When John Boehner takes over one of the most powerful jobs in Washington this week, he says his first order of business is to make himself less powerful.

On Wednesday the new speaker of the House of Representatives plans to offer a package of rule changes that, he says, will give minority-party members more of a say and decentralize power. In short, Ohio Republican Mr. Boehner is promising he'll be a different figure from many speakers throughout history—from Republican Joseph Cannon a century ago to his immediate predecessor,...