# Princeton Election Consortium

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## No path for Sanders…but it’s a long one

#### March 26th, 2016, 11:55pm by Sam Wang

One thing Sanders understands well is the need for a horserace. Without that, he and his principal issue, economic inequality, won’t get covered.

It is possible to put a probability on the outcome that Sanders has outlined above: less than 5%. It’s also possible to calculate how long he can keep saying there’s a path: until June 7th.

For estimating the outcome of the Democratic nomination race, thanks to the relatively transparent rules, it is not necessary to game out individual states. Indeed, excessive focus on detail can confuse matters.

To keep the calculation simple, let’s just focus on pledged delegates, which are driven entirely by voting. In other words, what is the probability that Sanders gets half of all pledged delegates? This is useful, since if such an event did happen, then superdelegates might potentially follow suit to give him an overall majority.

Sanders has won 44% of pledged delegates so far. How would he get to 50%-of-delegates-plus-1?

First, let’s work out a simple equation. If fraction F of delegates have been assigned so far, and Sanders has fraction S of those, then in order for him to get a majority by the end, the following condition has to be satisfied:

final fraction of pledged delegates = S*F + X*(1-F) > 0.5,

where X is what fraction of the remaining delegates he will win in the remaining races.

What X would have to be to get a majority: Rearranging the equation above, we get

X > (0.5 – S*F)/(1-F).

According to The Green Papers, F=0.56 as of today. At this moment Sanders has 1038 out of 2304 pledged delegates, so S=1038/2304=0.45. With those numbers, the above equation works out to X > 0.563. In other words, Sanders needs to earn 56% of the remaining pledged delegates.

Luckily, it is an easy problem to figure out what fraction of the vote Sanders needs. The Democratic Party’s rules assign delegates proportionally to the popular vote. (In this respect, the Democrats’ rules are more truly democratic than either the Electoral College or the Republican Party, which are both dominated by winner-take-all contests. Indeed, if the Democratic Party’s delegates were assigned on a winner-take-all basis, tonight’s delegate count would be Clinton 2020, Sanders 734, a 2.7-to-1 margin.) So Sanders needs to win the popular vote 56%-44% in the remaining elections, i.e. he needs Sanders +12%.

Now let’s look at national opinion surveys. In the last 8 polls (spanning March 17-23), Clinton led by a median of 9.5 +/- 2.1%. Overall, Democratic polls have been pretty accurate. Therefore, assume that the upcoming 22 primaries and caucuses will have an average margin that is similar to national opinion.*

For national opinion to come into line with what Sanders needs, there would have to be a change from Clinton +9.5% to Sanders +12%. That’s a 22-point swing. To put that into perspective, that is about how much the Clinton-Sanders margin has moved over the last seven months, since the start of August. Going forward, opinion would have to start moving about three times faster. And for this to happen, Sanders would have to start to cut into Clinton’s support, which has stayed in the 50-55% range this whole season. Basically, her support would have to drop to 40%. That simply isn’t going to happen.

The probability of a massive polling error (movement of at least four sigma) is basically zero. However, the real question is whether some unanticipated externality can impose a massive swing across all states at once. I estimate that the probability of such a drastic swing in the remaining 10 weeks of the primary season is quite low – well below 5%. Therefore the probability that Hillary Clinton will have a majority of delegates at the convention is greater than 95%.

How long can Sanders keep up his optimism? Although Sanders’s optimistic outcome is highly unlikely, he will probably still keep saying it until there are so few delegates left that it becomes impossible, even if he wins every single one.

That won’t happen until the very end. On the last day of voting on June 7th, nearly 17% of all delegates will be determined, in California, Montana, New Jersey, New Mexico, North Dakota, and South Dakota. As long as Sanders stays above 39.1% of pledged delegates, he can still say, technically speaking, that a last-minute win in June can put him over the top. Considering that he entered this race to get a message out, that’s probably what he will do.

