The first profile is Ayn Rand. I dont think that she would have thrown the switch base off her theory about the virtue of selfishness. Her theory promotes the philosophy of Individualism. Individualism states the moral stance, political philosophy, ideology, or social outlook that emphasizes the moral worth of the individual. Individualists promote the exercise of ones goals and desires and so value independence and self-reliance and advocate that interests of the individual should achieve precedence over the state or a social group.
The Second profile is Jeremy Bentham. He would have thrown the switch based of a principle of Utilitarianism. Utilitarianism is a theory in normative ethics holding that the proper course of action is the one that maximizes utility, usually defined as maximizing happiness and reducing suffering. In this case the trolley would have killed the one person instead of the group of people.
The Third profile Immanuel Kant, believed in a transcendental idealism. To be honest this is a very complex topic to define. Mr. Kant believed that ideas, the raw matter of knowledge, must somehow be due to realities existing independently of human minds, but he held that such things in themselves must remain forever unknown. Human knowledge cannot reach to them because knowledge can only arise in the course of synthesizing the ideas of sense. To put it shortly I would say yes he most likely would have thrown the switch just on mere principle of doing what he thought is the correct action.
Yes I would have thrown the switch because I tend to side with the utilitarian approach to this problem. Reason is because I can save multiple lives by sacrificing one for the good of all. What would bother me most about the trolley car wrecks would have been the fact that it was my decision. I was put in this position to make a split decision and no matter the outcome someone is going to be the loser.