Computational Complexity has a short blog post on the algorithm used to find the new House of Representative’s apportionment. The method currently in use is called Huntington–Hill method. To give you a snippet of this problems illustrious past: past solutions that were put in practice include those created by Daniel Webster, Thomas Jefferson and Alexander Hamilton.

Why is it called Huntington-Hill? This column I found from the AMS outlines the history of the method. The introduction also puts the problem quite well:

We can formulate the [apportionment problem] mathematically as follows:

Given states s1, …, sn with populations P1, …, Pn and a positive integer h (think of h as the number of seats in the legislature), determine non-negative integers a1, …, an where a1 + … + an = h. (It is customary to think of the value h as given in advance and fixed, since currently the size of the House of Representatives is fixed; however, for some applications one might have the freedom to vary h as part of solving the problem.)

The CAP problem differs from the one above in requiring that each ai be greater than or equal to 1, or more generally (mathematicians like to generalize!) greater than or equal to bi where bi is some positive integer. The Constitution does not specify the h which started at 65 in 1790 and has grown to the now permanent value of 435, though when Alaska and Hawaii were admitted to the Union the value of h rose temporarily to 437.

At first glance the AP problem does not seem hard. If a state has 10 percent of the population and there are 37 items (seats in the parliament, computer systems, libraries, etc.) to apportion, then .10 (37) equals 3.7. In a parliament interpretation, the problem is we can not send 3.7 people to the legislature (though some feel they do not get full representation from whole bodies); 3.7 is not an integer! What should be done with those nuisance fractions? The quota principle (fairness rule) would say, in this example, that 3 or 4 representatives be assigned. With 3 representatives a state would be underrepresented, with 4 it would be over represented, but the method we currently use to apportion the House of Representatives could assign fewer than 3 or more than 4 representatives!

The algorithm ultimately devised by Huntington (improving on the work of Hill) works as follows:

1. Calculate something called the standard divisor, which is the average number of people in each district over the population of the US. That is roughly 309 million divided by 435.
2. Calculate each state’s standard quota, which is the state’s population divided by the standard divisor. This is how you get a number like 3.7 above.
3. For each state, you take the lower rounding bound (3) and the upper round bound (4) and you take the geometric average of them, . Then  you compare the old quota (3.7) and round down if its below this mean and up if its above it. So in this case, the geometric mean is 3.46, and you would round 3.7 up.
4. Then you add up all of these quotas, and if they equal 435, you’re done. If they don’t you repeat step 3 with a smaller or larger divisor than the standard one depending on whether you’re summed quotas are above or below your goal.

A not particularly efficient algorithm for this process is given by Computational Complexity:

Input: Pop, a population array for the 50 states.
Output: Rep, a representatives array for the 50 states.

Let Rep[i] = 1 for each state i.
For j = 51 to 435
Let i = arg max Pop[i]/sqrt(Rep[i]*(Rep[i]+1))
Rep[i] = Rep[i]+1

This algorithm isn’t working as I described above, but is using the same method to add individual representatives to the state “most deserving.” Its the same method, and actually shows how Huntington-Hill works efficient to change the number of representatives. The Census has a pretty well made video on this whole thing:

The Census Bureau announced that the United States has 308,745,538 earlier this year. More people live west and in the South. NY continued its long relative decline population wise, and will lose two Congressional seats:

By that new count, Texas will gain four new seats, Florida will gain two, while New York and Ohio each lose two. Fourteen other states gained or lost one seat. The gainers included Arizona, Georgia, South Carolina, Utah and Nevada, and the losers included Illinois, Massachusetts, New Jersey and Louisiana.

Regionally, the northeast grew 3.2%, the Midwest grew 3.9%, the South grew 14.3% and the West grew 13.8%. The electoral map has changed for presidential races, with a net loss of 16 electoral votes in the States Obama won in 2008. The US News and World Report blog argues, counterintuitively, that the shift is good for Democrats because the “Republicans have a problem with minority voters.”

