Many of the companies with the largest number of employees say they’ll do almost anything to encourage their employees to get vaccinated. But a survey of some of them found that none would be inclined to mandate shots as a condition for holding a job. Almost all 15 companies surveyed — among the largest and most influential Fortune 500 companies — have strong pro-vaccine messages from their corporate leadership, emphasizing that the shots can both help protect individuals and bring the pandemic to a close.