## Saturday, March 5, 2016

### Prediction: 64% Sanders Wins Majority of Pledged Deligates

There are many ways so predict the future. All of them have a fair degree of uncertainty. Nate Silver at FiveThityEight uses a measure of ethnicity and political leanings to predict how well Sanders will do in different states. This seems like a sound method to me though it is not the only way to make predictions.

For the last month I have been playing with campaign contributions data and have seen a strong and steady increase in support for Bernie Sanders across the nation. I have mapped it county by county and the results are quite dramatic.

Yet, what does grassroots support really mean? Does it translate to votes?

In February, with only four states having voted, it was impossible to say how contributions translated to votes. But Super-Tuesday changed all of that!

With fifteen states having voted, we can now see if financial support maps to voting support.
 Figure 1: This figure shows a relationship between percent of support for all times reported as of January 31st coming from that state with percent of vote (delegates when not available) coming from that state at the primary.
From Figure 1, we can see there appears to be a pretty strong relationship between percent of vote actually cast and percent of support coming in for that candidate. Let's try a formal model:
$$Vote = \beta_0 + \beta_1 ContSanders + \beta_2 Primary + \beta_3 Closed$$ Vote is the actual vote in the state. The explanatory variables are percent contributing to Sanders (ContSander). Primary and Closed refer to the difference between primary vs caucus voting systems and closed vs open. For closed systems only registered democrats are allowed to vote.

Looking at Table 1, with 79% of the variance explained (r2), we can see that percent of support coming in for a candidate from a state at the end of February is a very good predictor of how the vote will go. Increasing the number of explanatory variables increases the r2 to 86%.

Table 1: The regression of  Vote on ContSanders is V1 while V2 and V3 allow the inclusion of the explanatory variables Primary and Closed.

V1V2V3
(Intercept)-24.317*-16.122-11.988
(Intercept)_se{10.175}{10.551}{10.352}
ContSanders1.155***1.118***1.134***
ContSanders_se{0.165}{0.155}{0.147}
Primary-8.118-10.711*
Primary_se{4.642}{4.710}
Closed-6.883
Closed_se{4.474}
r20.7900.8330.862
fstat48.929.923
pstat000
sigp < 0.001%p < 0.01%p < 0.01%
* Coefficient significant at 10%, ** at 1%, and *** at 0.1%

When examining the coefficient on ContSanders it is useful to reflect that while this value is statistically very different from zero, the point value estimate is reasonably close to 1. This is the target number we would like if we were to directly interpret proportion of supporters in a states as a good indicator of proportion of population in state supporting Sanders. This interpretation does not make sense since most of the contributions to Sanders campaign (72% of them) are not itemized (and thus included in this analysis) because they are less than the FEC threshold of \$200 while a much smaller number (about 12%) of those for the Clinton campaign are not itemized.

A priori I did not have any hypothesis as to how the Primary vs Caucus method was going to play out though I did expect those states with Closed voting to be less likely to vote for Sanders as he is strongly favored among independents.

From these numbers coefficients we can now make predictions about how the rest of the states would vote if all of the states voted today (well really March 1st, Super Tuesday). The results give a point estimate of 42% of primary locations going to Sanders with a total expected number of pledged delegates of 1740 to that of Clinton 2285. So Clinton is expected to win??

But wait! Not quite so fast!

The election will not be held tomorrow. The momentum has been strongly with Sanders and it should be expected to stay strongly with Sanders.
 Figure 2: Percent of contributions going to Sanders relative to that of Clinton in the South. Interestingly DC is the largest proportional supporter of Hillary. That is because it is the state/district which best exemplifies Hillary's primary backers, wealthy. States with black outlines have yet to vote.
 Figure 3: Percent of contributions going to Sanders relative to that of Clinton in the Northeast. States with black outlines have yet to vote.
 Figure 4: Percent of contributions going to Sanders relative to that of Clinton in the Midwest. States with black outlines have yet to vote.
 Figure 5: Percent of contributions going to Sanders relative to that of Clinton in the West. States with black outlines have yet to vote.

From the Figure 2 through 5, we can see that the growth in support for Sanders has been steadily increasing in all areas of the country. The regions most friendly to Clinton are the South and the Northeast while those most friendly to Sanders are the West and the Midwest.

