Political insiders used to scoff at the idea that Hillary Clinton would choose Elizabeth Warren for her running mate.

But multiple reports have found that she's one of the contenders on a shortlist that will soon be vetted by the Clinton team, alongside Virginia Sen. Tim Kaine, Housing and Urban Development Secretary Julian Castro, and potentially others.

And on Monday, Clinton and Warren will campaign together at an event in Cincinnati, in what could well be an audition for veep.

Many Democratic elites seem to be thrilled about the idea of a Clinton-Warren ticket. In April, the Huffington Post’s Ryan Grim quoted a "member of Clinton’s inner circle" saying, "Real folks are pushing Warren. I’m into it." Allies of Senate Democratic Leader Harry Reid have been very clear to the press that he thinks Warren would be the best choice.

But does this pairing make sense — for Clinton, for Warren, for progressives, and for the Democratic Party as a whole?

The answer to this question is complicated by the utter strangeness of the vice presidency. The office lacks practically any formal powers, which means that a vice president’s influence depends largely on the president’s whims. Consequently, there are good arguments that Warren can be more powerful if she's not vice president.

Some recent vice presidents — most famously Dick Cheney, but also Joe Biden — have had a great deal of influence, though. Plus, there’s the small matter that a twist of fate could make whomever gets the job the most powerful person in the world. And then there’s the fact that many presidential nominees seem to ignore all this in favor of choosing a running mate solely for short-term electoral reasons.

So, keeping this complex set of considerations in mind, here are the best arguments Democrats have been making for and against choosing Warren as Clinton’s No. 2.

The case for Vice President Warren

1) An important progressive voice would be on the ticket and in a Clinton White House: Symbolically and substantively, a Warren nomination would be a major acknowledgement of progressives’ importance in the modern Democratic Party. She'd be the most liberal vice presidential nominee in decades; her selection could help convince progressives that this Clinton administration won't pivot to the center and leave progressives behind. (After all, Warren would be around to give them hell for it if they do.)

Furthermore, Warren has already figured out how to exercise a surprising amount of influence even as a first-term senator — she’s managed to torpedo several high-profile Obama administration appointments. The vice presidential position would give her far more prominence and an even bigger media megaphone.

And depending on what President Clinton allowed her to do, Warren could have a great deal of influence on many crucial under-the-radar appointments and administrative matters like Dick Cheney once did. An unleashed Vice President Warren could champion progressive causes and combat corporate lobbyists and moneyed interests throughout the labyrinthine rulemaking process and federal government.

2) She’d unite Democrats, excite Sanders supporters, and turn out the left: With the Bernie Sanders campaign apparently winding down, the question of whether his supporters will rally around Clinton is on many Democrats’ minds. Most party elites currently assume that they will, since Sanders himself is highly likely to endorse her and since stopping Trump seems so important.

But much of Sanders’s support was drawn from voters who identified as independents — many of them feel disenchanted by a Democratic Party they view as calcified, corporate, and corrupt.

It’s possible that many of them could stay home unless the party makes a major effort to change its image — for instance, by choosing a populist anti–Wall Street crusader like Warren as Clinton's running mate. (A recent poll shows Warren is quite popular among Sanders voters who are currently saying they’ll refuse to support Clinton in the general election.)

More broadly, Warren could excite the Democratic base and galvanize turnout on the left — which could make a crucial difference in an increasingly polarized electorate where independent voters are less important.

3) She's an excellent attack dog who gets under Trump's skin: A traditional role of the vice presidential pick is that of the "attack dog" — someone who will aggressively go after the other party’s nominee while theoretically letting his or her own nominee remain at least somewhat above the fray.

And if Warren has proved one thing in the past few months, it’s that she’d be a fantastic attack dog against Donald Trump. On Twitter, she’s shown herself to be willing to provoke Trump with a slash-and-burn style. And in a speech earlier this month she tore Trump to shreds, calling him a "thin-skinned, racist bully."

Furthermore, Warren really seems to get in Trump’s head, and frequently provokes over-the-top reactions from him. A vice presidential nominee who could drive Trump up the wall and force him to wound himself in response would be great for the Clinton campaign.

Watch: Elizabeth Warren goes on attack against Donald Trump

4) She’d get tons of media attention: Relatedly, the Clinton campaign has reportedly been seriously concerned about whether its more traditional, reserved candidate could manage to get comparable coverage in a 24/7 Trump-driven media circus. But Warren is a charismatic personality who can command headlines, as we’ve recently seen — which could prove a potent antidote.

5) An all-woman ticket would make history: Sure, the reaction to Clinton's own historic nomination has been somewhat muted. But the idea of going from no women presidents or vice presidents ever to a Clinton-Warren ticket could capture the imagination and inspire women across the country — and make for a particularly stark contrast with Trump’s blatant sexism.

6) Warren’s populism could have crossover appeal: Donald Trump’s general election strategy is to portray "Crooked Hillary" as a corrupt tool of the establishment. But Warren has a sterling reputation for crusading against the influence of the wealthy and power. So her very selection as the VP nominee could seemingly debunk one of Trump’s most potentially damaging arguments against Clinton, and could help win independent voters who are disenchanted with both parties over to Clinton’s side.

