https://en.wikipedia.org/wiki/2016_United_States_presidential_election_recounts
Now that you bring that up? Those 3 recounts proceeded due to the Green Party insisting they take place. Hillary and the Democrats had initially turned them down and conceded, but agreed to support the Green's recount campaign to ensure it was fair. The recounts in the end produced no change. Other plaintiffs in Florida tried to ask for a recount there, but they were turned away.
None of the recounts were conducted by private companies.
Trump, however, went on to say all three recounts were a scam to fill the Green Party's pockets, and then later went on to claim fraud (still in 2016) occurred in California, New Jersey and Virginia. This foreshadowed his behavior in 2020, showing that he has been talking about a fraudulent election literally from day one.
All of those recounts were over and done with before the certification ever took place.
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https://en.wikipedia.org/wiki/Attempts_to_overturn_the_2020_United_States_presidential_election
https://en.wikipedia.org/wiki/Post-election_lawsuits_related_to_the_2020_United_States_presidential_election
Compare that to 2020, where there's a recount happing still to this day, over 6 months after Biden has been certified, and Trump is still claiming he won.
63 lawsuits have been filed so far for several states, most of these have been dropped, ruled against or dismissed by the courts. Trump ordered his administration to not cooperate with the transition to Biden's presidency.
Before the attack on the 6th, other protest occurred in other states, such as Dec 7 2020 in Michigan, where ""Stop the Steal" protestors gathered outside the private home of Michigan's Secretary of State Jocelyn Benson" and Dec 12, 2020, where protestors in Washington, D.C left 9 people injured.
During all of this, officials in contested states were receiving death threats from Trump supporters, while prominent Republicans said nothing about these threats.
There's so, so much more to this mess, but I'm not typing all that down.
Like I said: there is no comparing what happened in 2016 to 2020. In fact, if you want to compare, you get a difference so drastically different that it makes the Democrat's worst moments in 2016 look like saintly restraint.