Solar Panels in the Desert

Just over three years ago (has it really been that long?) I wrote a piece mocking a commercial that claimed "It would only take a square of desert 96 miles wide covered in solar panels to produce all the electricity that the United States needs." As I wrote at the time,

That's roughly 5.9 million acres of desert, or just over 7 times the combined area of all 5 of Utah's National Parks. And that's the problem right there: It's lovely to imagine that the entire southwestern corner of the United States is wide open, just waiting to be covered with solar panels, but, as it turns out, good portions of it are already being used for things like National Parks and the city of Phoenix.

Indeed, solar and wind power development frequently threatens otherwise pristine wilderness. Such is the case with a controversy that has erupted in California:

[April Sall's] small California group, the Wildlands Conservancy, wanted to preserve 600,000 acres of the Mojave. The group raised $45 million, bought the land and deeded it to the federal government.

The conservancy intended that the land be protected forever. Instead, 12 years after accepting the largest land gift in American history, the federal government is on the verge of opening 50,000 acres of that bequest to solar development.

Even worse, in Sall's view, the nation's largest environmental organizations are scarcely voicing opposition. Their silence leaves the conservancy and a smattering of other small environmental organizations nearly alone in opposing energy development across 33,000 square miles of desert land.

Power needs to come from somewhere, and it's almost unavoidable that some kind of wilderness will be destroyed along the way. Still, this provides a reminder that solar and wind power pose their own significant environmental problems.

The $656 Mega Millions Jackpot.

The Mega Millions drawing last night was the largest lottery jackpot in history at $656 million, considerably larger than the previous largest jackpot of $390 million. The massive jackpot was in part due to the record sales of tickets nobody won Tuesday night's jackpot of $363 million. The logic behind these tickets sales is simple enough: as the jackpot gets larger, the value of a winning ticket increases, potentially to the point where buying a ticket makes sense from a mathematical point of view.

However, this logic misses an important point: As more tickets are sold, the probability that the pot will have to be split between more than one winner dramatically increases. In general, this effect is more than offset by the increase in the value of the pot. With the incredible hype around yesterdays drawing, though, so many tickets were sold that the splitting effect actually outweighed the pot size effect. I ran the numbers, and the best drawing to play the lottery (in terms of expected value, aka EV, of buying a ticket) was actually last week, as the following table shows:


The first three columns are in millions. The bottom line number is given in the "Actual EV" column.  This number is the amount that you should expect to get back - post taxes - for every dollar you spend if you take the lump sum option. (Nominal EV uses the headline pot size figure rather than the lump sum amount.) As the table shows, playing the lottery is always a bad idea. The "best" drawing to play would have been Tuesday night, and even then the expected loss would be thirty cents on the dollar. Friday night's drawing was the worst in more than two weeks and barely even had 2/3 the return of Tuesday's drawing. The explanation for this lies in the Average Pot Proportion value- with the huge number of tickets sold before that drawing, a winner on average would only keep about 18% of the pot. (As it turned out, there were three winners, so they each got to keep a third of it.)

If you're interested, here's how I got the numbers. The pot sizes and lump amounts were pulled from Lottery Post's news section. I calculated the tickets sold for each drawing by assuming that thirty cents of each ticket goes towards the jackpot, which is consistent with the numbers I've found. Getting the Nominal EV was a bit more difficult: I used the total number of tickets sold to calculate the likelihood of exactly n winners for n=0,1,2... and then calculated the expected share of the jackpot based on the annuity value. (There are two subtleties to this calculation: First, I assumed that everyone selects their numbers at random, which is close enough to being true. Second, an individual who buys a lottery ticket only cares about the total number of winners if he is one of them- ie, conditional on his ticket being a winner. This inflates the expected number of winners in the calculation.) I got the actual EV by considering several other factors: First, I used the lump sum value instead of the annuity value. Second, I included a federal tax of 30% and a state tax of 5% (which is typical.) Finally, I added .14 to the EV to account for non-jackpot prizes (which are independent of the pot size.)

The two obvious sources of error in the calculation are both utility related. First utility is very much non linear by the time you get to hundreds of millions of dollars. Second, people derive utility from imagining the possibility of winning. I suspect that many of the people who bought tickets last night derived 53 cents per ticket of utility from fantasizing about winning.

Does College Make You More Liberal?

A recent article in the New York Times suggests that it doesn't:

But contrary to conservative rhetoric, studies show that going to college does not make students substantially more liberal. The political scientist Mack Mariani and the higher education researcher Gordon Hewitt analyzed changes in student political attitudes between their freshman and senior years at 38 colleges and universities from 1999 to 2003. They found that on average, students shifted somewhat to the left — but that these changes were in line with shifts experienced by most Americans between the ages of 18 and 24 during the same period of time. In addition, they found that students were no more likely to move left at schools with more liberal faculties.

Similarly, the political scientists M. Kent Jennings and Laura Stoker analyzed data from a survey that tracked the political attitudes of about 1,000 high school students through their college years and into middle age. Their research found that the tendency of college graduates to be more liberal reflects to a large extent the fact that more liberal students are more likely to go to college in the first place.

I'm skeptical of this analysis for two reasons. The author claims that college students become more liberal, but by only the same amount that most 18-24 year old adults do. However, he also states that college bound high school students are more liberal on average than students who don't go to college. This means that college students are moving away from the mean while non-college student young adults are moving towards it. If you assume that political views form some kind of unimodal distribution, then moving away from the mean is in some sense more significant. This doesn't necessarily invalidate the analysis, but it does add a wrinkle.

The other reason I'm skeptical is less sophisticated: The author of the article is clearly biased. Here's the last paragraph:

The main reason for this development is that attacking liberal professors as elitists serves a vital purpose. It helps position the conservative movement as a populist enterprise by identifying a predatory elite to which conservatism stands opposed — an otherwise difficult task for a movement strongly backed by holders of economic power.

If you include a paragraph like that in your article, don't expect to be taken as a serious researcher.

An Observation

The frequency of Romney hatred on the internet has risen to the point that I have no doubt that he will be the Republican nominee in 2012.

Drop the Box!

I have long believed that Ivy League universities shouldn't ask applicants to check a box indicating their race. Diversity of experience and background enriches a college community, which is precisely why schools like Yale heavily emphasize essays and recommendations during the application process. If the only basis for an applicant's claim that he will add diversity is his skin color, the reality is that the university will gain little if anything from admitting him. Indeed, at many schools, racial preferences in admissions form de facto quotas. It's heartening to read, then, that Asian students (who are clearly discriminated against during the application process) have stopped playing along with the system.

Oh- and I've missed blogging, so hopefully I'll be writing a bit more over the next six months or so.