House Speaker Nancy Pelosi on Tuesday announced a formal impeachment inquiry against President Trump. Though a contingent of congressional Democrats have long pushed for impeachment proceedings on a variety of bases, it was allegations that Trump coerced the president of Ukraine into investigating the Biden family which finally overcame Pelosi's longstanding resistance to the idea. Now that the process is underway, there are four ways it can go.

1. There's an inquiry but no impeachment.

This is the bare minimum scenario following Pelosi's announcement. The investigation will proceed, but it may not produce enough evidence to warrant drawing up and/or voting on articles of impeachment.

Impeachment proper is a sort of indictment; it is analogous, in ordinary legal matters, to being charged with a crime, not to being convicted. The House of Representatives has "the sole power of impeachment," per the Constitution, which means the House acts like a grand jury deciding whether to indict. Regular grand juries are notoriously easy to convince to bring an indictment, and historically presidential impeachment inquiries (there have only been three, against Presidents Andrew Johnson, Richard Nixon, and Bill Clinton) have resulted in affirmative impeachment votes. Johnson and Clinton were impeached, and Nixon almost certainly would have been had he not preemptively resigned.

Could Trump run for re-election? In this scenario, absolutely. In fact, as my colleague Matthew Walther has argued, an impeachment inquiry which does not successfully run Trump out of politics once and for all may be a strategic boon to his 2020 campaign. If a Democratic House majority can't be persuaded to impeach, Trump will endlessly tout the inquiry as proof positive of "PRESIDENTIAL HARASSMENT."

2. The House impeaches, then Trump resigns.

Our second option is a variant of the Nixon play: With an impeachment vote pending or accomplished (in Nixon's case, articles were approved in committee but not yet the full House), Trump could resign. As it would allow him to endlessly deny wrongdoing and claim political persecution until the day he dies, this option may be appealing to the president.

Could Trump run for re-election? Legally yes, but it would be extremely odd, and it is difficult to imagine Republican leadership — let alone a President (and presumptive GOP nominee) Mike Pence being too happy about the idea. It seems doubtful that the Republican Party would accept a newly resigned president as their 2020 ticket, and it seems equally doubtful that Trump would attempt to run without GOP support. But then, five years ago, I would have deemed wildly implausible about half of what occupies our daily news cycle, so what do I know?

3. Trump is impeached, tried, and acquitted.

In this scenario Trump would follow in the footsteps of Johnson and Clinton, successfully impeached by the House but acquitted in his trial by the Senate. Conviction in the Senate requires a two-thirds majority, which will be a high hurdle while the president's own party continues to control the upper chamber. That said, the Senate unanimously voted Tuesday to have the whistleblower complaint pertaining to Trump's dealings with Ukraine released to congressional intelligence committees, so maybe conviction over this Ukraine business is less of a long shot than it seems at first glance.

Could Trump run for re-election? Again yes, and again it could work to boost his campaign insofar as he can spin the story into his "witch hunt" narrative. However, that tactic could prove difficult to execute if, unlike in the first scenario, the House inquiry turns up evidence enough to convince independent and swing voters of Trump's corruption.

4. Trump is convicted.

The fourth and final possibility is that the president will be impeached in the House and convicted in the Senate, and that for whatever reason — delusion? False hope? Sheer enjoyment of the fight? — he will refuse to resign through the whole process. If that happens, Trump would be removed from office and Vice President Pence would succeed him.

Could Trump run for re-election? Depending on the exact vote(s) taken in the Senate, he could at least try. The Constitution discusses impeachment in several clauses. The best-known portion is in Article II, Section 4, which approaches the subject from the executive side, noting that the president "shall be removed from office on impeachment for, and conviction of, treason, bribery, or other high crimes and misdemeanors." But impeachment is addressed at greater length in multiple sections of Article I, which details congressional roles and responsibilities. "Judgment in cases of impeachment shall not extend further than to removal from office, and disqualification to hold and enjoy any office of honor, trust or profit under the United States," it says, "but the party convicted shall nevertheless be liable and subject to indictment, trial, judgment and punishment, according to law."

Whether removal from office and disqualification from holding office again must be the subject of separate votes is a matter of some controversy. In two cases, the Senate has held separate votes of removal and disqualification while impeaching judges, which suggests it is possible Trump could be convicted and removed without being separately disqualified from running for re-election. However, even more than with our second option, it is difficult to imagine the Republican Party running a nominee in such circumstances — which in this case would include conviction by the GOP's own Senate majority. So even if re-election were legally feasible, it would approach absolute political impossibility.

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