Wednesday, February 10, 2010

What are the odds that Malia or Sasha will be President?

Let's forget about politics for a moment, and look at this strictly as a probability problem.

How likely are Malia or Sasha to become one of our future presidents? Or rather, how much does the fact that their father is Barak Obama help them?

For an American chosen at random, his or her probability of becoming president is too tiny to imagine. But let's imagine it. The youngest president was Bill Clinton, elected at 42. The oldest would have been John McCain at 72. Throwing out those outliers, let's estimate that to have a shot at being elected President, you need to be between 45 and 65. According to the US census data, there were 62 million Americans in this age range in 2000, comprising 22.0% of the US population. So if we had no other information about a person other than his or her age and citizenship status, we could guess that there is a 1 in 65 million chance that he or she was elected President, if we guessed in 2000.

Now consider America in 1800. The free population of the United States was 4.3 million. The life expectancy in 1750 was 36. Well actually the life expectancy in the Northern States was 40. In 1950, that number was 68. So to be conservative, let's say that we can estimate the number of Americans over 45 in 1800 by looking at the number of Americans over 70, alive in 2000. By this generous measure, 9.0% of free Americans in 1800 had a hypothetical chance to be president, out of a population that was 50 times smaller. That amounts to a little better than 1 in 400,000.

I already factored in our country's ugly history of slavery. However one must also remember that in 1800, women were not eligible to be President. So if you picked a random free American man in 1800, you had a little better than 1 in 200,000 chance to pick the President of the United States.

Now those odds look a little better than 1 in 65 million! And I think I was being very generous with the age issues.

Presidents don't get elected randomly. However in 1800, if you got into politics early enough, stuck around, and lived long enough, you were a long shot to be President. At least statistically speaking.

As a kid, I always assumed that John Quincy Adams became president at least in part due to nepotism. Maybe it was so, but given the fact that his chance was 1 out of 200,000 before you even considered his qualifications, things are not so clear.

However, we are not looking at individual cases here. Instead, we are considering the probability of two presidents being close blood relatives, if selected at random. We've never had two Presidents who were brothers, first cousins or grandchildren of other Presidents. But if we had, I don't think that we would have though of this as any less nepotistic than father and son. Still, let's scratch cousin and brother. Although both RFK and Ted Kennedy had a non-trivial chance of becoming President, which is worth noting.

For the early years, there were too few former Presidents. But let's assume for now that there were always past Presidents, who each served either 4 or 8 years. Each President has on average 1 son, and on average 2 grandsons, who will live to be of Presidential age. Each of these men has a 45-65 window to be elected President. So he's got 3 shots at the top job. Thus each new President is contributing about 9 future nepotistic Presidential hopefuls over their lifetime. Thus in the long run, the average number of such hopefuls during a given Presidential race must be around 9. Let's make it 10, for a round number.

OK, so during every election cycle, there are 10 or so potentially nepotistic candidates (let's call them PNCs from now on).

If we lived in 1800, there would be a 1 in 20,000 chance that the electorate would choose a PNC, even if the election was a random drawing of free male citizens. (Not really, since there was not a full set of past Presidents to use as fathers and grandfathers, but bear with me.)

In 2000, there are still 10 PNC, but now that women have a real chance to be President, there is only a 1 in 6.5 million chance that we will elect a PNC by random drawing.

So far, I have not even mentioned one obvious fact: on average, the PNCs are much more qualified to be President than an average American of the correct age. Most people don't even want to be President. Even if we restrict eligibility to those who went to college (or the military), and score in the top 2/3 of Americans in IQ, public speaking and some measure of organizational skills, we would eliminate most people. Most people are not interested in a political career. Not all of those who are interested can pass the basic qualifications for election. However, it is probably safe to say that any PNC who wants to start a career in politics can do so. Not all PNCs will be interested in politics, but for now let's assume that they are at least as likely as an average American to be interested in a career in politics, but with perhaps a better chance to get started, because of their family connections.

So by the most conservative of measures, we can estimate that a PNC is about 10 times more likely to enter politics as an average American, given the same level of interest.

Therefore, we estimate that under the conditions of 1800, a PNC had a 1 in 2,000 chance of being elected President in a give election, even if the election consisted of a random drawing among all of the minimally qualified people. Let's review how we got here:

4.3 million Americans * 0.09 [aged 45-65] * 1/2 [men] = 200,000 eligible
200,000 eligible / 10 [estimated PNCs] = 1 in 20,000 to elect a PNC
1 in 20,000 chance / 10 [estimated advantage to a PNC] = 1 in 2,000 to elect a PNC

What this calculation actually suggests is that if there were 2,000 politicians on all levels of government in 1800, typically 1 of them might be a PNC. If we elected Presidents at random from all current politicians, then there is a 1 in 2,000 chance that we elect a PNC.

Given these odds, it is unsurprising that America elected a single PNC (John Quincy Adams) in its early days. You may say that his odds should have been much worse since he was 6th President, but I would argue any son of Benjamin Franklin, John Jay, or any other Founding Father could be considered a PNC.

In any case, I think that it's fair to say that during America's early history (ie before the 20th century), a PNC was not much more likely to reach a high political office than a similarly ambitious white male citizen, who was able to get a college education, or to become a reasonably high ranking officer in the army. This was simply because there were about the same number of high level posts as there are today, but with magnitudes fewer candidates.