The South happens to be the region least supportive of Sanders campaign though it has had more votes than all other states combined. Thus we may be getting a distorted picture of how the primary season may go based on how these first few states have voted.

If we fit a simple line to each state then assume that growth in support will continue at a steady pace until the primary at that state.
 Figure 6: Predicted support at time of primary mapped against support at end of January. ZZ are democrats abroad.
Predicting support based on historic rate of donations predicts that almost all states will have greater support for Sanders than they did at the end of January. States which have experienced more growth in support for Sanders or has later primaries tend to end up further to the right on the graph. The diagonal line is what happens if there was no growth in support for Sanders over time.

Using these new expected support levels at the time of the primaries that have already happened we can fit a new model.

Table 2:  This tables shows the results of using expected proportion of Sanders supporters as predictors for election results rather than actual support as of the end of January.
V1V2V3
(Intercept)-22.886*-15.49-11.352
(Intercept)_se{9.539}{10.37}{10.178}
ContSandersP1.053***1.02***1.032***
ContSandersP_se{0.144}{0.14}{0.133}
Primary-6.92-9.484*
Primary_se{4.63}{4.688}
Closed-6.864
cCosed_se{4.435}
r20.8050.8350.865
fstat53.630.423.4
pstat000
sigp < 0.001%p < 0.01%p < 0.01%

From Table 2, we can see that using predicted Sanders support rather than that last observed at the end of January gives us a slightly higher r2. However, those of us familiar with estimation will immediately realize that we have introduced a new level of uncertainty into the data. This is because we are using an estimated value to estimate yet another value.

Ignoring estimation uncertainty, using the best fit model I predict Sanders will get 57% of the pledged delegates. However, point estimates in statistics are almost never true. In order to estimate the error in the process I simulate randomly sampling from the distribution of possible coefficients for the Intercept, ContSanderP, Primary, and Closed coefficients and predict delegate distribution. 72% of the time Sanders is expected to get the majority of pledged delegates.

Yet, I have ignored the error in estimating the support for Sanders. Rather than doing something more complicated instead what I do is increase the standard error on all coefficients by a factor of 150% and simulate the delegate distribution again. Under this situation I predict Sanders will take the majority of the pledged delegates 64% of the time. (Note the more you increase the standard error the more watered down the predictions become until all you have is a 50-50 chance of Sanders winning.)

Conclusion
It will come as no surprise to anybody that I am an avid Bernie Sanders supporter. The level of corruption and deceit that seem endemic to the Clinton campaign combined with the consistent upright behavior and spot of messages of the Sanders campaign makes my endorsement of Sanders very easy. I might have considered supporting one of the Republican candidates, however Trump seems to be cleaning house.

It might come as some surprise that a self-described economist would openly support Sanders. However, the exaggerated claims that "economists" are opposed to Sanders does not add up when you look at the actual fiscal support Sanders has received from economists. As of the end of January, Sanders has logged 155 contributions from economists compared with Clinton's 189. That is to say 45% of contributions made to either campaign from economists have gone to the Sanders campaign.

So it was frustrating for me to see that Sanders seemed to be already getting behind in the pledged delegates for these first primary states. However, a few nights ago I built the models and crunched the numbers and was much relieved to find that not only was Sanders predicted to do well, but win the popular vote, and the majority of pledged delegates!

I know there is much uncertainty in any kind of predictions, especially one as surprising as this election season. Thus, I caution reading to much into this prediction or really any predictions that are coming out. Frankly, this model using contribution data seems to fit the data remarkably well and the results are encouraging. But even if the model predicted Clinton would take the pledged delegates and the popular vote, I would also strongly caution reading too much into such predictions.

Only 15 states have voted representing only 25% of the pledged delegates. All the while those who learn about Sanders seem to like him more and more while for Clinton the phenomenon seems to be going the other way.

As for my code. I am happy to release it however it is not in a good condition right now. I will have to revise it for public posting. That might take a few days but I wanted to get this out right now.

End Note:
I could imagine someone saying, "What do pledged delegates matter anyways since so many delegates are determined by unpledged or super-delegates?"

