A busted political myth

College degrees per capita by state political leaning

A common myth perpetuated by Democrats, the news media, and entertainment is that Republicans are stupid and uneducated. This chart clearly debunks the myth. It also highlights a very important irony. Popular culture universally agrees that everyone in Washington DC are idiots, yet they have the highest number of degrees per capita.

The college degree data comes from the National Center for Education Statistics. The political makeup of state governments comes from Wikipedia’s list of United States state legislatures and list of current United States governors and represents the years 2011-2012.

Nebraska is excluded because its legislature is non-partisan. The District of Columbia calculation for % Democratic leaning uses the city council in place of both the upper and lower houses and the mayor in place of the governor.

Counting the cost of an election

Cost of living by state

The cost of living data comes from the ACCRA Cost of Living Index for 2011 (the most current data available). The political makeup of state governments comes from Wikipedia’s list of United States state legislatures and list of current United States governors and represents the years 2011-2012.

Nebraska is excluded because its legislature is non-partisan. The District of Columbia calculation for % Democratic leaning uses the city council in place of both the upper and lower houses and the mayor in place of the governor.

$1.00 represents the average cost of living in the United States as a whole. Most states are subdivided into multiple areas and the cost of living calculated for each individual area. In this chart, the solid points are the median cost of all areas within a state. The error bars denote the highest and lowest cost areas within the state. The most extreme example of varied costs in a state is New York, where the median is $1.13, but the highest (New York City) is over $2.20.

Taxes are not included in the cost of living index. We can infer from this chart that including them would only make the differentiation larger.

Schneider Prime Sets

Fibonacci, Euler, Bell, and Lucas. Why do they get to have numbers or number sequences named after them? Well, because they came up with some crazy way of defining those number or number sequences. Now, I certainly don’t consider myself as great a mathematician as any of these fine gentlemen, but I do want some kind of number named after me. So, here is how I will do it.

I like food. Sometimes I like to use a microwave to cook or reheat my food. Now, most fine chefs will balk at that, but I, as an engineer, don’t. I can create a thermal profile using a microwave that will cook or reheat food just fine. The trick is to know a little bit about heat transfer and how thermal profiles work. You can’t just stick the food in the box, set the microwave to high and run it for minute. You need to use the power settings and be thoughtful about how much time you run at each power setting. A good thermal profile could heat the food on high for several seconds to get it hot, but then drop down to a 60% or 70% power for a prolonged time to “soak” the food, then drop down to a lower power to keep it warm until you are ready to take it out and eat it.

Now then, I have this little quirk. I like to use prime numbers for the number of seconds I have the microwave at each power setting. For example, a typical profile for melting cheese onto chips is something like this: 7 seconds on 100%, 17 seconds on 60%, 23 seconds on 20%. The problem is that once you add up the three primes, you may end up with a total time that is not a prime. Unacceptable. (Or OCD, you choose.)

So, I have decided to define a new type of number set which I conveniently call Schneider Prime Sets. A Schneider Prime Set is a set of three prime numbers whose sum is also a prime number. Now I can use those Schneider Prime Sets to appropriately cook in my microwave. Even better are Unique Schneider Prime Sets, a set where each number in the set is unique.

Note that a set is not order dependent. You can mix the numbers up in any order and it is still a Schneider Prime Set. In other words, (5,13,19) is equivalent to (13,5,19). Out of convenience my lists order the numbers ascending within the set.

A few Schneider Prime Sets which are good for microwaving:

Schneider
Prime Set
Sum
(5,13,19) 37
(7,11,23) 41
(13,17,29) 59
(13,23,23) 59
(17,19,23) 59
(13,23,31) 67
(17,19,31) 67
(23,29,37) 89
(29,29,31) 89
(19,29,53) 101
(19,41,41) 101
(29,31,43) 103
(41,43,43) 127
(23,31,103) 157
(43,47,167) 257
(47,61,149) 257
(11,79,173) 263
(31,41,191) 263
(41,61,167) 269
(47,103,157) 307

For a list of just over a thousand Schneider Prime Sets, click here (text file, 1.12 MB).

Santorum’s Dream — Santorum’s Bane

On Monday, Rick Santorum’s campaign published its “new delegate math.” Their delegate counts show the gap between Rick Santorum and Mitt Romney much smaller than what the Associated Press publishes. An article at ABC News summarizes how the campaign figures its numbers. Their numbers would change my previous chart to something like this:

Dreamland.

Recall that candidates above the dashed line are ahead of the delegate count to get the nomination; candidates below the line are behind. Santorum uses his numbers to contend that the GOP is heading for a brokered convention.

