What Does It Take to Make the Runoff with 24 Candidates on the Ballot?
In 1992, eight candidates ran in Louisiana's newly drawn Fourth Congressional District. Cleo Fields placed first with 48 percent of the vote, but Charles Jones finished second at 14 percent and made history. His vote share remains the smallest by which any candidate has ever secured a spot in a Louisiana runoff for state or federal office.
Today we have 24 candidates competing for the state's open U.S. Senate seat. In purely mathematical terms, more candidates makes it possible to place in the top two with a smaller share of the electorate. Hypothetically, the top finisher could hit exactly 50 percent - one single vote shy of the majority needed to avoid a runoff. All the remaining 23 candidates could split the remaining 50 percent almost equally with one of them receiving just one single vote more than the others. This candidate would make the runoff by placing second with barely more than 2 percent of the vote. So, sure, more candidates potentially lowers the threshold, but such hypothetical scenarios do not play out in actual elections.
Do More Candidates on the Ballot Mean a Lower Threshold for the Runoff?
Yes, but not as low as you might think. I pulled the election returns for all Louisiana primaries that went to runoffs for state and federal office since 1982. These 587 elections include all primaries for the U.S. Senate, the U.S House of Representative, governor, lieutenant governor, attorney general, secretary of state, commissioner of elections, state treasurer, commissioner of agriculture, commissioner of insurance, the Louisiana Senate, the Louisiana House of Representatives, the state Board of Elementary and Secondary Education, the state Public Service Commission, the Louisiana Supreme Court, appellate court judge, and district court judge that went to a runoff during this period. The only exceptions are the party primaries briefly used for federal offices in 2008 and 2010.
The chart shows (in green) how the average vote share won by the second place finisher in these elections moves with the total number of candidates in the race. The green line represents the linear association between number of candidates and average vote share for second place finishers. Clearly, candidates tend to make the runoff with a smaller share of the vote when more candidates are on the ballot.
The second place finisher is only part of the story. Another way to approach this is to look at the share of the vote for the third place finisher - the person who came closest to making the runoff but missed. The third place finisher's vote share (in red) also tends to decline with the number of candidates but not as dramatically as the second place finisher. This means that the margin by which the second place finisher edges out the third place finisher for the coveted spot in the runoff shrinks when more candidates are in the race.
No primaries that went to runoffs had anything close to two dozen candidates.
There are a couple of problems with this analysis. First, it tells us nothing about how things tend to look in a race with 24 candidates because, well, we haven't had one before. Or, at least, we have not had one for state or federal office that went to a runoff. The closest we have come are two elections with 17 candidates: The 2003 contest for governor and a 1993 special election in the 100th district of the Louisiana House of Representatives. Using this analysis to make a guess about the expected second place vote share in a contest with 24 candidates would be pure extrapolation well beyond the legitimate reach of the data.
Competitive candidates matter more than total candidates
The second problem with the analysis so far is that I have treated all candidates equally in terms of how much they matter for splitting up vote shares. That is not at all how our primaries play out. Instead, what tends to happen (especially in contests with numerous candidates) is that a few candidates register a noticeable percentage of the vote while many others languish below one or two percent. You can look at just about any open race for governor as an example.
If many of the candidates in an election fail to secure even a nominal share of the vote, then it makes no sense to think their presence on the ballot will reduce the share of the vote left to split across the second and third place finishers (and any other candidates).
To deal with this issue, I reanalyzed the primary results by the number of candidates who received at least five percent of the vote rather than by the total number of candidates on the ballot. This count ranges from three to nine candidates in these elections. [Admittedly, using five percent as the threshold for whether a candidate is a significant factor is arbitrary. However, using ten percent instead has little impact on the results discussed below.]
So what do the candidates in 2016 need?
The answer depends on how many candidates you think will receive a noticeable share of the vote. Barring some unforeseen catastrophe, the top five candidates (listed in alphabetical order) are sure to secure more than five percent: Congressman Charles Boustany, Public Service Commissioner Foster Campbell, attorney Caroline Fayard, Congressman John Fleming, and Treasurer John Kennedy. So, there will be at least five but perhaps more.
While it seems unlikely at this point that any of the other 19 candidates will get enough votes to make a runoff, it is certainly possible that some will get enough votes to impact the amount left for the top five to divvy up.
The biggest question is whether retired U.S. Air Force Colonel Rob Maness or former Imperial Wizard of the Ku Klux Klan David Duke (or both) can get over five percent. They are the only two other candidates on the ballot who won at least five percent of the vote in a previous statewide elections. Maness won 14 percent when he ran for U.S. Senate two years ago. Duke, who has not campaigned for office in nearly twenty years, won 12 percent in his last statewide run (the 1996 U.S. Senate race) and 19 percent in his last run for any office (a 1999 special election in the First District of the U.S. House of Representatives). The polling average at Huffington Post currently has them at five percent and four percent respectively. The folks at fivethirtyeight have them at 4.4 percent and five percent in their latest polling average.
Of course, we do not need to know exactly how many candidates will get enough votes to make a difference because we can look at the span of the second place finisher's average across several scenarios. When there are five candidates at five percent or higher, the second place finisher's average vote share is 24 percent. This dips to 22 percent with six candidates at five percent or more of the vote and to 20 percent with seven candidates.
How often do candidate make the runoff with less than 20 percent when there are five or more candidates winning noticeable numbers of votes?
Not often. Of course, in any single race a candidate does not necessarily hit or exceed the average second place finisher vote share to make a runoff. But when looking at the full range of second place finisher vote shares in elections when five to seven candidates get five percent or more of the vote, 20 percent still looks likes a good minimum target.
In the 99 primary elections when five candidates won five percent or more of the vote, the second place finisher's vote share exceeded the 20 percent mark in 85 of them (86 percent of these elections). In the 62 instances when six candidates came in at five percent or more of the vote, 42 had second place finishers exceed the 20 percent mark (68 percent of these elections). Only when you consider primaries in which seven candidates received five percent or more of the vote do you see a reasonable chance for a second place finisher to make the runoff with under 20 percent of the vote. In 17 of these elections, the second place finisher hit 20 percent or more in just eight (47 percent).