Friday, February 3, 2017

The Math Behind the Jury Selection Problem

I recently served on the jury for a trial in the county superior court system, and contrary to popular belief it turned out to be an interesting experience. The ordeal gave me confidence in the idea of being judged by a jury of one's peers, and I came away with an appreciation of the fact that the responsibilities of a jury are precise and straightforward, much like the role of computer hardware (jurors) carrying out the instructions of a software program (law) given a set of well-defined inputs (evidence).

As I sat through the initial jury selection process, I also got to thinking about some of the mathematics behind the process. In particular, is there a way to answer the two questions on every prospective juror's mind: will I be selected as a juror and how long is this process going to take?

Tuesday, March 8, 2016

Wheel of Fortune Mystery Wedge Problem

The Wheel of Fortune Mystery Wedge Problem is my attempt at a slightly more modern spin (pun intended) on the classic Monty Hall problem, which is a probability puzzle based on an older game show. Most modern American (and many international, so I've learned) TV viewers are likely familiar with Wheel of Fortune, but this specific problem can be framed in a way that doesn't require complete knowledge of the rules of the game:

  • You have X dollars in the bank and it's your turn to spin the wheel
  • You spin the wheel and land on the $10,000 Mystery Wedge, make a correct guess to win Y dollars, and Pat Sajak, the host, then offers you two options:
  • The first option is to do nothing. It is still your turn and you will end up with X + Y dollars in the bank.
  • The second option is to flip over the Mystery Wedge for a 50/50 shot at winning $10,000. If you lose, you lose all your money plus your turn.

Should you flip over the Mystery Wedge or not? At what values of X and Y should you flip the wedge and take the risk?

Saturday, December 12, 2015

California Drought Dashboard

The drought in California has been going on for a few years now, and the talk of an El Niño winter bringing much needed relief makes me wonder about the latest state of the drought situation as we move through a hopefully wet winter. Surprisingly, I was hard-pressed to find good, up-to-date sources of California drought conditions data that show changes over time.

For starters, the United States Drought Monitor provides great percentile data for different drought level intensities, updated on a weekly basis. However, the tables do a poor job of depicting the progression of the drought conditions on a weekly basis, even though that data is readily available and dates all the way back to 2000. The best visualization of this data that I've found, in time-series form, is the graph from the US Drought Monitor that almost gets the job done but lacks some fine grained control. So, I made a slightly tweaked version of this graph that is hopefully a solid dashboard that can serve as an up-to-date summary of drought conditions. The graph can be easily manipulated for comparisons over different time periods, and always loads the latest data from the aforementioned sources.

Sunday, March 10, 2013

Yelp is to Netflix as Foursquare is to Netflix

Pop quiz, hot shot. Here's an SAT-style analogy question for you. Yelp is to Netflix as Foursquare is to what? Answer: Netflix. To be precise, Yelp is to Netflix DVD as Foursquare is to Netflix Streaming. The reason for that is data.

Thursday, February 21, 2013

Winning Bar Bets With Mathematics

Benford's law is pretty neat. I first came across this phenomenon while watching a silly Internet TV show related to bar bets. The bar bet that exploits Benford's law is a little complicated, and relies (of course) on the law of large numbers.

The premise is that you challenge your fellow bar patrons to a bet: that humans are no good at generating random numbers. It makes sense intuitively since people tend to pick numbers that have a special meaning, and there's a finite number of numbers that have meaningful connotations (i.e. 3's a charm, lucky number 7, etc.). To add to the challenge, you'll throw in some randomness. Each person will come up with two randomly chosen quantities based on some data, such as the population of pet birds in the US and the volume of water in the Dead Sea in cubic feet. Then, multiply the two numbers to get a third number. The bet will be that even the first digit of *that* number is not uniformly distributed. On the surface, it seems counter-intuitive. But Benford's law will give you an edge in this silly bar game.

Thursday, November 3, 2011

Time Asymmetry and the Department of Motor Vehicles

Why do people dread going to the Department of Motor Vehicles? Why do the workers there seem so disgruntled? Because of time asymmetry. The amount of time you have and will invest in taking care of your errands at the DMV is orders of magnitude more than the amount of time a worker will invest in handling your matters.

You only have one appointment, whereas any given worker may go through dozens of customers in the span of a day. This imbalance and asymmetry is what leads to conflicting attitudes towards the same interaction between the representative and the customer, and why both sides seem to loathe the experience.

Saturday, June 18, 2011

The Nate Dogg Number

Nate Dogg was a rapper known for his prolific collaborations with numerous other hip-hop artists, whence he can usually be heard singing a catchy hook in between melodic rap verses. Nate Dogg passed away recently, and I thought it would be fun to honor him by creating the Nate Dogg number. Similar to the Erdős number, the Nate Dogg number is the collaborative distance between a person and Nate Dogg as measured by a collaboration on a musical track.