How undemocratic decision-making exists within a democratic world
Arrow’s Theorem Proves No Voting System is Perfect
One of the central issues in the theory of voting is described by Arrow’s Impossibility Theorem, which states roughly that no reasonably consistent and fair voting system can result in sensible results.
Named after Nobel Prize-winning economist Kenneth Arrow, the theorem starts by establishing a set of reasonable conditions on voting -- that is, on the method of aggregating individuals’ preferences into group preferences.
These conditions can lead to nonsensical group decisions, or manifestly undemocratic decision-making. As political scientists Ken Shepsle and Mark Bonchek put it in their book, Analyzing Politics, “The group is either dominated by a single distinguished member or has intransitive preferences.” For this reason, the theorem is sometimes known as the “dictator theorem.”
Understanding Arrow’s Theorem starts with understanding what economists and political scientists mean by “intransitive preferences.”
Preferences are known as “transitive” if they can be put in a sensible order. For instance, if you like apples best, then oranges, then bananas least, that means you prefer apples to oranges and to bananas, and oranges to bananas. If instead your fruit preferences cannot be put in best-to-least order -- you prefer apples to oranges and oranges to bananas, but prefer bananas to apples -- your preferences are known as “cyclic” or “intransitive.”
Arrow was trying to create a voting system that was consistent, fair, and would lead to transitive group preferences over more than two options. But in trying to create such a voting system, he proved that this was impossible ...(continued)