WASHINGTON — The Democratic presidential contest in California remains extremely fluid — but not enough, at least so far, to provide an opening for Michael R. Bloomberg, who entered the race two weeks ago and was banking on winning big in the delegate-rich state — a new poll for The Times has found.

The survey by the UC Berkeley Institute of Governmental Studies found that both Sen. Elizabeth Warren of Massachusetts — the commanding front-runner in a September California poll — and former Vice President Joe Biden have lost ground among the state’s likely Democratic primary voters over the last two months.

That erosion has benefited Sen. Bernie Sanders of Vermont, who narrowly tops the primary field, and Mayor Pete Buttigieg of South Bend, Ind., who has doubled his support since the September poll. With less than two months before voting starts in Iowa’s Democratic caucuses and three months before California’s March 3 primary, “the race is really unusually fluid,” said Mark DiCamillo, director of the Berkeley IGS poll of voters likely to go to the polls in the Democratic primary.

“Voters are struggling and not sticking with their candidates,” he said. “They are moving around from candidate to candidate.”

Bloomberg appears ill-equipped to break into the mix. The poll, which was taken Nov. 21-27, just as Bloomberg started advertising in California and elsewhere on Nov. 25, found that he began his campaign with the most negative image of any candidate in the field. About 40% of likely Democratic primary voters surveyed viewed him negatively, and just 15% had a positive impression.

“That’s a hole he’s going to have to dig out of and reintroduce himself to voters,” DiCamillo said. “It’s going to be tough.”

The upshot of the poll is that the field’s most liberal candidates, Warren and Sanders, are in a statistical tie for first place. The leading candidates making a more moderate pitch, Biden and Buttigieg, are lagging and essentially tied for third place.

Sanders is in the nominal lead, as the first choice of 24%; Warren is the first pick of 22%. That is a big change from September, when she led the field with 29%.

Biden is the first choice of 14%, down 6 points from September. Buttigieg is preferred by 12%, up 6 points from September.

The poll was taken before California Sen. Kamala Harris dropped out of the race. It asked whom her supporters would name as their second choice if she quit, and found that Warren and Biden would benefit the most. If Harris voters were reallocated based on those responses, the race would tighten at the top to Sanders, 25%; Warren, 24%; Biden, 17%; and Buttigieg, 13%.

California will affect the prospects of all candidates because it has the largest number of delegates at next summer’s Democratic nominating convention. It is especially important for Bloomberg, a multibillionaire and former New York mayor. He is skipping the first nominating contests and counting on a big splash March 3 in the so-called Super Tuesday primaries in 17 states and territories, including California.

The Berkeley IGS poll, which was three-quarters complete before Bloomberg’s ads started running, found 8% were considering voting for him.

Whether his big spending on ads can change the negative image he brings to the race will be a test of the power of money in politics, but the record on such efforts — by rich presidential candidates such as Ross Perot, who ran as an independent in 1992, and Steve Forbes, a Republican candidate in 2000 — is not promising.

California billionaire Tom Steyer also has made a heavy investment in his own 2020 presidential bid, and his campaign is still floundering: Just 1% of California voters in the Berkeley-IGS survey said he was their first choice, and only 18% viewed him favorably.

Among the top-tier candidates, the opinion shifts among Californians are similar to trends found in other polls nationally and in key early-voting states. Warren is coming back down to earth after a heady run-up in polling this summer and fall; Sanders is regaining traction after an October heart attack unsettled his campaign; and Biden is facing increased competition from Buttigieg among voters who think Warren and Sanders are too far left.

Warren’s image has suffered over the last few months, during which she has struggled to answer the question of how she would overhaul the healthcare system. Her favorability rating remains high, with 67% viewing her positively, but that is down 10 points since September.

Still, the poll found that Warren had more room to increase support among California Democrats than any other candidate: 58% said they at least considered supporting her, compared with the 49% who were considering Sanders, 41% considering Buttigieg and 39% considering Biden.

The poll also provided a window into the perceived strengths of the candidates — and why Biden has come in a weak third compared with his stronger standing in national polls.

Biden led the field when California voters were asked which candidate had the best chance of beating Trump and which was most qualified to serve as president: 29% said he was the most electable, and 28% said he was most qualified, compared with Sanders’ second-place ranking on those points, with 22% and 24%, respectively.

But Biden drops to single digits behind other candidates on other qualities: Just 6% said he was the candidate with the sharpest mental abilities, compared with the 24% who picked Warren, who leads the field on that attribute.

Sanders tops the field on three other attributes — being the candidate who would bring the right kind of change to Washington (28%), the one who comes closest to sharing voters’ values (27%) and the candidate who best understands the problems of “people like you” (28%).

The poll found that the four septuagenarian candidates — Sanders, 78; Biden and Bloomberg, 77; and Warren, 70 — faced differing levels of concern about their age.

About one-third said they were extremely or very concerned that Biden’s and Sanders’ age would hurt their ability to serve as president. Only 7% said that about Warren; 17% said so about Bloomberg.

The poll found an increasingly stiff three-way competition in California for older voters, a part of the electorate that has been especially important to Biden’s national standing. Both he and Warren lost ground among those 65 and older over the last few months, while Buttigieg gained among that group, a prized bloc because it tends to vote in large numbers.

Biden narrowly leads with 22% of the over-65 vote, down from 26% in September. Warren’s share dropped to 18%, from 32% in September. Buttigieg supporters, meanwhile, increased to 17% of those seniors, from just 7% in September.

Sanders’ campaign, by contrast, hinges on his ability to turn out younger voters, who are less inclined than their elders to vote: He barely registered among older voters but was the first choice of 46% of voters ages 18 to 29.

That contributes to the advantage Sanders has among Latino voters, who tend to be younger as a group than other ethnicities. In California, 32% of Latino Democrats favor Sanders, a solid 13-point margin over the next-closest candidate, Biden, who has 19% support.

California will be an important test of candidate strength because it has a much more diverse population than the first two states in the nominating process, Iowa and New Hampshire, which are predominantly white.

The poll was conducted online in English and Spanish from Nov. 21 to 27 among 1,694 Californians considered likely to vote in the state’s upcoming Democratic presidential primary.

The estimated margin of error for the Democratic sample is 4 percentage points in either direction.