An interesting read on Cheney's exact qualifications for making sound military judgments base on knowledgable people's recommendations. I recommend you read the entire article.
Troop Levels in Stability Operations: What We Don't Know | World | AlterNet
Troops Levels and Iraq
Army Chief of Staff Eric Shinseki set off a firestorm when he told the Senate Armed Services committee before the invasion that "something on the order of several hundred thousand soldiers" would be required to stabilize Iraq, a figure that began to approach 20 troops per 1,000 of the Iraqi population, the ratio that academics conventionally, if not universally, cite as necessary for successful stability operations. Secretary of Defense Donald Rumsfeld called this estimate "far off the mark," as did Deputy Secretary Paul Wolfowitz, who put the figure closer to 100,000 troops total for Iraq. As the war drags on, requiring orders of magnitude greater time, blood, and treasure than estimated by U.S. leadership, troop figures have become the foremost issue debated at all levels.