*Relatively recent polls are available in WI, NY, MD, PA, WV, CA, and NJ, which account for 69% of the remaining delegates. Clinton leads in six out of seven of these states. Using these numbers, and national surveys to fill in the rest of a delegate-weighted total, she currently appears to be headed for getting 54% to 60% of the remaining pledged delegates, similar to the 56% that she has won so far.

Update: as I describe in a later post, the aggregated poll average for all states to date has been off by only 3.0 percentage points. Therefore polls, taken as a whole, are a very good guide of where the race is today.

Tags: 2016 Election · President

### 41 Comments so far ↓

• Nick

Great, thanks! That makes sense if the polls are accurate

• Mark F.

At what point is Sanders going to say that it’s hopeless?

• Adam Morrow

The convention? Sanders went into this campaign presumably expecting little to no chance of victory; he’s now gone from <1% to 5%, tremendous growth (from his perspective). Meanwhile, as his campaign has progressed, he's seen the Clinton campaign assimilate more and more of his issues and agenda. Staying in the race to bleed more support from Hillary will continue to force her to address his agenda.

Presumably this will keep happening until an understanding emerges that his presence in the race harms Hillary's chances in the general. So far, that hasn't happened, and I'm not sure it ever will.

The one way he could undo this arrangement is if he starts going negative / personal on Hillary. He would be wise to avoid doing so, and so far seems to be acting like he knows this, being quick to extinguish several brush fires that have given the impression of a negative campaign (the data sharing kerfuffle, insisting Bill Clinton's activities as president are peripheral, various unsanctioned offensive "BernieBro" eruptions). Campaigning on specific issues rather than personalities is also a crucial part of his brand with voters, unlike some other prominent candidates still in this race.

• Matt McIrvin

In Philadelphia. When you do as well as he’s doing nationally, you stay in all the way.

• Bela Lubkin

You say 5%, or one in 20. Other methodologies and assumptions might calculate other probabilities — for instance, we can imagine that Bernie and his statisticians are looking at the details in the most rosy way possible. I expect they calculate more like a 10% chance.

But that’s irrelevant, as long as they’re calculating something higher than zero. People place roulette bets with far poorer odds than 5%. People buy lottery tickets with minuscule odds — especially when the pool is big. “Being US President” is a pretty high payoff; the pool IS big.

From video footage, I would say Bernie’s having the time of his life. He has the money, he has happy excited crowds, he has a friendly little bird who told him to stay on the trail…

Under those circumstances, why would he drop out when not actually mathematically eliminated?

• Of course. There are plenty of reasons for him to stay in. Who said anything about dropping out?

• Jay Medina

This fails to consider which states are remaining. The South was always Bernie’s worst region, so national polls show him with lower support than he has is the states yet to vote. I’d say his support in the states that are voting in the rest of the election is about 5-10% higher than in the nation as a whole. That still leaves him well behind where he needs to be to win, but he got amazing margins in yesterday’s three contests. He will have to make up significant ground in upcoming big contests, like California and Pennsylvania. 10% chance may be about right. But it isn’t quite as hard as the national numbers suggest.

• Matt McIrvin

My guess is that Clinton is going to widen her lead in the remaining Northeastern primaries (which are outside of Sanders’ natural home turf of northern New England), but that if Sanders goes all in for California between now and the summer, he has a decent shot at winning it and taking a majority of the delegates there on the very last day of the contest. It won’t be a Washington-State-sized majority, though.

• No, this statement is false. Public polls are available in seven states, which together account for 69% of the remaining delegates. Clinton leads in all seven states.

• Craigo

The “but the second half of the season favors Bernie” argument always depended on closing one’s eyes and pretending that California, New, York, Pennsylvania, Maryland, and New Jersey do not exist.

• Matt McIrvin

I think the idea was that Sanders was well-positioned to get the series of Western wins we just saw, which would create “momentum” and lead to him sweeping the rest of the states.

Political media are doing their bit by getting excited about his wins, and there aren’t a lot of polls yet to indicate whether he’s suddenly doing much better in all those big primary states, so anyone’s free to speculate. But it’s a much tougher road than it sounds like if you mostly pay attention to stories about surges and momentum.

