How are sector capacity constraints set in the current US ATC system?
I think January 25th, 2017 is close enough.
For Eurocontrol—

To evaluate sector capacities, the Network Manager uses the Air Traffic Control (ATC) Sector Capacity Analyser (CAPAN) methodology – using a fast-time computer simulation model that calculates the capacity of an ATC sector based on the controllers' workload. CAPAN is used with the Reorganised ATC Mathematical (Model) Simulator (RAMS) simulation engine.

Above quotation answers the question in a general form. The workings of CAPAN are laid out in this PDF, titled Capacity assessment and planning guidance document.

The FAA (US) isn't much different—

... the US and Europe use a comparable methodology to balance demand and capacity.

More on that here (PDF), titled 2015 Comparison of Air Traffic Management-Related Operational Performance: U.S./Europe.