I can tell you this for certain if Clinton does not win by taking the majority of pledged delegates but rather though internal party politics then it is highly unlikely the majority of Sanders supporters are going to support her in the general election. Already, many of us are put off by the games the DNC have been playing by first restricting the debate schedule so as to minimize air time of democratic challengers to Clinton then by trying to cut Sanders off from access to the voter database.

This behavior coupled with ongoing ethical and potential legal violations by the Clinton campaign have given Sanders supporters a very strong dislike for underhanded tricks. Using party insiders to win the nomination against the will of the electorate, would be seen as intolerable.

Appendix:
Just for fun I have included the following list of predicted outcomes and actual outcomes as well as the predicted number of pledged delegates if all pledged delegates where distributed proportionately to that of the vote. Notice that the predicted outcomes for any given state can vary quite significantly. However, it is only across states that we hope to come up with a cumulative expected outcome that may be reasonable.

StatePrimary DatePredictionTRUEPledged SandersPledged ClintonN
1IA2/1/2016465022243950
2NH2/9/201662611595030
3NV2/20/2016444717204105
4SC2/27/2016452614293757
5AL3/1/2016382010332547
6AR3/1/2016303110223473
7CO3/1/20165959392713735
8GA3/1/2016382829648820
9MA3/1/20166149453625573
10MN3/1/2016616247309623
11OK3/1/2016535621183111
12TN3/1/2016513322335575
13TX3/1/201646347511927077
14VA3/1/20164535345215702
15VT3/1/2016978614012563
16ZZ3/1/201686NA112920
17KS3/5/201659NA19142997
18LA3/5/201637NA19322853
19NE3/5/201644NA11141724
20ME3/6/201663NA1693829
21MI3/8/201665NA854511472
22MS3/8/201656NA2016854
23FL3/15/201639NA8313128191
24IL3/15/201666NA1025421651
25MO3/15/201659NA42296384
26NC3/15/201658NA624511057
27OH3/15/201657NA826110091
28AZ3/22/201670NA532210288
29ID3/22/201677NA1851677
30UT3/22/201658NA19142859
31AK3/26/201672NA1241891
32HI3/26/201661NA15102823
33WA3/26/201685NA861528682
34WI4/5/201670NA60267374
35WY4/9/201673NA104696
36NY4/19/201638NA9515255636
37CT4/26/201659NA32239237
38DE4/26/201644NA9121119
39MD4/26/201646NA445114771
40PA4/26/201656NA1058416231
41RI4/26/201659NA14102494
42IN5/3/201670NA58255346
43WV5/10/201668NA2091632
44KY5/17/201662NA34212921
45OR5/17/201687NA53815170
46PR6/5/201620NA1248566
47CA6/7/201681NA38392113314
48MT6/7/201685NA1831658
49ND6/7/201692NA171427
50NJ6/7/201653NA675913513
51NM6/7/201691NA3136658
52SD6/7/201685NA173714
53DC6/14/201610NA2189298
Total:22491691

1. Sweet. I knew the upcoming states were going to be good. WA state it has been reported has given more to Bernie's campaign than any other and were 118 delegates. I hope this holds true.

2. Yes we have given more than anywhere in USA from here in seattle. We are bernin up here in seattle!!!!

3. I don't understand this analysis. It doesn't show through path to 2382 delegztes for nomination

1. I apologize. The predictions I originally posted where based on one of the simulations rather than the expected values. The above table is corrected. Notice though that 2249 is not 2382.

4. The biggest driver of the win seems to be California. Sanders winning over 75% of the delegates in California seems...hard to imagine. I'm from CA, it's a liberal state, and I think he has a very good chance to win it (especially if he continues to have momentum going into June), but beating her by 249 delegates in California feels like a stretch.

I hope you're right, though!

1. That may be right. However, eliminating CA he still would win the majority of pledged delegates. And as I said, no matter what the DNC says if Clinton does not win the majority of the popular vote then she is sunk because I don't believe she can win the general election without the popular support of democrats.

5. Interesting, do you have an update? I have entered your projections into this site. http://DemRace.com/?share=kZVAQ4pg Check it out.