George Bush's choice of Sen. J. Danforth Quayle III to be his running mate on the Republican ticket was a very revealing one, and also hazardous in the extreme.

The fact that he decided not to select any of the highly experienced and formidable Republicans, such as Bob Dole and Jack Kemp, tells us about Bush's decision making. Whether Bush got along smoothly with Dole or Kemp was not as important as the stature each would have brought to the ticket.It seems a safe assumption that Bush suffered from the fears of other presidential candidates who chose a running mate on the basis of youth and inexperience, in the hope that he would not over shadow him. Since most presidential candidates worry about such things, it is usually safer to choose an older political figure who could easily be seen as elder statesman.

Dukakis did that with Bentsen, choosing someone who has been well respected and experienced, and yet is unlikely to run for president himself some day. Obviously, at 41, Quayle could use the vice presidency as a stepping stone in the same way as Bush.

In the meantime, Quayle has to fight the immediate revelations about his past, including the flap over the National Guard and the worrisome weekend with Paula Parkinson, and the controversial and probably ill-advised suggestion made by some that his good looks may inspire women to vote for him. (Bush and Sundance?)

Clearly, women would have been much more likely to have supported Elizabeth Dole, or some other outstanding woman, rather than an attractive man who has never shown any support for women's issues.

Bush should now try to learn from the other problem vice presidential selections. Most recently, in 1984, Walter Mondale selected Geraldine Ferraro, believing that she was an outstanding woman in Congress who could represent new opportunity for women. Mondale's motives were probably noble, but he failed to exercise enough care about her background. Unfortunately, her husband had major financial and ethical problems, which forced her to be consistently on the defensive. As a result, she hurt the Democratic ticket more than she helped it, and made it undesirable for any 1988 candidate to choose a woman.

In 1968, Richard Nixon, the GOP presidential candidate, chose Spiro Agnew, a completely unknown governor of Maryland with no national track record. Like Bush, Nixon could have chosen any number of qualified and well-known Republicans, but he went for someone he did not know, who eventually turned out to be an old style political crook. As Baltimore County executive, as Maryland governor and later as vice president, Agnew accepted envelopes with money in return for political favors. But it was a Republican year, and Nixon was elected in spite of a bad choice.

In 1952, Dwight Eisenhower made a selection similar to Bush, when he tapped Richard Nixon, only 39 years old and unknown nationally, who had some immediate financial baggage. Nixon was charged with involvement in a "slush fund" that was considered illegal and unethical, and after horrendous criticism, he went on national television and managed to turn the tide with his trite but successful "Checkers" speech.

The truth is that Ike could have beaten anyone that year, and so the Nixon embarrassment was not as important as it could have been. Bush simply does not have that kind of personal popularity and cannot afford a VP candidate with problems. Even so, Ike also gave us a future president, one who would be seen by historians as one of our most corrupt. Without the vice presidential stepping stone, it is unlikely that Nixon ever would have been president.

But the most serious mistake ever made by a presidential candidate choosing a running mate was George McGovern's in 1972. McGovern, who was almost unknown himself and became the Democratic candidate as a dark horse, chose Sen. Thomas Eagleton of Missouri. When it was revealed that Eagleton had been hospitalized three times for "fatigue and nervous exhaustion," and that he had undergone electric shock therapy, he became a burden to the Democrats.

McGovern declared his "1,000 percent support" for Eagleton, then dumped him. Since McGovern had little chance of defeating Nixon that year, he was rejected by several potential replacements before Sargeant Shriver finally accepted. McGovern would have been better advised to stand behind Eagleton, no matter what his problems had been.

So Bush should beware. He has made the selection and he will have to live with it. He should stick with Quayle and hope for the best, but since he is without the popularity of an Eisenhower, he may have made his fatal mistake.

* Dennis Lythgoe, a professor of history at Bridgewater State College in Massachusetts, is working on the Deseret News staff during August.