Evaluation of the U.S. governors' decision when to issue stay-at-home orders

In the United States, the reluctance of the federal government to impose a national stay-at-home policy in wake of COVID-19 pandemic has left the decision of how to achieve social distancing to individual state governors. We hypothesized that in the absence of formal guidelines, the decision to close a state reflects the classic Weber-Fechner law of psychophysics - the amount by which a stimulus (such as number of cases or deaths) must increase in order to be noticed as a fraction of the intensity of that stimulus.

On 12 April 2020, we downloaded data from the New York Times database from all 50 states and the District of Columbia; by that time all but 7 states had issued the stay-at-home orders. We fitted the Weber-Fechner logarithmic function by regressing the log₂ of cases and deaths, respectively, against the daily counts. We also conducted Cox regression analysis to determine if the probability of issuing the stay-at-home order increases proportionally as the number of cases or deaths increases.

We found that the decision to issue the state-at-home order reflects the Weber-Fechner law. Both the number of infections (P = <.0001; R² = .79) and deaths (P < .0001; R² = .63) were significantly associated with the decision to issue the stay-at-home orders. The results indicate that for each doubling of infections or deaths, an additional four to six states will issue stay-at-home orders. Cox regression showed that when the number of deaths reached 256 and the number of infected people were over 16 000 the probability of issuing "stay-at-home" order was close to 100%. We found no difference in decision-making according to the political affiliation; the results remain unchanged on 16 July 2 020.

when there are not clearly articulated rules to follow, decision-makers resort to simple heuristics, in this case one consistent with the Weber-Fechner law.