• Matt McIrvin

Sanders’ campaign people are starting to talk about persuading the superdelegates to switch on the basis of claimed superior electability. It looks to me as if that is going to be theoretically viable all the way to the convention, so Sanders probably isn’t going to give up until the actual roll call.

• Matt McIrvin

It’s interesting to try to imagine how things are going to play out at the convention. The Democratic convention is going to be just one week after the Republican one, which looks like it might be a nightmarish event one way or another. There’s probably going to be a lot of pressure on the Democrats to display party unity. Unfortunately this is in the realm where statistics are not much help. But while this is a real race, the 2008 primary campaign was a much, much closer fight than this one has been, and the Democrats were intelligent enough to come together then.

• whirlaway

I think the Republican Convention will prove to be a relatively tame affair, especially if one of the candidates (likely Trump) makes it past the 1237 mark.

The party will look at how to retain the Senate, and more importantly, the House. The Democrats have virtually ensured that the House will stay ‘red’ – by either putting up no candidates in several winnable races, or at best having candidates that are pathetically weak.

https://newrepublic.com/article/131919/retaking-house-democratic-pipe-dream

• You didn’t weight your analysis by population demographics but Washington, Hawaii, and Alaska are 3.6%, 1.6%, and 3.3% African American (2010 data).

By comparison, NY is at 16% AA.

• Unnecessary – there is opinion polling in NY.

• Yes of course I was just making the rather obvious point that an average move towards Sanders, if it occurs, might have demographic variations. In particular if older AA voters do not participate in this move then states where they make up a large fraction of Dem voters might not see as big a swing.

• See this graph of Sanders support vs. African-American population.

• George

Seems you posted before all returns in from HI, WA and AK. With that delegate swing (lead down to 220+/-) thoughts on your analysis? I agree that the rest of the road looks tough for Sanders but it has been a race of vacillating momentum (granted with Clinton always ahead since SC). Are there mathematical models that address “momentum” and “buzz” – whatever those words might mean?

• No way. A few hours of counting votes changes nothing that I have written. In fact, I posted this in the middle of vote-counting in order to make precisely this point.

I think the words “momentum” and “buzz” mean “I am a journalist or pundit, and I feel excited about writing about this person.” I believe they carry no other meaning.

• Jason Bennett

That delegate swing brought Sanders’ required percentage of future delegates from 57.8% to 56.5% – a relatively negligible shift.

• This seems to overstate his probability. Even if the probability of him turning a 20% deficit to a 10% win is as high as 20% in any one state, he has to do it in state after state after state to overcome Hillary’s pledged delegate lead. Just the chance of him doing that in 3 major states is .2x.2x.2 which is less than 1%. Ofcourse there is potential for momentum swings but we have seen that is not much of a factor considering Bernie wasn’t able to leverage his NH win into NV and SC or the MI win into OH and FL. If anything the most consistent predictors of the outcome have been the demographics, election type (primary or caucus) and party affiliation (closed vs open participation). Even more so than the polls. All of these 3 are not favorable for Sanders in NY, NJ, MD and PA and at least 2 or more are not in favor in many of the other states including CA.

• Agree. However, it is hard to accurately estimate the far tail of a distribution in a situation like this. Basically, the question is whether an externality could impose a massive swing across all states at once.

• GeoffT

“Just the chance of him doing that in 3 major states is .2x.2x.2 which is less than 1%”

Disagree. That result requires the presumption that there is zero correlation in the results between states, which is obviously wrong. Black swans happen and shift needles strongly in one direction or another albeit not uniformly.

• counsellorben

It is a pipedream to think that many superdelegates will switch their allegiance from Hillary, especially if Hillary wins the majority of votes and delegates (as Sam puts very conservatively at 95% likely). Keep in mind that Hillary has received over 2.5 million votes more than Bernie to date, and it would take an extremely significant exogenous event to move enough remaining Democratic primary voters for Bernie to catch up in votes, especially given Hillary’s lead in polls in many of the remaining states.

Thus, superdelegates will be able to state that they are honoring the will of the majority of Democratic voters by pledging to Hillary. That is sufficient justification, especially given the potential costs of supporting Bernie in opposition to much of the party hierarchy.

