The Mathematics of the Delegate/Superdelegate System

Although some pundits are claiming that the 2008 Democratic Primary is decided (with Barack Obama to be the nominee), in reality, the race is far from over, and very well could drag out all the way to the national convention in August. I’m a big proponent of voter equity, so this news is bittersweet to me. On one hand, many more states are getting to vote, and have their vote matter, than usually occurs (the last brokered convention occurred back in 1952). Unfortunately, the process also brings into play the entire delegate and superdelegate system, which I find nearly as unfair as the BCS system for college football rankings (the DNC delegate system gives approximately 800 to individuals, out of about 4000 total delegates, while the BCS gives a third of the vote to 6 computer algorithms). Thus, I set about finding out exactly how messed up this system is, by the numbers.

I compiled the following data from Wikipedia:

Raw Data

Data with Analysis Calculations

A note on the raw data: for ease of transcribing, I rounded the population to the nearest hundred thousand people.

Now let’s take a look at what I analyzed. My first step was to calculate the number of people represented by each “standard” delegate, each superdelegate, and each delegate in total. Of course, it is reasonable to expect some variation here, given the wide spectrum of possible population values and the number of available potential delegates. There may even be some significant variation, as occurs with electoral college vote distribution due to a minimum number of votes. Allow me to interject for a moment to point out how ridiculous it sounds for one superdelegate to represent hundreds of thousands of civilian votes. Anyway, the data, however, shows much more variation than expected:

The range for people per “standard” delegate is 40000 on the low end (Vermont), and 122798 (Texas) on the high end. We’ll see as we go along that Texas voters seem to get screwed in every category. For the superdelegates, 75000 (North Dakota) to 703846 (Florida), but since their delegates aren’t being counted, we’ll go to second place, 677143 (Texas). Poor Texas. For the overall total representation, we have 26087 (Vermont) to 103947 (Texas). This is quite staggering! When considering superdelegates, some states’ standard voters have nearly ten times less power than other states!

N.B. (note): I am ignoring whether states hold closed or open primaries for this analysis, because it would have taken a long time, and most of this is back-of the envelope style analysis. I am also aware that only a portion of the entire population is of voting age, but again, too many details.

The next thing to consider is the distribution of superdelegates. Do some states have a greater representation in this crucial 20% of delegates than their population’s proportionally purports? Why yes indeed. A quick glance at the data shows that “standard” delegates are fairly close to being proportionally allocated, and we see that they correlate well with the number of electoral college votes. Thus, if we calculate the number of delegates per superdelegate, and if the superdelegates are proportionally allocated, we should have a fairly constant value for the calculation. Of course, this does not occur:

The average number of delegates per superdelegate was 3.742, with a standard deviation of 1.714. The range was 0.500 to 7.115, with 24 of the 58 districts studied lying outside a standard deviation (more than 40%). States with notably low superdelegate representation are; Texas, Indiana, Louisiana, Kentucky, Georgia, North Carolina, Alabama, Ohio, and Florida. States with notably high superdelegate representation are; North Dakota, Rhode Island, Montana, Vermont, South Dakota, Delaware, and Wyoming.

The last thing I considered was how difficult it would be for the superdelegates to overturn the popular vote of the primary or caucus in each state. First, I tabulated the margin of victory for those states which have held elections (again using Wikipedia). Then, I determined what I called the “safe margin,” that is, the required margin to ensure that superdelegates could not overturn the popular vote on a state-by-state basis. This is given by the following formula:

formula

where T is the total number of delegates, and S is the number of superdelegates. We then compare this value to the actual margin to determine which states are “safe.” We see that there currently are 16 “safe” regions and 34 “unsafe” regions, with 7 undetermined. Interesting stuff. We’ll see how it plays out as the last few regions are decided.