The Santorum campaign assumes that the Republican National Committee will force Florida and Arizona to allocate their delegates proportional to the statewide vote. There are two major flaws with this assumption. First, the RNC already penalized Florida and Arizona for their early winner-take-all elections by taking away half of their delegates. If the RNC were to force the states to allocate their delegates proportionally, the RNC would have to give back the penalized portion. Second, most states that allocate their delegates proportionally do it by congressional district, awarding all delegates per district to the winner within the district. It is a winner-take-all by district allocation.

So, let’s assume that the RNC does force Florida and Arizona to allocate their delegates proportionally, and that by doing so they give them back their penalized delegates. Further assume that the states then allocate those delegates proportionally the same way the other states do, giving them out winner-take-all by congressional district. (Two big assumptions, but more reasonable than Santorum’s). How do the results change? Not the way Santorum assumes, and certainly not in a way he would like. Romney would still win all of Arizona’s 58 delegates since he won in every congressional district. Romney would get 84 of Florida’s delegates and Gingrinch would get 16. The net effect is that Romney would increase his lead over Santorum and Gingrinch would close the gap between himself and Santorum. And my chart would look like this:

Math is his bane.

Santorum’s dream could become his bane.

Delegate Countdown

It's the math, stupid!

Candidates above the dashed line are ahead of the delegate count to get the nomination; candidates below the line are behind.

Picking up 69% of the remaining delegates is a tall order, especially when you’ve only gathered 26% of those currently allocated. This explains why Santorum wants to come up with his own recounts, especially his creative option of forcing Florida and Arizona to proportionally allocate their delegates. He claims they need to do it to follow Republican National Committee rules. The fact is that they were already penalized half of their delegates for holding their winner-take-all elections early. If the RNC reallocates them proportionally, then they should give back the half that they took away. They would also have to permit the States to come up with their own proportional allocation, which does not always go directly by statewide voting totals. Many states use county level or congressional district level allocation, which is considered proportional. Many proportional states also do hybrids. Bottom line, Santorum really can’t win this unless he pulls off a backroom deal with the establishment — though clearly a different establishment than the one he claims is throwing this to Romney.

Make a budget

Military spending per person worldwide

The data sources are a little old, but you get the picture. If you take away the logarithmic scaling then the USA stands out like a sore thumb, but you can’t see the nuances amongst the rest of the pack. The data is not corrected for relative earnings which could bring the USA more in line with the others given higher wages paid to soldiers and other personnel than most other countries.

This provides a slightly different outlook than this previous post on livestock.

Women’s World Cup predictions and results

Whether or not you’ve been waiting all month for these, here they are.

Match Group
54% Germany 2 1 Canada 46% A
45% Nigeria 0 1 France 55% A
54% Japan 2 1 New Zealand 46% B
47% Mexico 1 1 England 53% B
53% USA 2 0 N Korea 47% C
44% Colombia 0 1 Sweden 56% C
52% Brazil 1 0 Australia 48% D
59% Norway 1 0 Eq Guinea 41% D
60% Germany 1 0 Nigeria 40% A
48% Canada 0 4 France 52% A
54% Japan 4 0 Mexico 46% B
45% New Zealand 1 2 England 55% B
59% USA 3 0 Colombia 41% C
46% N Korea 0 1 Sweden 54% C
51% Brazil 3 0 Norway 49% D
58% Australia 3 2 Eq Guinea 42% D
47% France 2 4 Germany 53% A
55% Canada 0 1 Nigeria 45% A
49% England 2 0 Japan 51% B
48% New Zealand 2 2 Mexico 52% B
49% Sweden 2 1 USA 51% C
54% N Korea 0 0 Colombia 46% C
36% Eq Guinea 0 3 Brazil 64% D
48% Australia 2 1 Norway 52% D
56% Germany 0 1 Japan 44% 1A v 2B
54% Sweden 3 1 Australia 46% 1C v 2D
51% England 1.3 1.4 France 49% 1B v 2A
51% Brazil 2.3 2.5 USA 49% 1D v 2C
47% Japan     Sweden 53% Semi
48% France     USA 52% Semi
            3rd place
            Championship

Based on these probabilities, with 28 matches played I would have expected 54.47% accuracy on the predictions. The model has actually had 69.64% accuracy. My conclusion: Well, the FIFA rankings (on which these probabilities are based) seem to represent the teams fairly well. I manipulated the FIFA rankings a bit. I increased Germany’s points by about 10% (host advantage); decreased Japan, Australia, and New Zealand’s points by about 2% (geographic separation); increased the European teams’ points by about 2% (geographic proximity); and decreased North Korea’s points by about 4% (political and geographic isolation). We can expect some exciting semifinals and although as of now Sweden statistically should come away with the Cup, expect the USA to win it all.

© 2011 John Schneider. All rights reserved.