So, given that Bernie has (realistically) a <1% chance of getting more pledged delegates than Hillary, and that superdelegates will support Hillary if she gets the most votes and delegates, how can Bernie maximize his influence, both at the convention and in the period between the convention and general election? He will have significant leverage, given the votes and delegates he will have received, and also given his ability to date to mobilize voters who should be a significant voice in the Democratic party.

Anyone care to weigh in?

• Stephen J. Marmon

It also should be noted that 10 of Sanders 14 victories have come in caucuses. There are only two caucuses remaining.

• Caucuses are correlated with %white population. See this plot from Will Jordan.

• Matt McIrvin

The two great exceptions in that chart are Alaska and Hawaii–but their nonwhite populations are also both relatively unusual for a US state.

In 2008, gaming the caucuses was key to Obama’s win. But he was also doing better in the primaries.

• Nuq

Coincidentally, all Deep South states were primaries. Regional culture and exposure to candidate (quality and quantity) have a stronger impact on outcome.

• Siobhan

Alaska and Hawaii nonwhite populations are mostly Asian and native, not black or Hispanic, and caucuses tend to draw more from white voters. Caucuses disenfranchise large portions of the population who can’t take off work or family responsibilities

• James

Dr. Wang, I have a couple things to consider. First off, let’s assume things keep going the way they’re going, that there are no huge changes. The HuffPost chart above with Clinton/Sanders polling over time has some fairly clear trend lines. What happens if you draw those lines out, with Secy Clinton’s support slowly declining and Sen Sanders’s support rising at its demonstrated pace? June 7 looks a lot different– and that’s if the trends continue with no remarkable changes. Second, while the 2008 Dem primary was a slow slog and this one kinda looks similar, we’ve seen other primary seasons with turns and twists– 1972Dem and 1992Dem, for instance. The Republican side is downright weird this year and sudden changes there could impact the Dem voting enough to make a difference. Don’t you think the chance that something else odd will happen this year or that the demonstrated trend will continue to play out make your odds for Sanders winning a bit low.

• Glenn Dexter

Let’s not forget the money. When has Sanders ever had the chance to raise this kind of money? Certainly not in Vermont. As long as he stays in the race, he gets money and gets to keep it for other election purposes. Perhaps he’s looking at a governor run in Vermont or another state he could move to that’s supportive of him.

• MikerW

Good analysis. Once again math trumps punditry (sorry, couldn’t resist).

Whenever attention turns to Superdelegates it is important to keep in mind the Sanders is an Independent who caucuses with the Democrats. Whereas Clinton is firmly part of the establishment. One key in all of this is the amount of money each raises for down ticket candidates. The Clintons a veritable ton, Sanders essentially none. Even if he were to squeak by her in pledged delegates it would be an enormous ask to suggest the establishment turn against the Clintons and all the money they represent.

This is borne out by the endorsement scorecard where Clinton leads 489 to 6, and given how this game is played one has to suspect there are many more high profile endorsements to be rolled out as needed.

A final point, at the risk of sounding like a pundit, Clinton not going hard negative on Sanders (yes, his supporters there is a lot there to go after) likely tells you that while the “fat lady has yet to sing” that they know they pretty much have this wrapped and don’t want to offend Sanders’s supporters.

• Olav Grinde

Donald Trump just announced that he is rescinding his promise to support the GOP candidate, even if it is not him. The background is that Trump feels himself “unfairly treated” (no surprise).

Several states, including South Carolina, made it an official requirement that its delegates could only support candidate who have pledged to support whoever the nominee is.

With Trump having dropped that pledge, are we now in uncharted waters, where the delegates of South Carolina and other states with that provision, have suddenly become UNBOUND? In other words: free to vote for a candidate other than Trump already on the first ballot.

Has Trump unintentionally created a situation where “winning” the a delegate is not enough to ensure that they are bound to vote for him? If so, then is it not natural to ask: how many such states are there? How many delegates does Trump risk losing?

And the crucial question: How does Trump now need to perform in the remaining GOP primaries and caucuses to compensate for that potential loss?

