Nondictatorship

Nondictatorship is a property that a social choice function or voting system can possess. A social choice function takes individual preferences over a set of alternatives and produces a single collective choice. A dictatorship is a specific type of social choice function where one individual's preferences always determine the collective outcome, regardless of the preferences of all other individuals.

A nondictatorial social choice function is one where no single individual is a dictator. In other words, for any given outcome, there is at least one other individual whose preferences, if they were to change, could potentially lead to a different collective choice. This concept is fundamental in social choice theory and is closely related to Arrow's Impossibility Theorem, which states that no voting system can satisfy a certain set of desirable criteria (including nondictatorship) when there are three or more options.

The property of nondictatorship is considered desirable because it implies a degree of fairness and responsiveness to the preferences of multiple individuals within the group. A dictatorial system, by contrast, is inherently unfair as it completely disregards the opinions of everyone except the dictator. Therefore, in the design and analysis of democratic processes and collective decision-making mechanisms, nondictatorship is a key criterion for evaluating their legitimacy and fairness. Many fair voting methods aim to avoid dictatorial outcomes, though achieving this while also satisfying other desirable properties can be challenging.