## Delegate Allocation in the Democratic Primary

Posted 3/24/2016 9:54:50 AM
Tags: R

There has been some discussion by Bernie Sanders supporters about the delegate allocation process in the Democratic primary. One complaint is that states that generally vote for Republican presidents seem to be allocated an unfair number of delegates. This hurts Bernie Sanders and the Democratic party as a whole, because the southern states, which have gone strongly to Hillary in the primary, are not in contention in the general election. To allow those states to select the Democratic candidate is unreasonable, because they don’t matter for the general election. Sanders is thought to win states that are more relevant to the general election. Thus, if states that mattered more in the general election were given more weight, Sanders might be doing better in the primary.

According to Wikipedia, Democratic primary delegates are mostly allocated by the DNC based on 1) the proportion of Democratic vote share in the last three presidential elections and 2) the number of electoral votes that state has. Rather than using these exact variables, I wanted to model the data using state population and how early in the primary season that state votes. I used the order in which the states voted (1 for Iowa, 2 for New Hampshire, etc), which seemed to work well as a predictor.

First I used a model that predicted delegate count based only on state population using simple linear regression. The correlation between population and delegate count is very high, r = 0.98, which suggests using it as a single predictor. I then used that model to predict the number of delegates that should be allocated to each state using the model. The results are plotted below.

Note that this plot is log log to account for large variations in delegate counts. The states are colored in based on what party they tend to vote for in general elections. Each state is either safe Democratic (D, blue), safe Republican (R, red), or swing (S, green). I did this based off of the 2000 and 2008 presidential elections, where a safe state is one that voted the same way in both elections. The line has an intercept of 0 and a slope of 1, which means that any points above the line are allocated more delegates than the model would predict and and points below the line are allocated less delegates than predicted. Notice that safe D states tended to get more delegates than predicted based on population and R states tended to get fewer delegates, which is in line with the DNC claim that delegates are allocated in part based on vote share in previous presidential elections.

I then added primary voting order to the model, but it didn’t really change much, except moving a number of red states with low delegate counts from getting more delegates than expected to getting less delegates than expected. Basically, if you think that voting order should matter, then R states are getting fewer delegates than you would expect when you take voting order into account. Voting order is a statistically significant predictor of delegate count, but it accounts for only a tiny fraction of the total variance accounted for by the model (less than 1%).

There are two states in the bottom left that get far more delegates than predicted by population and voting order. These are New Hampshire and Vermont (New Hampshire voted for Bush in 2000, which is why it is green). For larger states, one clear outlier is the R state just below the prediction line, which is Texas.

To summarize these analyses:

1. There is no reason to believe that delegates are allocated by the DNC differently from how they claim to allocate the delegates
2. safe Republican states are not allocated a disproportionate number of delegates
3. swing states are also not given any preference, but there is an argument that maybe they should be because they are important in deciding the general election

### Which candidate is favored by the delegate allocation?

Now, to answer the question of who is favored by any variation in how many delegates are allocated, let’s consider the spread in delegates won by Berine and Hillary in different states that have already voted in the primary. What I’ve plotted below is 1) how many delegates each state was allocated above what is predicted by the population and voting order model (x-axis) and 2) how many more delegates Bernie won than Hillary (y-axis). Thus, higher points on the plot indicate states that Bernie did better in and lower points indicate states that Hillary did better in. Points more to the right indicate states that got more delegates than would be predicted based on their size and voting order.

The outlier in the bottom left is Texas. The one in the top right is Washington state.

We already knew that blue states are allocated more delegates than would be predicted based on population and voting order. We also know that Bernie tends to be better in blue states. Thus, it should be no surprise that he does the best in states that have more than the expected number of allocated delegates. Hillary does better in states that have fewer than the expected number of delegates. Thus, there does not seem to be any evidence that the delegate allocation was unfavorable to Bernie Sanders. What this plot shows is that, if anything, Hillary was probably hurt by the fact that the states she won by the widest margins were red states.

### Which States have the most Delegates per Person?

Another concern is that some states have undue influence because they are allocated more delegates per person than other states. If some states get additional delegates, even though they have a small population, it gives people in those states more say than people in more populous states. Below, I’ve plotted the number of delegates allocated per person, normalized so that the state with the fewest delegates per person (Texas) has a value of 1 for normalized delegates per person.

I’ve also included a table with the data used to make the plot below. I have ordered the states by normalized delegates per population.

##             State NormalizedDelPerPop Delegates Population
## 34   North Dakota            3.031372        18     672591
## 45        Vermont            2.896279        16     625745
## 50        Wyoming            2.812847        14     563767
## 41   South Dakota            2.782412        20     814191
## 8        Delaware            2.649059        21     897936
## 39   Rhode Island            2.581839        24    1052931
## 2          Alaska            2.551685        16     710249
## 26        Montana            2.404129        21     989417
## 19          Maine            2.131776        25    1328361
## 11         Hawaii            2.081722        25    1360301
## 29  New Hampshire            2.064997        24    1316466
## 31     New Mexico            1.870251        34    2059192
## 20       Maryland            1.863720        95    5773785
## 37         Oregon            1.803546        61    3831073
## 48  West Virginia            1.772710        29    1853011
## 7     Connecticut            1.743057        55    3574118
## 49      Wisconsin            1.712817        86    5687289
## 47     Washington            1.701282       101    6724543
## 38   Pennsylvania            1.685300       189   12702887
## 12          Idaho            1.661866        23    1567652
## 23      Minnesota            1.644414        77    5303925
## 15           Iowa            1.635749        44    3046869
## 30     New Jersey            1.623319       126    8791936
## 21 Massachussetts            1.574210        91    6547817
## 27       Nebraska            1.550515        25    1826341
## 22       Michigan            1.489782       130    9884129
## 6        Colorado            1.486456        66    5029324
## 28         Nevada            1.467949        35    2700691
## 14        Indiana            1.449898        83    6484229
## 5      California            1.444217       475   37254503
## 32       New York            1.443789       247   19378087
## 17       Kentucky            1.435674        55    4339349
## 35           Ohio            1.404013       143   11536725
## 13       Illinois            1.377093       156   12831549
## 24    Mississippi            1.373856        36    2968103
## 44           Utah            1.352419        33    2763888
## 46       Virginia            1.344914        95    8001045
## 25       Missouri            1.342849        71    5988927
## 3         Arizona            1.328989        75    6392307
## 16         Kansas            1.310116        33    2853132
## 40 South Carolina            1.297909        53    4625401
## 9         Florida            1.289041       214   18804623
## 18      Louisiana            1.274255        51    4533479
## 33 North Carolina            1.271011       107    9535692
## 1         Alabama            1.255897        53    4780127
## 4        Arkansas            1.243044        32    2915958
## 42      Tennessee            1.195842        67    6346275
## 10        Georgia            1.192486       102    9688681
## 36       Oklahoma            1.147316        38    3751616
## 43          Texas            1.000000       222   25146105

You can see that North Dakota, for example, has about 3 times as many delegates per person as does Texas. You can compare individual states by taking the ratio of their delegates per population. For example, if you compare California (1.44) vs Oregon (1.80), you find that California has 80% as many delegates per person as does Oregon.