Posts filed under “Mathematics”
Over at the NYT’s economics blog, Economix, David Leonhardt is running a prediction market contest, looking at odds of various Intrade contests. Pick any 3 of the 20 questions to answer, and the winner gets showered with untold glory and fame.
The contest has an interesting twist: Its based upon the betting at Intrade. That makes the choices less obvious and the strategies for winning the contest more intriguing. David asked me to submit a “guest” contest post for the Economix blog, which I did. You will find it at the New York Tmes.
In addition to my post, David graciously invited all of you to participate, saying: “You have a lot of really smart readers. Let’s see how well they can do in the contest.” Challenge accepted. The contest runs til tomorrow morning at 6am. Go over to the prediction market contest and submit your best guesses.
Let me begin with this (weasely) caveat: While I have spent many years studying markets, I am not remotely a political analyst. In fact, I dislike politics, and I especially detest how it has polluted economics.
Also be aware that my preferences in 2000 were the exact opposite of what actually occurred. My choices were McCain, Bradley, Gore, Bush – and that was pretty much the order they lost in.
And by way of full disclosure, I am probably best described as a Liberal Republican – low taxes, balanced budget, strong defense, no unnecessary overseas involvement, and no government involvement in personal matters (birth control, abortion, gay marriage, etc.) Liberal Republicans are now mythical creatures that no longer exist. I do not recognize the abomination that now calls itself the GOP. I guess that makes me an Independent.
OK, let’s move on to the contest, where whatever mathematical skill I may have could be of some small assistance battle of wits and luck.
My first thought: Picking the frontrunners and favorites appears to be a surefire path to the middle of the pack. To “win” this requires identifying which of the long shots really aren’t such long shots after all. In the markets, this is called variant perception – what the crowd (and the money they bet) thinks is an unlikely outcome, but is actually a higher probability result than most realize. (The best parallel company example is deep value stocks).
If this were actual money, I would most likely pick two favorites, and a single long shot. Something like:
9. North Carolina: Obama wins (1.9)
3. Obama’s electoral votes 379 or fewer (1.3)
11. Pennsylvania McCain wins (7.1)
[Tiebreaker] Winner popular vote share: 51.5%
That is the fiscally prudent thing to do, but that’s no fun. And since its not real cash, why not go for it?
What might be the variant outcome that most people think is very unlikely? I come up with 3: 1) A McCain victory; 2) A surprisingly tight race; 3) An Obama blowout. A McCain victory is (in my terrible political judgment) highly unlikely. The next variant perception scenario is either a very tight race, or an Obama blowout.
Looking at the questions, there are only a few that fit into this scenario. They are: Q2. Greater than 65%; 3. Obama’s electoral votes (out of 538) 380 or electoral votes more; 7. Obama wins Georgia; 10. Ohio McCain wins; 11. Pennsylvania McCain wins; 12. Virginia McCain wins; 13. Democrat-Republican breakdown 271 or more;
I don’t see McCain winning Ohio, Pennsylvania, or Virginia; He does have a good shot in Florida, but its not a great payoff (2.7 pts). Same with Obama winning Indiana (2.4 pts) and Georgia is a long shot.
That leaves the Obama blowout option the best odds (low possibility) relative to the points (highest points) So the picks I would make are:
2. Greater than 65% turnout;
3. Obama’s electoral votes (out of 538) 380 or electoral votes more
13. Democrat-Republican breakdown 271 or more.
[Tiebreaker] Winner popular vote share: 53.5%
While I give this a less than 20% chance of occurring, it’s the highest payout.
In an election where one of candidates ran many Hail Mary’s, it is only fitting.
One last caveat, so my clients don’t have a heart attack: This sort of low probability, high payoff is the exact opposite of how we run money in the office. It is why we’ve stayed out of trouble most of this year . . .
Prediction Markets and the Election: A Game
October 31, 2008, 6:42 pm
Nova discusses fractals, and the significance for various disciplines, such as Physics, mathematics and even markets:
Click for Video
In five parts:
They’re odd-looking shapes you may never have heard of, but they’re everywhere around you—the jagged repeating forms called fractals. If you know what to look for, you can find them in the clouds, in mountains, even inside the human body.
running time 11:36
THE MANDELBROT SET
In 1958, Benoit Mandelbrot begins using computers to explore vexing problems in math. They help him to understand repeating patterns in nature in an entirely new way. He coins the term fractal to describe them and develops the Mandelbrot set in 1980.
running time 9:51
ON THE DEFENSE
Though many colleagues initially scorned Mandelbrot’s work, his mesmerizing fractal images launched a popular culture fad. More importantly, his book The Fractal Geometry of Nature explained how his ideas could be applied in the real world. Mandelbrot’s ideas inspire an ever-increasing number of applications, including the fractal antenna.
running time 10:40
FRACTALS IN THE BODY
Fractal patterns turn up everywhere in biology, from the irregular rhythm of the heart to basic eye function. The fractal nature of such physiological processes, which obey simple mathematical rules, offers hope of better diagnosis and treatment of problems as well as new insights into how such processes work.
running time 10:15
NATURE’S FRACTAL NATURE
With carbon dioxide levels around the world rising, a team of American scientists travels to a rain forest in Costa Rica. They employ fractal geometry to analyze how much CO2 the rain forest can absorb.
running time 7:52
Economist Nassim Nicholas Taleb and his mentor, mathematician Benoit Mandelbrot, speak with Paul Solman about chain reactions and predicting the financial crisis.
click for video
RAY SUAREZ: Finally tonight, we return to a subject on many minds these days: the financial crisis. Our economics correspondent, Paul Solman, checked back in with one particularly prominent voice in the investment world and his colleague, who guided his thinking.
Here is the pair’s sobering conversation on what may lie ahead.
PAUL SOLMAN, NewsHour Economics Correspondent: One of the world’s hottest investment advisers these days, Nassim Nicholas Taleb, author of "The Black Swan," who’s been warning of a crash for years, betting on one, and winning big.
He’s been ubiquitous in the financial media of late, from cable TV’s "Colbert Report" to the BBC’s "Newsnight," where he was infuriated by what he called "bogus accounting."
NASSIM NICHOLAS TALEB, Scholar and Author: The first thing I would get immediately, immediately, I would suspend something called value at risk, quantitative measures of risk used by banks, immediately.
PAUL SOLMAN: We sat down with Taleb and the man he calls his mentor, mathematician Benoit Mandelbrot, pioneer of fractal geometry and chaos theory. And even more than feeling vindicated, they’re both scared.
NASSIM NICHOLAS TALEB: I don’t know if we’re entering the most difficult period since — not since the Great Depression, since the American Revolution.
PAUL SOLMAN: The most serious situation we’ve been in since the American Revolution?
Top Theorists Examine Rippling Economic Turbulence
PBS, October 21, 2008