Arbitrary here means that the rule wasn’t decided rationally. The government must typically establish a “rational basis” for any rule that they want to impose on people.

It is commonly understood that being indoors with a lot of people increases the risk of transmitting a virus between those people. The risk is understood to go up when more people are present, but it is also higher when the building is smaller than when it is larger.

Thus, a rational basis for the maximum occupancy of a building during a pandemic would be based on the number of people per square foot. A rule such as “1 person per 100 square feet” treats both large and small groups fairly, as well as treating large and small buildings fairly.

When we look at specific rules that were actually in place during the pandemic, we often find that there was no such rational basis. The rules were instead arbitrary. In NYC, churches were limited to a flat 10 people in the building at any one time, regardless of the size of the church building. This limits a large church more than a small one, and thus the rule is arbitrary. It would have been no more arbitrary if they had rolled dice to pick the number.

Similarly, the same rule in NYC did not apply to big–box hardware stores. A Home Depot could have hundreds of people in it all the time! No matter how important hardware stores are, this is an arbitrary distinction. There is no rational basis under which the virus is dangerous to a group of 11 people who are in a church, but not to a group of 11 people who are in a Home Depot. The relative importance of churches and Home Depots is not important. What is important is that the difference in how the rule applied to them was arbitrary.