Democratic Primary Delegate Math: A Tutorial

We are down to two candidates on the Democratic side. If you think that means there will be a relatively short race, you would be wrong. The winner will not have the majority of delegates pledged to her or him until June 3^rd, at the earliest. That will be true even if the race is not close. The only way to avoid the long slog is if one of the candidates sees the writing on the wall and quits. For this to occur it does not even require a close race because 17% of delegates are selected on June 3^rd or later. Thus to win 50% of the delegate total, without this 17%, requires winning 61% of the first 83% of the vote. The number to reach 50% is actually even higher because Iowa is already basically a tie, meaning even more is needed of what is left.

Because of the principle of proportionality that will be very hard to achieve by June 3. As we saw in Iowa on Monday, because each precinct caucus gets a select number of delegates, and a delegate cannot be split in half, there can be strange results. If a precinct has an odd number of delegates, then winning by one vote means you win the extra delegate. But if the precinct has an even number, then the candidate has to win by much more to avoid a tie. A tie in delegates is therefore much more likely, even if one person is ahead substantially in votes.

These same rules apply for national convention delegates and this is where the math becomes so important. New Hampshire will be electing 24 Democratic delegates on Tuesday based on the results: eight a piece in each of New Hampshire’s two congressional districts and, as in the case in every state, two kinds of statewide delegates based on the statewide totals. In New Hampshire, that means three of one kind of statewide delegates and five of the other for a total of an additional eight delegates.

Because of proportionality, winning is not enough to win more delegates. What is most important is winning by large margins. In New Hampshire, if Hillary Clinton wins at least 31.25 of the vote in each Congressional district (which seems very likely), she will end up walking out of New Hampshire with at least 9 of the 24 delegates up for grabs, or 40%. (This is only among viable candidates; votes for non-viable candidates who remain on the ballot are not used in the calculation.) That translates to three delegates in each of the two Congressional districts, one of the three and two of the five statewide delegates. This may not seem fair but the truth is there is no way to elect delegates without rounding and any other system of rounding would be even less fair.

By the same token, if Sanders wins (which also seems very likely), he is guaranteed at least 13 delegates: four in each Congressional district, and two of three and three of five statewide. That means the real battle is for the last two delegates, one in each of the Congressional districts. For Sanders to “crack” Clinton, a term of art meaning being awarded more delegates and avoiding a tie, Sanders needs at least 56.25% of the vote in a district. If he doesn’t, even if he gets as much as 56% of the vote, he and Clinton will split those delegates four/four. So Sanders, who is very likely to win, will get more delegates than Clinton but it could be just by a count of 15 to 9 at the most, and might be 14 to 10, or even 13 to 11, if she’s able to avoid being cracked in both districts.

This math is crucial because a very large percentage of delegates are decided at the district level. New Hampshire is just an example. This is the case throughout the country, which is why it will take so long to get to get a majority of pledged delegates. Even if a candidate is winning, if he or she is not able to get the margins to crack in a particular district, a delegate tie will be the outcome. For every delegate number there is a different percentage of the vote required to crack or in some cases double crack.

Here is how each delegate district shakes out:
For a 3-delegate district, to get all 3 you need 83.5%
For a 4-delegate district, to split 3-1 you need 62.5%
For a 5-delegate district, to split 4-1 you need 70%
For a 6-delegate district, to split 4-2 you need 58.333%
For a 7-delegate district, to split 5-2 you need 64%
For an 8-delegate district, to split 5-3 you need 56.25%
For a 9-delegate district, to split 6-3 you need 61.1%
For a 10-delegate district, to split 6-4 you need 55% (to double crack, you need 65%)

This may all seem esoteric but the Obama campaign’s understanding of these rules, more than any other factor, led to his victory.

In our New Hampshire preview, we will give a delegate prediction as well. The first real big delegate prize is coming March 1^st. One of the key things about a proportional contest is that it is very difficult to overcome a deficit because of the ever-escalating vote totals you need. If one candidate is cracked often, but the other has difficulty cracking, winning soon becomes not enough for the person being cracked. This chart shows what each candidate needs for a tie.

We will be stuck doing a lot of delegate math throughout the rest of the primary seasons and this should help.