — to change the outcome in Wisconsin and award its electoral votes to her. (Below we show the basis of this calculation.) Even still, winning Wisconsin would not be enough for her to win the electoral college.

For many advocating a recount in Wisconsin, a primary concern is that computers were involved in counting at least some of the ballots. In 2016, 90 percent of all votes were cast in municipalities that used computerized optical scanners to count votes. It seems obvious that we should be more skeptical of machines that count ballots than humans who count ballots. But the evidence suggests that machines actually do a better job.

Republicans and Democrats react to the announcement that Hillary Clinton's campaign plans to join a vote recount in Wisconsin initiated by former Green Party presidential candidate Jill Stein. (Bastien Inzaurralde/The Washington Post)

Recounts help us study the accuracy of the methods that provided the initial — and often only — vote count in an election. If the recount is a fully accurate vote count, then we can use it to gauge the accuracy of the original count. Better yet, if we have one set of ballots that were originally counted by hand and another set of paper ballots counted by computer scanners, then we can assess the accuracy of the two methods.

In the only study we know of, political scientists Stephen Ansolabehere and Andrew Reeves examined every recount in New Hampshire from 1946 to 2002. From 1946 to 1962, when New Hampshire had only hand-counted paper ballots, the average discrepancy between the original count and recount was 0.83 percent. In 2002, when there were recounts in six New Hampshire races, the discrepancy was 2.5 percent in races in which the ballots were originally hand-counted, but only 0.6 percent in races in which they were machine-counted.

Closer scrutiny revealed a race in one town, Bradford, where the hand-counting had gone terribly wrong. According to an interview with a state official, the team that was hand-counting votes in Bradford for one particular state legislative race decided to knock off for the night and never resumed counting the next day. Removing Bradford’s data reduced the average discrepancy in hand-counted jurisdictions to 0.87 percent, but this is still higher than the discrepancy in races with machine-counted ballots.

The same finding emerges in Wisconsin. When we analyzed the 2011 Wisconsin recount, we found that the average discrepancy for scanner-counted paper ballots was 0.17 percent, compared with 0.28 percent for hand-counted paper. In other words, both methods are highly accurate, but scanners are slightly more so.

Why would scanners be superior? As the Bradford story illustrates, scanners don’t get tired or bored as easily as humans do. Human counters also feel pressure to get the job done quickly and accurately, which creates stress that machines do not feel.

Of course, even if scanners are more accurate on average, this won’t always be true. A machine that malfunctions could cause a big discrepancy.

Leaders of the Green Party in Wisconsin and Hillary Clinton's campaaign said that it will participate in the recount, exploring whether there was any "outside interference" in the election results. (Reuters)

Human error can also occur when scanners are used. In the 2011 Wisconsin recount, the jurisdiction with the greatest discrepancy between the original count and the recount was the town of Larrabee, which recorded 322 total votes on election night and 391 (69 more) in the recount. The reason is that on election night the results from one of the town’s scanners were not written down on the tally sheet that was sent to the county clerk. Thus, the problem was not with the scanner but with the procedure to transfer the results from the scanner to the paper report form.

Of course, past patterns may not apply to this recount. And regardless of the recount’s outcome, we believe it is valuable to scrutinize the accuracy of vote-counting. The big downside in Wisconsin is that a full recount takes a lot of time and resources. This is actually a good reason to favor what are called “risk-limiting audits” rather than statewide recounts to verify election results when there is no hard evidence of widespread fraud or malfeasance. Risk-limiting audits, advocated by mathematicians such as Philip Stark and Ron Rivest, use a small number of randomly selected ballots to test whether the original vote count most probably called the correct winner.

But with a full recount underway regardless, all eyes will be focused on Wisconsin for the next few weeks. We should expect three things: the recount will discover only small discrepancies between the election night totals; both methods of counting ballots — hand and scanners — will prove highly accurate; and scanners will be more accurate than humans.

Stephen Ansolabehere is professor of government at Harvard University.  Barry C. Burden is the Lyons Family Chair in Electoral Politics at the University of Wisconsin at Madison and director of its Elections Research Center.  Kenneth R. Mayer is professor of political science at the University of Wisconsin at Madison. Charles Stewart III is Kenan Sahin Distinguished Professor of Political Science at MIT and co-director of the Caltech/MIT Voting Technology Project.

[Our estimates of how large of a discrepancy is needed to change the Wisconsin outcome are based on the following. Clinton currently trails Trump by 22,177 votes.  If the recount revealed only 22,178 new votes for Clinton and none for Trump, she would win by one vote. There are currently 1,404,000 votes for Trump and 1,381,823 for Clinton. The calculation then is (22,178 + 0)/(1,404,000+1,381,823) = 0.80 percent.  More likely, however, both Trump and Clinton would gain votes. Let’s say that Clinton got 55 percent of the new votes uncovered in the recount. Then, to get a net 22,178 new votes for Clinton, Wisconsin would have to uncover 199,594 new votes — for 110,886 for Clinton and 88,708 for Trump.  This works out to a discrepancy of 7.2 percent.]

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