Princeton Election Consortium

A first draft of electoral history. Since 2004

Under GOP rules, 30% before Iowa/New Hampshire implies a delegate majority: Simulating the “proportional” rules

January 13th, 2016, 2:24pm by Sam Wang

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.

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)

4) These hypothetical election results were fed into a script that calculated delegate numbers according to rules that are documented at The Green Papers. (primary_states.m and 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.

Tags: 2016 Election

28 Comments so far ↓

  • Patrick L. Anderson

    I’ve attempted to extend the analysis to include already-voted states. However, I am having trouble running “primary states” under R21015b (error at line 215); can you confirm it runs?

    More importantly, excellent work on implementing the arcane delegate selection rules by states.


    • Sam Wang

      Hmmm. It runs for me. Lines 214-219 are just there to make sure the total number of delegates comes out exactly right. It is a small correction, so you could just try commenting those lines out.

  • Ezra!

    Also. I just wanted to say that this is an amazing simulator and thank you for taking the time to put this together.

    One way to improve it might be trying to factor the level of support that each candidate gets in different districts in order to help better model how district level delegates are allocated. For example, Georgia’s fifth CD, represented by John Lewis, is a +32D district. In 2012, Romney won 40% of the districts vote. By contrast, GA-8, a +15 GOP district, Romney got just over 20% of the vote and was beaten by both Gingrich and Santorum.

    While I understand that district level is impossible to come by, perhaps using the 2012 results by CD to try and model 2016 outcomes might be a useful tool, especially when data starts coming in from some of the early voting states.

    • Sam Wang

      Partisan voting index is not obviously predictive. In cases where I looked up data, district-to-district variability is notably now. See Georgia and Maryland, Wisconsin, and Arkansas, standard deviations of 1-9% (median = 3.5%). In these cases, Republicans are similar statewide. For now, in my calculations I assumed a statewide SD of 7%.

    • Amitabh Lath

      Another problem with using 2012 as a template is the voting demographics may be changing. Sean Trende did an analysis pushing back against the GOP post-mortem, saying that they do not have to reach out to minorities if they can energize white voters that sat out.

      If indeed Trump (Cruz?) are energizing these populations that did not vote before, then expect voting patterns to be clearly different certainly in the primaries and maybe a big enough effect to be visible in November as well.

  • Dave

    Wow. Great work.

    Thank you for your terrific efforts with the website.

  • Bela Lubkin

    Have not read any of the rules, but — is there a GOP and/or legal rule against “some candidate” simply offering $100,000 to each delegate who will switch to him on the 2nd ballot?

    1st ballot? There’s definitely a rule against that, but AFAIK it only applies to the delegates, not the candidates. How many delegates would subject themselves to whatever the GOP convention rules’ slap-on-the-hand penalty is, in exchange for $HoweverMuchTrumpWantsToSpend?

    • Bela Lubkin

      Ok, according to 2012 rules (, 16(a)(2), “if a delegate [is unfaithful to their elected mandate], the delegate shall be deemed to have concurrently resigned as a delegate and the delegate’s improper vote or nomination shall be null and void. Thereafter the secretary of the convention shall record the delegate’s vote or nomination in accordance with the delegate’s obligation under state law or state party rule.”

      – I don’t see where this applies only to the 1st round, but this must be the case. So $$ shenanigans seemingly must wait until the 2nd round. Or be remitted directly to the secretary of the convention.

  • 538 Refugee

    Does anyone think that Trump, having come this far, won’t go 3rd party if he doesn’t get the Republican nomination? That is going to have to factor into the Republican leader’s decision process because their chances at the white house would be distant at best if that happens. It could potentially damage Senate and House votes if Trump supporters won’t pull the lever for ANYONE Republican as a result. Which is more the nightmare scenario for them? A first round ballot victory might actually let them off the hook.

    The up side to a Trump nomination for the Republican Party is that they would be able to put all of their money into down ticket races.

    • Petey

      “Does anyone think that Trump, having come this far, won’t go 3rd party if he doesn’t get the Republican nomination?”

      Can’t do it, unless he does it very early. Filing deadlines start passing in March. By the time we near the convention, it’ll no longer be even a remote option.

    • 538 Refugee

      That makes no sense. The deadlines pass before the major parties even formalize their nomination?

    • daddyoyo

      @ 538 Refugee: Actually it makes a lot of sense, since both parties are motivated to suppress third party efforts, even if they might work to their advantage now and then. When you look at the rules state by state, though, most of the toughest requirements are in red states.

  • Doctor Science

    The idea that the field will be down to 4 after NH strikes me as extremely unlikely. The grift factor in this set of candidates is too high: not enough of them are running to have a chance at power, most are running to “enhance” their “brand”, encouraged by consultants who keep getting paid.

