Since late December, polls have become predictive enough to point toward Trump as the eventual nominee. New in The American Prospect, I give a detailed analysis of the GOP Presidential delegate-assignment process. This analysis includes a simulation of how vote share translates to delegate share. My principal conclusion is that if his current levels of support hold in a divided field, Donald Trump could well win his party’s nomination in the first round of voting at the Republican National Convention. These same mechanisms cause Marco Rubio’s chances to shrink. Unless the Republicans get their act together soon after New Hampshire and cull the field, it could be too late for anyone but Trump.
NH rules: if vote=Trump 30%, Rubio 14%, Kasich 13%, Cruz 11%, Christie 9% delegate outcome: Trump 12, Rubio 3, Kasich 3, Cruz 2, Christie 0.
— Sam Wang (@SamWangPhD) January 14, 2016
Here, I focus on the fine details of how the simulation of delegate selection was done. This is a work in progress, and I will be glad to correspond on improvements to the approach. It is available at GitHub.
First, to review some basics. In the GOP nomination process, 2,472 delegates are assigned. Winning the nomination requires getting a majority of these delegates.
Delegates are assigned by a byzantine process. However, this process has one general feature: when a candidate wins the most votes in a state, he/she gets a disproportionately high share of the delegates. For example, here are binding-delegate results from the first phase of the 2012 Republican nomination process, from Iowa/New Hampshire to Super Tuesday.
It is important to note that this graph represents a phase of the primary season that is often called “proportional.” Evidently, there is more to it than that.
To read about the ways in which the rules disproportionately favor the first-place finisher, see the Prospect article. Graphically, the rules tend to look like these plots. The actual rules are not fully captured, but the plots do give a sense of their consequences.
Marco Rubio’s big problem is that he is polling around 12-15%. In many states this is below threshold for receiving any delegates at all. One consequence is that Rubio may arrive at the convention with so few delegates that they could fit into a conference room.
The basic challenge of simulation is to capture this process accurately. I used MATLAB (see Github for the scripts – they are a bit rough for now).
The simulation assumes that after New Hampshire, the GOP field may narrow to four candidates, the number of candidates who survived to that point in 2012. In 2012, those four candidates were Mitt Romney, Newt Gingrich, Rick Santorum, and Ron Paul. This year it is likely to be Donald Trump, Ted Cruz, Marco Rubio, and at least one other candidate, such as Jeb Bush.
The four-candidate simulation consists of the following steps.
1) The state-by-state early-state vote results for Romney, Santorum, Gingrich, and Paul all had a standard deviation of 12-13%. This was true whether a candidate had general national appeal (Romney) or more regional support (Gingrich). Therefore, to generate mock results for 2016, a random-number generator was used to produce a set of hypothetical results (primaries.m).
2) For all states after Iowa/New Hampshire, the sum of these four vote shares was normalized to a sum of 100%. This has the effect of reassigning the dropouts’ support to the four survivors, in proportion to their existing support.
3) Where necessary, individual district-level percentages were created to allow assignment of delegates corresponding to Congressional districts. (primary_districts.m)
5) The second, third, and fourth-place candidates were set to the current levels of national support for Cruz, Rubio, and Bush. The calculation was then repeated while varying the front-runner’s percentage between 25% and 50%. In each case the simulation was run 300 times. The average looks like this:
This graph shows that a 30% level of support in current polls could reasonably be expected to yield 50% of delegates between now and Super Tuesday. That means that if the field were to remain divided, Donald Trump is currently on track to get the Presidential nomination on the first ballot at the Republican National Convention in Cleveland. That puts him in a similar position as Mitt Romney in 2012.
The key word is “divided.” As far as I can tell, the most likely alternative to this situation is if after New Hampshire, the Republican field narrows to three candidates. However, that will not happen if Cruz, Rubio, and even one other semi-serious candidate stays in. For example, Kasich and Bush may be motivated to stay in until March 15th, the date of the Ohio and Florida primaries.
I thank Richard E. Berg-Anderson and Tony Roza of The Green Papers for discussion of the nomination process.