She was a political novice who wanted to start at the top by running for the U.S. Senate seat in a state where she hadn't lived for decades. Her maiden campaign had more than its share of snafus: She paid a fine for obtaining a resident Wyoming fishing license despite not meeting the residence requirement. When she opposed same-sex marriage, she found herself in a public spat with her sister's lesbian partner. But Liz Cheney figured she had something that would flatten all obstacles: a famous political name and the connections that go with it.

It didn't turn out quite as she had hoped. The incumbent Republican she was challenging, Mike Enzi, reportedly enjoyed a big lead in internal polls. She didn't get the warmest of welcomes from GOP politicians in Wyoming, who resented the internal fight. On Monday, she withdrew, citing unspecified "serious health issues" in her family.

Political nepotism is an old American tradition: John Quincy Adams, the sixth president, was the son of the second, John Adams. Cheney is not the first to demonstrate its limits. Bill Daley, brother of the longtime mayor of Chicago, gave up his campaign for governor of Illinois after two months. Caroline Kennedy, who let it be known she'd like to be appointed to the Senate seat vacated when Hillary Clinton became secretary of state, withdrew amid the sort of unflattering publicity she had never faced before. (She later got a consolation prize, the job of ambassador to Japan.)

But these are more the exception than the rule. Truth is, many a successful politician has pulled relatives along on his coattails. Ted Kennedy won his brother John's Senate seat in 1962 over an opponent who jeered, "If your name was simply Edward Moore instead of Edward Moore Kennedy, your candidacy would be a joke." It's unlikely George W. Bush would have been elected governor of Texas had he chosen a different father.

In election campaigns, name recognition is often half the battle. And a name that has strong, positive associations in the mind of voters is even more valuable. Political brands are like commercial brands: They convey instant information about what to expect. Liz Cheney's pedigree might be fatal in many states, but it didn't hurt her in deep-red Wyoming, which her father once represented in the House. On the contrary, it was an asset that made an otherwise preposterous candidacy plausible.

Maybe she'll stick around her new house in Jackson Hole and eventually run for office again. In that case, the first piece of advice she'll get from any campaign strategist will be: Whatever you do, don't change your name.