The Biden administration has not released any specific invitation criteria, as such, but it has provided some guidelines that were apparently followed when considering invitees. There was, as far as I can tell, no explicit working definition of democracy used in the selection process.
The Congressional Research Service report IN11817 The U.S. Summit for Democracy notes:
The Administration invited a total of 111 governments, but has not
publicly articulated the criteria that guided invitation decisions
beyond a stated desire to be "as inclusive as possible" and ensure
participation among "a regionally diverse set of well-established and
younger democracies whose progress and commitments will advance a more
just and peaceful world."
These quotes have been drawn from the response to the question "Why were some countries invited while other countries were not invited?" on the State Department's website:
- The United States reached out to a regionally diverse set of well-established and younger democracies whose progress and
commitments will advance a more just and peaceful world.
- Our goal is to be as inclusive as possible. We are working to ensure that all relevant voices and viewpoints feed into the Summit process.
- We will continue engaging with Summit participants and other governments around the world to counter democratic backsliding,
promote respect for human rights, and fight corruption both at home
and abroad – whether that work occurs within or outside of the Summit
- We seek to engage any and all countries that show a genuine willingness in making commitments that support the Summit’s goals.
Furthermore, in a background press call on the 7th of Decemeber, administration officials made the point that democracy at all levels of government and society were taken into account - they give the examples of parliamentarians and municipal-level leaders.
... with respect to both governments that are invited to the summit — and
some that aren’t — we are very conscious that democracy is about more
than just a single leader or a single party or a single moment in
time. It’s a process that involves many actors inside and outside of
government at national and subnational and local levels.
that’s why, as my colleague mentioned, part of the full agenda of the
summit brings in not just national leaders, but also parliamentarians
and municipal-level leaders.
We really want the summit to be about entire societies. And so, we made our invitation decisions with all of those factors in mind.
And one of our objectives is to highlight the great work that’s being
led in some countries, as I mentioned, by local leaders, while urging
positive democratic reform at the national level.