Five years ago, the Gates Foundation put $450 million in to 43 grants designed to address the world’s largest public health problems. Bill Gates notes in this article, “We were naïve when we began.” In 2007, instead of making more multimillion-dollar grants, he started making hundreds of $100,000 ones:

That little won’t buy a breakthrough, but it lets scientists “moonlight” by adding new goals to their existing grants, which saves the foundation a lot of winnowing. “And,” he added, “a scientist in a developing country can do a lot with $100,000.”

The article is mostly about what went “wrong” in many of the grants–including those on dried vaccines, a lab in the box, a better banana, etc–and you should read it for a fun slice of the ups and downs of science.

As my friend Jon said to me in an email “Watch this episode. I’ve never seen anything like it.”

In the middle section, Stewart interviews four of the 9/11 first responders:

Earlier in the show he called Senate Republican’s blockage of the James Zadroga 9/11 Health and Compensation Act “an outrageous abdication of our responsibility to those who were most heroic on 9/11.”

When I was in high school, PBS had a documentary called Commanding Heights. A fine documentary about the history of economic thought and globalization in the 20th century, much better than the book that proceeded it.  (The books predictions and tone got turned upside down by September 11). Ultimately the documentary is  slightly too full-throated in its defense of globalization. Nonetheless, a comment by Jeffrey Sachs may have been what prompted me to think about development economics for the first time in my life:

The world is more unequal than at any time in world history. There’s a basic reason for that, which is that 200 years ago everybody was poor. A relatively small part of the world achieved what the economists call a modern economic growth. Those countries represent only about one-sixth of humanity, and five-sixths of humanity is what we call the developing world. It’s the vast majority of the world. The gap can be 100-1, maybe a gap of $30,000 per person and $300 per person. And that’s absolutely astounding to be on the same planet and to have that extreme variation in material well being.

I tend to think that economists can be too focused on models of the modern macroeconomics of the developed world when thinking about development. That is why I loved my Theory of Economic Development class at Brown, It included modern models, but Professor Oded Galore is an advocate for thinking about the long-view of economic history, and suggested we read books such as Guns, Germs and Steel. He calls his model Unified Growth Theory (Wikipedia page), and I’m not sure how much traction it has had among economists. The first paragraph from his overview of UGT:

The evolution of economies during the major portion of human history was marked by Malthusian Stagnation. Technological progress and population growth were miniscule by modern standards and the average growth rate of income per capita in various regions of the world was even slower due to the offsetting effect of population growth on the expansion of resources per capita. In the past two centuries, in contrast, the pace of technological progress increased significantly in association with the process of industrialization. Various regions of the world departed from the Malthusian trap and experienced initially a considerable rise in the growth rates of income per capita and population. Unlike episodes of technological progress in the pre-Industrial Revolution era that failed to generate sustained economic growth, the increasing role of human capital in the production process in the second phase of industrialization ultimately prompted a demographic transition, liberating the gains in productivity from the counterbalancing effects of population growth. The decline in the growth rate of population, and the associated enhancement of technological progress and human capital formation, paved the way for the emergence of the modern state of sustained economic growth.

This is all by way of introducing an interview with Deirdre McCloskey in the National Review. I find her incorporation of dignity and rhetoric as economic drivers to be fascinating. It makes modern economic growth part of a larger historical movement going back to the enlightenment. The article’s introduction does a good job of closing out my post:

Economic history looks, in graphic representation, like a hockey stick. For tens of thousands of years we traced nasty, brutish, and short lives along the shaft. Children anticipated a world no different from their grandparents’. Shakespeare’s audiences had only marginally better lives than Sophocles’. But at the beginning of the 18th century, mankind — beginning with the British and Dutch — hit the blade of that hockey stick, enjoying an unprecedentedly sharp and irreversible upturn in prosperity, life expectancy, and health. Ever since, the world has changed more quickly in every generation than it had previously in millennia. By all criteria, human life has improved in ways unthinkable 300 years ago.

Solving the mysteries of the birth of the Industrial Revolution (and, subsequently, the modern world) has been the primary task and test of economic history. And, according to Deirdre McCloskey, all explanations so far have failed. Those failures, in turn, indicate the failings of modern economics. Her magnum opus, an explanation of the birth and flourishing of the bourgeoisie and its subsequent transformation of the modern world, will occupy at least six volumes. This month, Chicago University Press releases the second installment: Bourgeois Dignity: Why Economics Can’t Explain the Modern World.

