We investigate how the choice of decision makers can be varied under the presence of risk and uncertainty. Our analysis is based on the approach we have previously applied to individual decision makers, which we now generalize to the case of decision makers that are members of a society. The approach employs the mathematical techniques that are common in quantum theory, justifying our naming as Quantum Decision Theory. However, we do not assume that decision makers are quantum objects. The techniques of quantum theory are needed only for defining the prospect probabilities taking into account such hidden variables as behavioral biases and other subconscious feelings. The approach describes an agent's choice as a probabilistic event occurring with a probability that is the sum of a utility factor and of an attraction factor. The attraction factor embodies subjective and unconscious dimensions in the mind of the decision maker. We show that the typical aggregate amplitude of the attraction factor is $1/4$, and it can be either positive or negative depending on the relative attraction of the competing choices. The most efficient way of varying the decision makers choice is realized by influencing the attraction factor. This can be done in two ways. One method is to arrange in a special manner the payoff weights, which induces the required changes of the values of attraction factors. We show that a slight variation of the payoff weights can invert the sign of the attraction factors and reverse the decision preferences, even when the prospect utilities remain unchanged. The second method of influencing the decision makers choice is by providing information to decision makers. The methods of influencing decision making are illustrated by several experiments, whose outcomes are compared quantitatively with the predictions of our approach.