Contrast this with today's conditions. There is still only one President. Only one Secretary of State. Only one Speaker of the House of Representatives. There are a few more lower ranking secretaries and a lot more advisors. However the pool of Americans aged 45-65 who are full citizens has increased by a factor of over 100. Let's consider the chance of America electing a PNC in 2000 purely by chance:

280 million Americans * 0.22 [aged 45-65] = 65,000,000 eligible
65,000,000 eligible / 10 [estimated PNCs] = 1 in 6,500,000 to elect a PNC
1 in 6,500,000 chance / 10 [estimated advantage to a PNC] = 1 in 650,000 to elect a PNC

So everything else being equal (except a 1ox advantage to a PNC for getting started in politics), America should only have elected a PNC with 1 in 650,000 chance in 2000. But we did in fact elect a PNC, George W. Bush. I don't think that anyone thinks that this occurred simply by chance. I think we all know that George W. Bush had a huge advantage in becoming President because his father was also President.

This in itself is not remarkable. What is remarkable is that this was not really the case in 1800.

In 1800, there were exponentially fewer candidates per high level post, so anyone who was qualified, ambitious, and had talent for politics had a non-trivial shot at a top job in his lifetime (provided that he lived long enough).

Nowadays, there are many many more candidates per top job, and as such, each qualified candidate's chances at a top job are much lower. Except for PNCs, that is!

By my estimates, if there were 2,000 politicians (and high level military brass) in 1800, about 1 of them would be a PNC, and all would have a roughly similar chance to become President. That is not all that inconsistent with what actually took place in the 1800's.

By these same estimates, if there were 650,000 politicians (as well as high level military, influential businessmen, and politically active preachers) in 2000, then about 1 of them would be a PNC, and all would have a roughly similar chance at the Presidency. All those numbers sound reasonably accurate for 2000, except that the one politically active PNC had a disproportionately large chance of being elected President.

Moreover, George W. Bush knew of his advantage from his first days in politics, if not earlier. Everyone else knew it too, which helped him on every step along the way to the top.

I am not suggesting that nepotism handed George W. Bush the Presidency. But nepotism gave George Bush a much better shot at the Presidency early in his political career. Also, I am suggesting that nepotism is stronger in American politics now than it was 200 years ago. And that it will get stronger still, simply as a result of our population growth.

I think we know intuitively that it is hard to rise up a hierarchy on merit alone. As the hierarchy becomes increasingly complex, or the pool of qualified candidates increases, this becomes even harder. To rise up a highly competitive hierarchy, one needs to be either really lucky, or to have some sort of advantage. The instant name recognition of a PNC helps him or her at every level. Even if the difference is small at the highest level of the hierarchy (ie national elections), it gives him or her enormous benefit in getting to that level in the first place.

One result of this phenomenon is that some of the best qualified candidates drop out of the hierarchy early on. Many others never even enter the fray, deciding to pursue promotion in smaller hierarchies, or avoiding hierarchies entirely. There are probably about 500,000 Americans today who are relatively young politicians, military types, or the right kind of businessman or preacher to break into politics. All have a relatively equal chance to become President. Except for the PNCs. Even a minor PNC like Mitt Romney has a better than equal chance because his father reached a second-tier position in the hierarchy of government. However his advantage is nowhere as big as that of George W Bush, or Hilary Clinton.

The fact that unconnected individual like Bill Clinton, Barak Obama, Sarah Palin, Mike Huckabee and John Edwards all became President, or almost became President should not distract from the fact that individually, unconnected people have almost no chance to become President (even if their cumulative chances are good).

The old days had their fair share of strange, crazy and incompetent candidates, to be sure. America almost elected Aaron Burr over Thomas Jefferson, and neither Andrew Johnson nor Franklin Pierce were remotely the best man for the job. And yet, for a well qualified, ambitious and talented politician, his chances of reaching a top job in the old day wasn't bad.

In 1787, 55 of the most brightest political minds in the United States gathered in Philadelphia to write our greatest political document to date. Today, that would not be possible. Consider the mess in California, where no one can agree on how to select the delegates for a new constitutional convention.

Is this a problem, and what can be done about it? That is beyond the scope of this discussion.

However, I think we should consider the example of India. The world's largest democracy has had both many PNCs at the top job, and also some completely unconnected candidates, in a roughly 50-50 split. I think that this is where America is headed.

So how does this all relate to Malia and Sasha? If they want to become President one day, their chances are exceptionally good. Even if we say that their chances are 1 in 30 each (based on a rough historical average), those odds are much better than the 1 in 500,000 or so for a typical minimally qualified candidate.

I have argued that America is headed toward more nepotism at the top, so their chances of becoming President might be as much as 100,000 times higher than those of their Sidwell Friends classmates. This is even assuming that their classmates are likely to be wealthier, smarter, more educated, and better politically connected than your average American.

On top of that, Malia and Sasha are possibly the most qualified 9 and 11 year old future Presidents ever. They are incredibly young for Presidential children, giving them a head start in just about everything. By they time they are 45 years old, being black women will not hurt them in national elections, even if one argues that being a black woman is still a disadvantage today. Also, our country will be 30+ years removed from the first Obama Presidency. We always remember our Presidents well, given enough time. So their father's legacy, whatever that may be, will help them more than ever before for a PNC.

The biggest obstacle to a Obama 2050 (or so) coronation would be the chance that neither of the girls wants their father's old job. That could happen. But I would still be willing to place a 10 to 1 wager that one of the Obama daughters achieves a top 4 position in our country's government within her lifetime.

Given that our country will by then have 500 million other eligible citizens, such odds are truely remarkable.

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