    Of course, this makes Trump’s position much stronger — but I don’t know which of them will be willing to take the fall, to drop out and throw their support to e.g. Rubio.

    • Josh

      Even more than that, because there are so many candidates, and because no one candidate will have an insurmountable lead any time soon, there’s no real incentive for serious candidates to drop out. People are speculating that Kasich and Bush, for example–candidates who are, generously, 5th and 6th in the current pecking order–will stick around at least until the middle of March, when Ohio and Florida have their primaries. By that point, a large percentage of delegates will have been allotted.

  • MAT

    Sam, if you married the support reallocation to the Condorcet-style polling results you described in an early post (current, of course and ideally on a state by state level) you would have an enormously powerful prediction tool.

    • Sam Wang

      I played around with that. My concern is that Condorcet preferences may change over time. Anyway, this could certainly be attempted.

    • MAT

      Sure. What I had in mind was a constantly updating Condorcet polling. It’d be expensive, but could really paint a forward looking picture accurately. Hard for me and you to justify, but certain large media organizations that you sometimes publish articles with? It could be quite the differentiator.

    • Sam Wang

      I priced it out once – not that cheap. Thousands of dollars per survey, if I recall correctly. I agree, though – it is within the reach of a major media organization.

      There is this online Condorcet poll from

  • Petey

    And one quite minor dissent from Sam’s Prospect article.

    Re: Trump not winning 1st ballot:

    “Party insiders should not necessarily be consoled by this idea … If current trends were to persist, the convention floor in Cleveland would be filled with close to 1,000 Trump delegates. These delegates won’t be from the usual pool of party loyalists. They seem like an unpromising starting point for elites to work their magic.”

    If Trump can’t get the 1st ballot, I see only two paths for him to win the nomination;

    1) He makes a deal with Cruz, and Cruz has enough delegates, and is able to swing his now-unbound delegates into line.

    2) ‘The Party’ decides Trump is preferable to Cruz, as Mitch McConnell now seems to think. Cruz has enough delegates, Trump threatens to throw his delegates to Cruz, and ‘The Party’ responds by putting Trump over the top.

    Absent either of those two paths, I find it difficult to imagine any scenario where those 1,000 delegates are able to accomplish anything. Seems much, much more likely that a consensus ‘Anybody But Trump’ figure is eventually settled upon. Paul Ryan, anyone?

    Also, if Trump can’t get 1st ballot, it also means that he can’t control convention rules and seating challenges, as MAT touches on. So all kinds of shenanigans can take place, if there is an ‘Anybody But Trump’ majority.

    However, all this is a bit besides the point, IMHO, as the delegate allocation process seems to make a 2nd ballot a semi-absurd fantasy.

    • Amitabh Lath

      Predicting 1st ballot is really really difficult but there are rules and it can be done, as Sam has shown. Predicting 2nd (and beyond) ballot is impossible. Sam’s “apres Trump le deluge” comment is basically the best one can do. Your two scenarios are plausible but so are a host of others. There are no rules to guide an analysis.

    • Petey

      “Predicting 2nd (and beyond) ballot is impossible … Your two scenarios are plausible but so are a host of others. There are no rules to guide an analysis.”

      I do hear you, Amitabh.

      But the one rule that does guide an analysis is that a majority of delegates rules everything. If, (and it’s a massive “if”), there is an “Anybody But Trump” majority, then his 1,000 are utterly useless.

      But sure, there are other theoretical scenarios that could make his having 1,000 delegates relevant. But for a while, I’ve simply been unable to imagine any that don’t tightly revolve around Cruz in one way or another…

    • bks

      If there’s no first ballot victory the GOP is going to be glad that they’re in Cleveland instead of a city where extending one’s hotel stay is out of the question. (CWRU alumnus speaking here.)

    • Amitabh Lath

      If we go beyond 1st ballot, we have almost 2500 people, none of them legally bound to any specific candidate, all with their own preferences and agendas, all being wooed and swayed by multiple campaigns and interest groups…ugh. Monte Carlo is useless. You need some serious statistical mechanics tools.

      You could then define temperature and entropy metrics where the delegates are changing their minds constantly and then as things cool down there is a phase transition and things coalesce around Trump or Anybody-But-Trump.

    • Ezra!

      “These delegates won’t be from the usual pool of party loyalists. ”

      It’s not that simple. This gets into a whole different part of the delegate process that is alluded to frequently in GreenPapers which is the delegate selection process. As with the delegate allocation, it varies wildly by state. However, how delegates are selected can broadly fall into three categories.

      1. Elected on ballot–each candidate has a set of delegates that independent of the candidate’s consent are placed on the ballot. If that candidate is eligible to receive delegates, than those delegates are the ones that are chosen to go to the convention. An example of this is Alabama. A slight variation on this is West Virginia, where delegates are placed on the ballot, and the highest vote getters are chosen as delegates and then pledged to the winner of the WV primary vote (so in a sense, their are two elections).

