With Iowa’s vote earlier this week, the winnowing process has begun.  However, it is still early enough that there is a good chance that more than two candidates will reach the 15% needed to win delegates.  And that will complicate the delegate math with fractional delegates.

(Normally, the early states — starting with Iowa — perform a winnowing function.  Candidates who finish at the bottom of the pack in Iowa tend not to survive for much longer.  And candidates who do well in terms of finishing near the top of the pack tend to survive for several more rounds.  With the delay in reporting results, it is unclear if Iowa will have its usual impact this year.  But even if it does, it would not be unusual to have multiple candidates getting 10% or more of the vote in New Hampshire. Starting in 1976, five of nine primaries have had at least three candidates getting 10% of the vote, and three primaries have had three candidates getting over 15% of the vote.  Since three of the remaining six primaries occurred in races that were perceived — at least heading into Iowa — as only having two candidates who were viable, about half of the races that had more than two “viable” candidates resulted in three candidates winning delegates in New Hampshire.  In short, Iowa only starts the winnowing process.  And this year, that means that more than two candidates have a legitimate shot at winning delegates in New Hampshire.)

Now back to the basic rules that apply to all states.  A candidate needs to get 15% of the vote (either state-wide or in a district) to be eligible to win delegates. If there are enough delegates available, every eligible candidate gets a delegate even if that reduces the number of delegates that another candidate gets.  If there are more eligible candidates than delegates, delegates are awarded in the order of finish.  Generally speaking, the formula for calculating delegates is the share of qualified votes (i.e. only the votes cast for candidates who got 15%) times the number of delegate available.  Since that typically will result in a fraction (say 2.3 delegates for candidate X), you start by giving out the whole numbers and then the remaining delegates are assigned in fractional order (i.e. .7 is ahead of .6 for getting the next delegate).  Technically, the rules say round up and round down initially, but the ranking then comes into play if round up and rounding down results in the wrong number of total delegates.

New Hampshire has two congressional districts.  Unlike some states (for example, neighboring Maine), the two Congressional Districts in New Hampshire are actually pretty balanced.  As such, both districts will have eight delegates to allocate in the primary.  With eight delegates, 15% of the total vote will win at least one delegate; 25% will win at least two delegates; 37.5% will win at least three delegates.  (Once a candidate gets past 40%, the mathematical limits on the number of candidates who could qualify allows some assumptions about rounding to come into effect as 1.5 delegates is 18.75%).  From that point, 43.76% will win at least four delegates; 56.26% will win at least five delegates; 68.76%will win at least six delegates, 81.26% will win at least seven delegates, and 85.1% will win all eight delegates.

There are three party leader delegates.  Simply put, due to the rule that all candidates who qualify get delegates, the top three candidates will each get one delegate.  If only two candidates qualify, the winner in New Hampshire would get two delegates and the runner-up would get one delegate.

Finally, there are five at-large delegates.  Mathematically, it is theoretically possible that six candidates get 15% of the vote.  If that happens, the top five gets one delegate each.  Taking into account the 15% rule, a candidate who gets 40.1% of the state-wide vote will win two delegates (only three other candidates could get to 15%); a candidate who gets 55.1% should win at least three delegates (only two other candidates can get to 15% and the leading candidate would have a higher fraction than the other two candidates); a candidate who gets 70.1% should win at least four delegates (only one other candidate could get to 15% and the candidate would have a higher fraction than the other candidate); and a candidate who gets 85.1% will win all five delegates.

At the end of the day, New Hampshire has even fewer delegates at stake than Iowa does.  Unless the race is really, really close (making a second ballot at the convention likely and bringing the automatic delegates into the equation), the exact number of delegates won in New Hampshire is not the main story out of New Hampshire.  Instead, what will matter (and be the center of coverage until the Nevada results) is who appears to be doing well.  A candidate who does poorly in both Iowa and New Hampshire (with the possible exception of Michael Bloomberg who is not even on the ballot in New Hampshire and has made it clear that he is not really competing in the early states) will probably not be in a position (both in terms of financial support needed to run a campaign and being able to convince voters that they still have a chance) to continue.  On the other hand, finishing in the top two in either Iowa or New Hampshire is probably enough to allow the candidate to continue to Super Tuesday and, perhaps, further.