Michael Noer and Nicole Perlroth, Forbes.com

“I love power. But it is as an artist that I love it. I love it as a musician loves his violin, to draw out its sounds and chords and harmonies.” –Napoleon Bonaparte

Power has been called many things. The ultimate aphrodisiac. An absolute corrupter. A mistress. A violin. But its true nature remains elusive. After all, a head of state wields a very different sort of power than a religious figure. Can one really compare the influence of a journalist to that of a terrorist? And is power unexercised power at all?

In compiling our first ranking of the World’s Most Powerful People we wrestled with these questions–and many more–before deciding to define power in four dimensions. First, we asked, does the person have influence over lots of other people? Pope Benedict XVI, ranked 11th on our list, is the spiritual leader of more than a billion souls, or about one-sixth of the world’s population, while Wal-Mart CEO Mike Duke (No. 8) is the largest private-sector employer in the United States.

Then we assessed the financial resources controlled by these individuals. Are they relatively large compared with their peers? For heads of state we used GDP, while for CEOs, we looked at a composite ranking of market capitalization, profits, assets and revenues as reflected on our annual ranking of the World’s 2000 Largest Companies. In certain instances, like New York Times Executive Editor Bill Keller (No. 51), we judged the resources at his disposal compared with others in the industry. For billionaires, like Bill Gates (No. 10), net worth was also a factor.

Next we determined if they are powerful in multiple spheres. There are only 67 slots on our list–one for every 100 million people on the planet–so being powerful in just one area is not enough to guarantee a spot. Our picks project their influence in myriad ways. Take Italy’s colorful prime minister, Silvio Berlusconi (No. 12) who is a politician, a media monopolist and owner of soccer powerhouse A.C. Milan, or Oprah Winfrey (No. 45) who can manufacture a best-seller and an American President.

Lastly, we insisted that our choices actively use their power. Ingvar Kamprad, the 83-year-old entrepreneur behind Ikea and the richest man in Europe, was an early candidate for this list, but was excluded because he doesn’t exercise his power. On the other hand, Russian autocrat Vladimir Putin (No. 3) scored points because he likes to throw his weight around by jailing oligarchs, invading neighboring countries and periodically cutting off Western Europe’s supply of natural gas.

To calculate the final rankings, five Forbes senior editors ranked all of our candidates in each of these four dimensions of power. Those individual rankings were averaged into a composite score, which determined who placed above (or below) whom.

U.S. President Barack Obama emerged, unanimously, as the world’s most powerful person, and by a wide margin. But there were a number of surprises. Former President George W. Bush didn’t come close to making the final cut, while his predecessor in the Oval Office, Bill Clinton, ranks 31st, ahead of a number of sitting heads of government. Apple’s Steve Jobs easily made the list, while Arnold Schwarzenegger, the movie star governor of California (alone, the world’s fifth largest economy) did not.

This ranking is intended to be the beginning of a conversation, not the final word. Is the Dalai Lama (No. 39) really more powerful than the president of France (No. 56)? Do despicable criminals like billionaire Mexican drug lord Joaquín Guzmán (No. 41) belong on this list at all? Who did we overlook? What did we get wrong? Join the conversation by commenting now.