The case against Vice President Warren

1) Warren could be marginalized as veep: There’s one major reason that Warren and her allies might not be too thrilled about the prospect of her becoming Clinton’s running mate — the long, sad history of vice presidents who become completely marginalized and utterly miserable once in office.

This lore dates back to the first vice president, John Adams, who called the job "the most insignificant office that ever the invention of man contrived." FDR’s first vice president, John Nance Garner, later said the job was "the worst thing that ever happened to me." Lyndon Johnson memorably said that "being vice president is like being a cut dog." There’s even an entire HBO comedy about an ignored and derided vice president.

As mentioned, this is because the vice president has hardly any formal powers. The past vice presidents who have been powerful have been so because of their influence on the president, or because the president has chosen to delegate power to them. It’s noteworthy that even Johnson, who is frequently described as having wizard-like political powers, couldn't make anything of the office.

Overall, whether Warren has influence in a Clinton administration will depend almost entirely on Hillary Clinton. And in taking the job, Warren would necessarily give up her role as a top outside critic who can push the White House in a more progressive direction from the Senate. It’s a risky move, to say the least.

2) Vice President Warren could be a huge headache for President Clinton: But picking Warren could also be risky for Clinton. Any president naturally wants a vice president who is a loyal team player, rather than someone who is constantly going against the administration and causing trouble.

But Warren is independent-minded and, even more importantly, has a big media following and popularity among progressives. If she disagrees with the president’s decisions or other administration activities — like an effort to appoint a big donor to a nuclear weapons advisory board despite his lack of any qualifications — she might well speak up, and could do Clinton’s presidency a great deal of damage.

3) She has little governing and foreign policy experience: Another question about Warren, of course, is whether she would in fact be ready to step in to the presidency if something should happen to Clinton.

After all, Warren has served in the Senate for less than four years and has never held any other elected office. And she seems uninterested in foreign policy, one of the most important responsibilities for a president. All this led former Pennsylvania Gov. Ed Rendell, a Democrat, to say in June that Warren is "not in any way, shape, or form ready to be commander-in-chief."

Of course, Barack Obama had no governing experience, with his main foreign policy credential being, as Clinton famously put it, "a speech he made in 2002." And Trump has even less, though he has run a large organization. Still, Clinton will have to decide for herself whether she thinks Warren is prepared enough for the office.

4) A "safe" pick might be better: The conventional wisdom is that the general election is Clinton's to lose. If that’s the case, then perhaps Clinton’s goal should be to nominate a "safe" pick, rather than Warren, who’s a riskier, outside-the-box choice.

Sure, Sen. Tim Kaine of Virginia, who's been name-dropped for months as a top Clinton VP option, might excite fewer people. But he has conventional credentials and executive experience, and he's from a swing state. He seems unlikely to win over many voters, but he seems unlikely to alienate them either, and perhaps that’s what Clinton will want.

5) An all-woman ticket could backfire electorally: Relatedly, a history-making all-woman ticket could excite voters and help Democrats. But to increase her lead on Trump, Clinton really needs to be doing a lot better with men, and Trump has been winning men by around 16 points.

Could the prospect of a ticket with two women lead to a backlash, with men breaking to Trump even more strongly? Considering how deeply rooted gender stereotypes are, it sure doesn’t seem impossible — and Clinton, who was very cautious of the challenges facing a woman candidate in 2008, may prove to be cautious about this too.

6) Warren's Senate seat could fall into Republican hands: The battle for control of the Senate is expected to be very closely fought this year. And should Warren resign, the Massachusetts governor who would appoint her replacement for the 160 days until a special election can be held is Charlie Baker — a Republican who’d likely appoint a Republican.

However, apparently Harry Reid has looked into this and found out there’s a loophole that could minimize this problem, as the Boston Globe’s Matt Viser reports. Warren can announce her intent to resign months in advance, so the 160-day clock toward the special election to replace her could start ticking while she still has the seat, meaning any Baker-appointed successor wouldn't be there long, if at all.

But to keep the seat, Democrats would of course still have to win that special election, which they famously failed to do in the Martha Coakley/Scott Brown race for this very seat in 2010.

7) She’s not a unity pick: Finally, there’s the flip side of the argument that Warren’s selection could energize progressives — it could also drive away moderates and, perhaps more significantly, rich people and business interests.

There’s an argument that Republicans’ nomination of the erratic, inflammatory Donald Trump gives Clinton an unusual opportunity to win over Republican constituencies, like wealthy donors and businesspeople, to her side, in some kind of mainstream unity coalition. (After all, the Clintons have a lot of experience raising money from rich people.)

Progressives might blanch at this, but it’s also possible that the bigger Clinton’s coalition and the broader her support, the more Democrats will be elected to Congress — and that that bigger majority will make it easier to get more liberal laws enacted. (This is the "campaign as a moderate, govern as a liberal" argument.)

Whether you buy this or not, it’s pretty indisputable that wealthy business elites loathe Warren — they see her as a far-left, anti-capitalist maniac. According to a recent piece by Politico's Ben White, major Democratic donors in finance are vowing to cut off contributions to the Clinton campaign if Warren is selected.

So while progressives hope that Warren's selection could clarify the choice between Trump as the candidate of big money and unite swing voters against him, it could also drive the 1 percent straight into Trump’s arms, help the billionaire greatly improve his dismal fundraising, and make for a closer race in the end. We don't yet know.

How Clinton’s nomination could improve politics