• counsellorben

Because he signed an affirmation that he “intend[s] to support the nominees and platform of the Republican Party in the November 8, 2016 general election” as part of his registration for the South Carolina primary, the argument would be that by announcing his intention to violate that affirmation if he does not win the nomination, his registration for the South Carolina primary has been rendered invalid.

If the registration was held to be invalid, then any votes cast for him in South Carolina would no longer be valid votes (since he was not properly registered). Therefore, the second place finisher statewide (Rubio) would then get the statewide delegates, and the second place finisher in each congressional district would get those delegates.

While the legal argument has a fair likelihood of success, it’s akin to burning down the house to get rid of a squirrel in the attic.

• Froggy

To add a few more words to what Ben quoted, “I hereby affirm that I generally believe in and intend to support the nominees and platform of the Republican Party in the November 8, 2016 general election.”

Unlike Ben, I think the prospects for a successful legal challenge would be dismal indeed. Trump could say that he was truthful, in that’s what he intended at the time. And of course he could reverse himself and renew his commitment at any time if the delegates were threatened. (And I doubt there’s any precedent for stripping him of delegates for the statement he made, nor do I view the pledge, with that weasel word “generally,” as providing an enforceable basis for doing so.)

• Mitsu Hadeishi

I’ve always been a huge fan of yours, Sam, but I think you’re missing a big trend here. Yes, in general I think you’re right that “momentum” stories are often meaningless — but I don’t think you’re correct that the momentum story is meaningless in this case.

The biggest vulnerability Clinton has had has been among nonwhite voters — even though on a policy and record level Sanders has by all accounts a much more attractive record than Clinton for most non-white Democrats. It appears that the chief reason for the gap may simply have been lack of information — many nonwhite voters simply had no idea who Bernie Sanders was.

But there is, in fact, a very strong trend, which has been ongoing for the last couple of months, and it is trending heavily against Clinton and in favor of Sanders. I think you should take a look at these numbers and factor them into your thinking. Simply asserting that “momentum” is meaningless *in general* I think isn’t enough in this case. You have to look at the underlying details.

Clinton’s support among nonwhite voters has been plummeting, as this article points out:

http://www.huffingtonpost.com/seth-abramson/hillary-clintons-support-_b_9579544.html

The real question is, is it declining fast enough to turn around the outcome for Sanders? It may not be, but it is a bona fide trend.

• In my view, Abramson engages in motivated reasoning. That writer is very focused on one type of evidence, which is a risky move. National and state-level numbers have a far better track record than crosstab-based arguments. Go back and read his other essays on this subject, and see how they have held up.

Also, crosstabs focus on subsets of the voter population, who then have to swing pretty hard. What would it take for this effect to give an overall swing of 20 percentage points in the total population? For example, if minorities are 35% of the Democratic vote, they would have to swing from 80-20 (Clinton over Sanders) to 50-50. He cites a single survey that comes kinda close to that – this is very weak evidence. My own estimate comes from dozens of surveys, aggregated.

This is why I emphasize the fact that the national preference number simply aren’t moving fast enough to flip the final outcome. My goal in this post was to collect all the evidence (for example data from all states, not just outliers such as Michigan) and see what it told us. In principle, that gives a highly accurate answer.

Back to Abramson: he wrote a bunch of narrative about individual polls. I have no idea if he has cherrypicked. A good procedure would be: in each state, take a median of all polls that are less than 2 weeks old, and calculate the delegate-weighted average. I thought an automated tracker wasn’t worth the effort. Obviously I am keeping an eye on the situation (which is why the Democratic national poll matchup is in the right sidebar, so you can do it).

• mediaglyphic

Dr. Wang,
i realize this thread is about Sanders, but i wonder if i can go off topic and ask what you calculate the probability of Trump getting the requisite delegates before the convention. I notice some polls in have turned in Wisconsin and it looks like the probability may have declined materially.

• Agree it’s more interesting…and something may have changed. Requires some figurin’.

• MikeD

Yes, please update when you get the chance! Regular reader, first-time poster.