LIMA, Peru (AP) — The tears welling in the Paris mayor’s eyes told the story one way. The words the Los Angeles mayor spoke told it another.This was one of those rare Olympic moments when everyone walked away a winner.Paris for 2024. Los Angeles for 2028. And the International Olympic Committee for transforming its unruly, tension-filled and sometimes corrupt bidding process into a history-making, two-city victory that secures the future of the Games for the next 11 years.“This is a pretty radical revolution today,” LA mayor Eric Garcetti said. “Usually, we have two or three cities crying in a corner, and one glorious victory. In this world, there are enough losers today, enough people who go after dreams to have them crushed. Today, we model something that can be different.”Different, as in the first time the IOC has granted two Summer Olympics at once. And different, in that there was no need for a secret ballot or any last-minute, back-room deal making. This result came after a year’s worth of scrambling by IOC president Thomas Bach, who had only the two bidders left for the original prize, 2024, and couldn’t afford to see either lose.There was no drama — the decision had been locked in for more than a month. But to say there was no emotion would not be true.After Bach called for a show of hands to approve the dual award, dozens of arms shot skyward from the audience; moments later, Paris mayor Anne Hidalgo stood next to the IOC president dabbing tears from her eyes.“It was a very strong, very emotive moment,” Hidalgo said. “We are all united. Altogether, it’s very special for us, because in France, and in other countries, that’s not usual.”Moments after the vote, Bach handed cards with the winners’ names on them to Hidalgo and Garcetti. One read “Paris 2024,” and the other “LA 2028.” It was a mere formality, yet both mayors held them aloft with wide smiles on their faces.Both cities will host their third Olympics.The Paris Games will come on the 100th anniversary of its last turn. That milestone, plus the fact that Paris has been on the losing end of these bids for 1992, 2008 and 2012, would have made the French capital the sentimental favorite had only 2024 been up for grabs.Los Angeles moved to 2028, and those Olympics will halt a stretch of 32 years without a Summer Games in the United States. In exchange for the compromise, LA will grab an extra $300 million or more that could help offset the uncertainties that lie ahead over an 11-year wait instead of seven.“We’re ready now,” Garcetti insisted, speaking of a city that has virtually every sports venue already in place.Without any nail-biting conclusion to see, the post-vote celebration at the Eiffel Tower was a sparsely attended near rain-out. Los Angeles held a small event with Olympians Nastia Liukin and John Naber standing beneath the blazing Olympic cauldron at the famous LA Coliseum, but it was mostly media, and no fans.Meanwhile, in the Lima exhibition hall, the California-cool LA delegation wore sneakers to the presentation, and was going to forego neckties, too, before thinking better of it.In this never-before-seen style of selection, Bach asked the 94 IOC members to allow the real contests to play out at the Olympics themselves and transform the vote from a game of sorts into a pure business decision.It wasn’t such a bad idea considering the news still seeping out about a bid scandal involving a Brazilian IOC member’s alleged vote-selling to bring the 2016 Olympics to Rio de Janeiro.More than that, Bach needed to ensure stability for his brand.The public in many cities is no longer keen to approve blank checks for bid committees and governments that have to come up with the millions simply to bid for the Olympics, then billions more to stage them if they win.That reality hit hard when three of the original five bidders for 2024 — Rome, Hamburg, Germany, and Budapest, Hungary — dropped out, and the U.S. Olympic Committee had to pull the plug on its initial candidate, Boston, due to lack of public support.“This is a solution to an awkward problem,” said longtime IOC member Dick Pound of Canada.It was solved by Paris and Los Angeles, two cities with a storied tradition of Olympic hosting and an apparent understanding of Bach’s much-touted reform package, known as Agenda 2020. It seeks to streamline the Games, most notably by eliminating billion-dollar stadiums and infrastructure projects that have been underused, if used at all, once the Olympics leave town.Can they deliver?Paris will have the traditional seven-year time frame to answer that.Only one totally new venue is planned — a swimming and diving arena to be built near the Stade de France, which will serve as the Olympic stadium. In all, the projected cost of new venues and upgrades to others is $892 million.To be sure, Paris already has much to work with. Beach volleyball will be played near the Eiffel Tower; cycling will finish at the Arc de Triomphe; equestrian will be held at the Chateau de Versailles. And what would an Olympics be without some water-quality issues? There will be pressure to clean up the River Seine, which is where open-water and triathlon will be held. Los Angeles, meanwhile, will get an extra four years that Garcetti insists is hardly needed. Los Angeles proposed a $5.3 billion budget for 2024 (to be adjusted for 2028) that included infrastructure, operational costs — everything. A big number, indeed, though it must be put into perspective: Earlier this summer, organizers in Tokyo estimated their cost for the 2020 Games at $12.6 billion.Traffic could be a problem — it almost always is in LA — but the city will be well along in its multi-decade, multibillion-dollar transit upgrade by 2028. Those with long memories recall free-flowing highways the last time the Olympics came to town, as locals either left the city or heeded warnings to use public transportation or stay home.Those 1984 Games essentially saved the Olympic movement after a decade of terror, red ink and a boycott sullied the brand and made hosting a burden. The city points to its Olympic legacy to explain a nearly unheard-of 83 percent approval rating in a self-commissioned poll — not an insignificant factor when the IOC picks a place to bring its crown-jewel event.Along with Paris, LA is stepping in again to try to change the conversation about what hosting the Olympics can really be.“I think it’s a very positive message about the value of the Olympic movement and the value of the Olympic Games,” said Sergei Bubka, the Olympic champion pole vaulter, who is an honorary member of the IOC. “I think we’re going in the right direction.”———AP Sports Writers Beth Harris in Los Angeles and John Leicester in Paris contributed to this report.