Traditional economic models — the ones we find in Econ 101 — center on labor, capital, technology, population, etc. McCloskey’s economics incorporates two more factors: dignity and rhetoric. Economics, she argues, has failed be a humane science that accounts for the ways in which things like human speech — rhetoric — influence the way a society lives and works. After a detailed examination of traditional explanations of economic growth, McCloskey concludes that each is inadequate, and that the only explanation for the peculiar birth of the modern world is speech: At the beginning of the 18th century, people in the Netherlands and Britain began talking about commerce as a good thing — a novelty at that time. They gave dignity to the bourgeoisie. And that drove capitalism, giving birth to the modern world.

The Museum of the City of New York has a great new site on old photographs of New York (Kottke via Eater via City Room). A photo of the corner I live on from 1922:

Yesterday six people were charged with a $80 million fraud case around the City’s new payroll system called CityTime. I’m annoyed at a professional level, since as a contractor with the City I think I do good work, and now contractors and their fraud/waste will be a target of criticism. But my immediate question was how can you possibly steal $80m from the City, starting in 2005, and have no one notice. I understand if you have trouble accounting for every nickle and dime, but when a few hundred thousand dollars go missing, doesn’t someone take notice? The indictment raises questions of the city’s oversight of the CityTime project, and how this could happen. The program is overseen by the Office of Payroll Administration, which is run by both the mayor’s and comptroller’s offices, but it isn’t yet clear how one can lose control of a project to such an extent that this much money can go missing and it isn’t noticed. The WSJ notes that “The project’s costs skyrocketed to more than $738 million from $68 million, and in September the city reached an agreement in which it wouldn’t make any more payments related to the project.” Things are going poorly when you have someone steal more money than the whole original project costs. Even worse, when you look at the City’s organizational chart, the office reports directly to the Mayor and Comptroller. Even if the Director of Payroll Administration is incompetent, you would have hoped that someone on the Mayor’s staff would have noticed a missing $13 million a year.

Interesting article from Vanity Fair on Goldman Sachs, the firm’s history, the crisis, and their minting of money.

On Thursday morning, Robert K. Steel, the deputy mayor for economic development, announced that the city would seek a “top caliber academic institution” as a partner in building a school for applied science and engineering. The city is willing to consider locating it on one or more of its properties, including the old hospital campuses at the Brooklyn Navy Yard and on Roosevelt Island.

I’m not entirely sure what that means. Are they looking for a new school to form a campus in the city, or for an already existing university to expand? Are they willing to give land/money to Columbia’s Fu, NYU-Poly or Cooper Union or do they want MIT to have a satellite campus? The NYT article continues:

“New York has had some of the best science in the world for years, and it hasn’t translated into a first-rate center for technology start-ups the way it has elsewhere,” said Jonathan Bowles, director of the Center for an Urban Future. “It’s a mistake to think that any other region can become the next Silicon Valley, but New York can and should develop more of a technology presence than it has now.”

New “scientific analysis” shows that if a nuclear attack happens near you, that you shouldn’t flee. Your chances of survival go up a great deal if you stay inside some structure (even a car, but preferably something like a basement): “a nuclear attack is much more survivable if you immediately shield yourself from the lethal radiation that follows a blast, a simple tactic seen as saving hundreds of thousands of lives.” The Times’ reporting on the results continue:

The results were revealing. For instance, the scientists found that a bomb’s flash would blind many drivers, causing accidents and complicating evacuation.

The big surprise was how taking shelter for as little as several hours made a huge difference in survival rates.

“This has been a game changer,” Brooke Buddemeier, a Livermore health physicist, told a Los Angeles conference. He showed a slide labeled “How Many Lives Can Sheltering Save?”

If people in Los Angeles a mile or more from ground zero of an attack took no shelter, Mr. Buddemeier said, there would be 285,000 casualties from fallout in that region.

Taking shelter in a place with minimal protection, like a car, would cut that figure to 125,000 deaths or injuries, he said. A shallow basement would further reduce it to 45,000 casualties. And the core of a big office building or an underground garage would provide the best shelter of all.