If defeating Donald Trump rests on the Democratic Party unifying early and strong around a nominee, then the current state of things looks ominous. Polling suggests a scenario in which four different candidates could each win each Iowa, New Hampshire, Nevada, and South Carolina—with a fifth candidate, Bloomberg, the one with the deepest pockets, only then entering the primaries. Not a recipe for rapid coalescence—and conceivably a situation in which the Democratic convention arrives next July with candidates still scrambling for delegates and no one in possession of a majority. In that case, who could play the role of party elder to mediate among the various factions?

Barack Obama would seem to be the natural choice; he’s not only the last Democratic president, and the only one since Franklin Roosevelt to be elected twice with majorities of the electorate, but he remains the most popular figure, by far, in the Democratic Party. Yet it would be hard for him to appear to remain neutral. He’s good friends with one top-tier candidate, Joe Biden, his vice president for eight years; he’s expressed public doubts and private annoyance about the socialism-inflected movement inspired by another, Bernie Sanders; he’s had an uneasy relationship with a third, Elizabeth Warren, since she briefly worked for him setting up the Consumer Financial Protection Bureau; and Buttigieg has explicitly tried to position himself as the next Obama. (Obama actually has deeper roots and a closer friendship with a fifth candidate, Deval Patrick, than with any of these four.) But beyond this, Obama doesn’t want to be the party mediator or convention broker. Part of why he’s retreated from the public is because he’s hoping the party will move past him, and he doesn’t think that his being seen to have handpicked Trump’s opponent would be good for Democrats’ odds in the general election. There’s also the more self-interested worry about his legacy: What would it say about him if he couldn’t get a deal done, or if his handpicked candidate loses to Trump?

So if not Obama, then who? Not Bill or Hillary Clinton—they’re too loathed by some of the very factions they’d be trying to soothe. House Speaker Nancy Pelosi is the de facto leader of the party, and people close to her hope and expect that she might be asked to mediate, based on her skill at steering the party toward the center-left. But she doesn’t have much of a relationship with any of the candidates or their campaigns aside from Biden, so she wouldn’t be able to exert personal suasion effectively.

That leaves the man, hairless due to chemotherapy, sitting across from me.