* Bloomberg will have to contend with emboldened rivals
* Seen by some voters as out of touch with average people
By Edith Honan
NEW YORK, Nov 4 (Reuters) - New York Mayor Michael Bloomberg won a third term on Tuesday, but the combination of a smaller than expected victory and the rise of newly emboldened rivals could make for a rocky four years, experts say.
Critics said Bloomberg would have to counter the perception of arrogance that stemmed from his pushing through a change in term limits last year that enabled him to run for a third term, as well as the idea he bought the election.
Bloomberg defeated the city's Democratic comptroller, Bill Thompson, by a surprisingly close 51 percent to 46 percent after pouring at least $90 million of his own money into the race -- a U.S. record for personal campaign spending. Opinion polls had shown Bloomberg as recently as Monday with a double-digit lead.
Polls have shown that while most voters approved of Bloomberg's job performance, others faulted his leadership style and perceived the billionaire mayor as out of touch with average New Yorkers.
"He ran a campaign that was devoid of any sense of humility, and I think that was a mistake," said journalist and Bloomberg biographer Joyce Purnick. "People don't like to feel like they're being bought."
She added, "He's still a mayor in a city where the mayoralty is all-powerful and that's not going to change."
Bloomberg pushed City Council last year to extend term limits on the grounds his financial skills and experience were invaluable for guiding America's most populous city through hard economic times.
As mayor, Bloomberg has won praise for fiscal prudence, the city's 36 percent drop in crime since 2001, and taking control of the much-criticized public school system.
Bloomberg, 67, is founder of the Bloomberg LP news and information company, which competes with Thomson Reuters (TRI.N) (TRI.TO). He ranks 17th on the Forbes list of the world's richest people with a net worth of $16 billion.
On Wednesday, Bloomberg rejected the idea his narrower than anticipated re-election margin clouded his victory.
"What people are going to judge this administration on is accomplishments, and over the last eight years a majority found those accomplishments to justify another four years," Bloomberg told reporters.
NO MORE 'ONE-MAN SHOW"
Political analysts said Bloomberg would have to tweak his style in order to have a successful third term -- especially since rivals will see battling with Bloomberg as an opportunity to win political points with disaffected voters.
City Council Speaker Christine Quinn, incoming Comptroller John Liu and incoming Public Advocate Bill de Blasio have all been named as possible 2013 Democratic mayoral candidates.
"Over the last four years, many people looking to succeed him were looking to have a good relationship with him," said Richard Briffault, a Columbia Law School professor. "And now they're going to be less interested in that."
A longtime Democrat, Bloomberg became a Republican to run in 2001, but dropped his party registration in 2007. He ran this year as the candidate for both the Republican and Independence parties.
The depth of New York City's economic problems might be worse this year than when Bloomberg's first term began in January 2002, when the city was still shaken by the Sept. 11, 2001, attacks and multibillion-dollar budget deficits.