Utahns don't have strong feelings about who Massachusetts Gov. Michael Dukakis or Vice President George Bush should pick as their vice presidential running mates, but many believe that the Rev. Jesse Jackson would harm Dukakis' presidential campaign should he be added to the Democratic ticket.

With the Democratic National Convention just a week away, the general speculation is that Dukakis will name his vice presidential choice before delegates gather in Atlanta. Many close to the Dukakis campaign believe the governor doesn't want to waituntil the convention to act because he doesn't want to give the Jackson forces that opportunity to press for their man.

Dukakis will name his choice early, and thus nip any Jackson movement in the bud, the thinking goes.

Forty-four percent of those questioned by Jones didn't know who Dukakis should pick as his vice president running mate. Twenty-one percent said the governor should pick Jackson, 14 percent said he should pick Sen. Albert Gore, D-Tenn., who also ran for the Democratic presidential nomination this year. All others mentioned fell well back in the pack.

Jones found that Sen. Bob Dole, R-Kan., was picked by 24 percent of Utahn's as Bush's vice presidential running mate. Dole was Bush's closest challenger in the GOP presidential primary race until he was knocked out in March's Super Tuesday southern primaries. Utah's Sen. Orrin Hatch was named by 19 percent. Hatch is not being actively considered by Bush, however. Eleven percent mentioned White House Chief of Staff Howard Baker and 28 percent didn't know who Bush should pick.

Bush says that he won't pick his vice presidential running mate until after Dukakis has named his, thus giving Bush the advantage of measuring the geographic balance, as well as political philosophy, of the Dukakis ticket before making his choice.

Even though a quarter of all of those polled think Dukakis should pick Jackson, 57 percent said Jackson as a vice presidential candidate would harm Dukakis' campaign. Only 8 percent said Jackson would definitely help Dukakis.

Jackson says his good showing in Democratic primaries, plus his popularity among minorities and disadvantaged, has earned him the right of a vice presidential offer. He's hinted that he'd accept that offer.

But 47 percent of those polled by Jones said Jackson's second-place finish doesn't earn him the right of a vice presidential offer. Forty-one percent think Jackson has earned that right.

POLL

Who should George Bush select as his vice presidential running mate?

Bob Dole 24 percent

Jean Kirkpatrick 7 percent

Elizabeth Dole 5 percent

Howard Baker 11 percent

Jack Kemp 4 percent

Orrin Hatch 19 percent

Paul Laxalt 1 percent

George Deukmejian 1 percent

Other 1 percent

Don't know 28 percent

Who should Michael Dukakis select as his vice presidential running mate?

Bill Bradley 6 percent

Joe Biden 3 percent

Albert Gore 14 percent

Sam Nunn 6 percent

Jesse Jackson 21 percent

Lloyd Bentson 1 percent

Bill Clinton 1 percent

Lamar Alexander 1 percent

Other 3 percent

Don't know 44 percent

Do you feel Jesse Jackson has or has not earned the right to be Michael Dukakis' vice presidential running mate?

Definitely has 15 percent

Probably has 26 percent

Probably has not 16 percent

Definitely has not 31 percent

Don't know 12 percent

Would Jesse Jackson help or hurt Michael Dukakis' campaign if Jackson were selected as Dukakis' running mate?

Definitely help 8 percent

Probably help 21 percent

Make no difference 6 percent

Probably hurt 27 percent

Definitely hurt 30 percent

Don't know 9 percent

Sample size: 603; margin of error plus or minus 4 percent