Bloomberg says he and Biden considered running together

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New York Mayor Michael Bloomberg (R) speaks with US Vice President Joe Biden (L) at a press conference with and families from Newtown, Connecticut to discuss the need for federal gun laws March 21, 2013 at City Hall in New York. AFP PHOTO/Stan HONDA (Photo credit should read STAN HONDA/AFP/Getty Images)

WASHINGTON (CNN) — What prevented 2016’s highest-profile almost-rans from seeking the presidency together? Both wanted to be on top.

At least that’s how Michael Bloomberg described it Tuesday when he introduced Vice President Joe Biden at a cancer research event in Baltimore.

“We actually talked about doing a joint ticket, but we couldn’t agree on whether it was reverse or straight alphabetical order,” the former New York City mayor joked during the ceremony at Johns Hopkins University.

Both men grappled publicly with making a bid for president, and both eventually decided to forgo a run. Biden announced in October that he wasn’t emotionally ready for a campaign after his son’s death from cancer. Bloomberg said earlier this month it would be impossible for him to win enough electoral votes to make it to the White House.

Both were seen as potential spoilers for those already in the race — Biden as a candidate who could block front-runner Hillary Clinton from the Democratic nomination, and Bloomberg as a siphon for both Republican and Democratic votes.

A Biden-Bloomberg ticket — or a Bloomberg-Biden one — would have extended both men’s political careers as each one looked to his next chapter.

Biden on Tuesday pressed his case for a cancer “moonshot,” announcing a new institute for immunotherapy at Hopkins. Bloomberg’s name graces the university’s public health school.

“Whatever you’re engaged in, Mike, it’s always been something that’s been not about you,” Biden said. “It’s about something bigger. It’s always organized, it’s always committed, and everything Mike has done has been consequential.”