The American Medical Association's Code of Ethics states that while an individual’s opinion on capital punishment is a personal moral decision, physicians should not assist in executions no matter what their personal opinions on the death penalty may be, since the duty of physicians is to save lives whenever possible. Suppose that you were an anesthesiologist and were contacted by a state that wanted your assistance in formulating an effective drug cocktail for executions. Would a virtue theorist say that you should help them in doing so? Why or why not?

Virtue theorists, who follow the field of virtue ethics, emphasize the importance of character over the importance of performing one's duty and over the importance of carrying out actions that have good results. There are three branches of virtue ethics--eudaimonism (which emphasizes the importance of human flourishing), agent-based theories (which emphasize that virtue arises from observing virtue in others), and ethics of care (which emphasizes ethics not just based on fairness but also on caring for others).
Using any of these three branches of virtue theory would likely result in the decision that the anesthesiologist should not work with the state to formulate a drug cocktail for executions. You can use the basic ideas of the three branches of virtue theory to reason why. For example, eudaimonism emphasizes the importance of performing one's function well in society. A doctor who formulates a drug cocktail would not be carrying out his or her function. Agent-based theorists would likely want the anesthesiologist to model his or her behavior on other doctors who would not carry out this type of work (though the problem with this branch of virtue theory is that it does not specify what virtuous behavior actually is or how to model our behavior on others who act virtuously). Using the idea of the ethics of care, which states ethics involve caring, you can reason whether the doctor should help formulate a drug cocktail or not.