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(CNN) —  

On Thursday morning the House approved – on a largely party-line vote – a set of formalized rules to govern their ongoing impeachment inquiry into President Donald Trump’s pressure campaign against Ukraine to force an investigation into Joe Biden.

The vote wasn’t terribly surprising – Democrats have a considerable majority in the House – but that the party leadership decided to hold it at all was. After all, House leaders had resisted holding a floor vote to formalize the impeachment inquiry for weeks.

So, what changed their mind? Simple: Public opinion.

Remember that, at its root, impeachment is a political, not a legal process. And that past attempts to impeach presidents – most notably Bill Clinton – have had disastrous political consequences due to the majority party not paying enough attention to public sentiment.

That reality is why House Speaker Nancy Pelosi (California) was long reluctant to trigger any sort of impeachment inquiry, for fear that the public’s lack of support for the impeachment and removal of Trump might boomerang back on her party with the 2020 election approaching.

But the continued revelations about Trump’s July 25 phone call with Ukrainian president Volodymyr Zelensky forced Pelosi’s hand. And changed – at least temporarily – how people thought about impeachment. A recent CNN poll showed 50% said Trump should be impeached and removed from office while 43% said he should not.

What’s become clear over the past 10 days or so, however, is that the current closed-door approach to the investigation could jeopardize the rising public support for impeachment. While House Republicans’ storming of the hearing room last week was a pointless symbolic act, it’s clear that the attacks from Trump and his GOP allies in Congress that all of this investigating was happening out of public sight was a sore spot for Democrats.

While Democrats might not have been feeling the pinch just yet from these “they’re hiding behind closed doors!” attacks, they were clearly fearful that they could lose public backing for the proceedings over just such an attack. After all, there is only so much power in leaked opening statements and snippets of what this official or that official said behind closed doors. And that setting allows for several versions of the “truth” to be spun – a Democratic take and a Republican one.

Voting to formalize a set of rules that, most importantly, makes it very likely that we will hear publicly from the likes of Bill Taylor, the US’s top diplomat in Ukraine, and National Security Council official Alexander Vindman, among others, is also a clear bluff-calling by Democrats. Based on what they’ve heard in private, Democrats believe that the airing of testimony from Taylor and Vindman will put Republicans in a very tough place. Denying these witnesses said what they said behind closed doors will not be a viable option.

And so, Thursday’s vote serves as a recognition of the political realities – and stakes – at play in the impeachment investigation. Democrats are placing a big bet that making these hearings public will box Republicans in and, in so doing, keep the public on their side when it comes to the correctness of the course they have chosen to follow.

Like all big bets – I see you Mattress Mack! – there’s a huge downside if they’re wrong. But the second Pelosi allowed an impeachment inquiry to begin, the gamble was made. This is just a doubling down on that original wager.