      2. Elected at convention–many state parties have party conventions to elect delegates. Usually to become a RNC delegate, you first need to become a delegate to your district convention, then their you get voted to be a delegate to your state convention, then from their you get voted to be a delegate to the RNC. This method rewards people heavily involved in the local party (or the Ron Paul people in 2012). States such as Minnesota or Iowa use this method.

      3. Candidate selection–This is the most straightforward. Basically after the vote, an election official gets in contact with the candidate, tells them they are entitled to X delegates, and then the candidate gives them X names who become delegates. New Hampshire and Hawaii use this method.

      With these three systems, it is only the third one that can ensure that the delegates are actually supporters of the candidate, and even so it is impossible to know for sure. This has never been an issue in recent memory, because delegates are NOT free agents on the first ballot (this year at least). However, if it goes past the first ballot, many states release their delegates from their pledge and they become autonomous actors. At that point, it could become highly relevant how the delegates were selected and who they are.

      Two final caveats. One: each state also has different rules as to how long delegates are “bound” for at the convention. Some states only bind their delegates for one vote. Other states bind their delegates until the candidate of choice drops out. So just because it goes past a first ballot does not mean that all (or even most) of the delegates are released. Second, it is unclear what happens to pledged delegates if their candidate who they are pledged to drops out. Let’s say that Kasich wins 3 delegates in NH but drops out before the convention. Are they free agents? Can he tell them what to do? It is eminently unclear, only about 4 states (to the best of my knowledge) have any rules whatsoever dealing with that scenario.

    • Petey

      “This has never been an issue in recent memory, because delegates are NOT free agents on the first ballot”

      Ezra! You raise interesting points about the true allegiance of delegates once they are no longer bound. A fair bit of that aspect of delegate selection was completely unknown to me.

      However, something like that has been an issue in the open primary era. In both the ’76 GOP convention, and the ’80 Dem convention, there were crucial test votes of the delegates in determining the rules.

      In both cases there were rules votes where the second place candidate in bound delegates sought to unbind delegates on the 1st ballot, for obvious reasons.

      (It is my strong understanding that no matter what state party delegate rules say about such matters, a majority of the convention delegates are sovereign. In other words, they can do whatever the hell they want. If a majority wants to change the rules to unbind everyone, they can.)

      In both those test votes, the freely given, unbound votes of those bound delegates almost perfectly accorded with their bound candidate allocation.

      In short, in the only two case studies we’ve had in the open primary era, delegates do seem to have allegiance to their selected candidate. Why that is, given what you’ve detailed about how they are selected, I don’t know. But I thought it might be an interesting data point to note.

  • MAT

    Wow. Color me impressed – I went thru this exercise in 2008 modeling the Dem delegate allocations in Excel (without the Monte Carlo runs) and it was a *lot* of work. Thank you for this.

    Another factor to consider is GOP Rule 40, which states no candidate can receive the nomination without winning at least 8 state primaries and/or caucuses. It’s not hard to imagine a scenario where Trump shows up just shy of 50% delegates use but is the only candidate to satisfy Rule 40. It can be changed at the convention, but can you imagine the s***storm that would ensue if Trump had the nomination ‘taken away’ in this fashion? Get the popcorn ready.

    Finally, I believe there will be enormous pressure to drop out between whoever of Bush & Rubio does worse in Iowa & New Hampshire before the March 15 ‘SEC’ primary. 99 winner take all delegates in Florida and Trump is leading big right now with Bush/Rubio splitting the vote. There is no compelling reason for either candidate to continue if they can’t win their home state where the rules were stacked in their favor.

    Again, outstanding work.

  • Petey

    Excellent work, Sam.

    “I cannot believe you went down to the district level in your Monte Carlo sim.”

    Literally, it’s the only way to make sense of the GOP delegate allocation. So many of the delegates are awarded at the CD level in the so-called ‘proportional’ states that you simply can’t do it otherwise.


    One additional thing I’d note, that Sam touches on in his Prospect article:

    The real key in my mind is the 3/15 – 4/1 period when WTA and ‘hybrid’ pseudo-WTA contests happen.

    Trump can accumulate 60% of delegates up until 3/15, which would certainly put him in the driver’s seat, but that can still be overcome, if an unusually successful ‘Anybody But Trump’ effort is mounted.

    But if Trump can keep winning states in the 3/15 – 4/1 period, he can accumulate enough of a massive delegate lead that even an unusually successful ‘Anybody But Trump’ effort just won’t be able to stop him from a 1st ballot win.

  • Amitabh Lath

    This is great work. I cannot believe you went down to the district level in your Monte Carlo sim.

    For the last plot (with 300 toys) can you indicate where the 1 sigma bands would be?