A committee is using a ranked-preference voting system to decide on a new project. Initially, the choice is between Project A and Project B. The vote is held, and the collective preference is for Project A over Project B. Later, a new option, Project C, is introduced for consideration. A second vote is conducted with all three options, and the new collective preference ranks Project B over Project A. Which principle of an ideal voting system has been violated in this scenario?

Evaluating the Implications of Voting Theory

Arrow's Impossibility Theorem states that no ranked-voting system can simultaneously satisfy a set of specific fairness criteria. Match each criterion below with its correct description.

An economist is studying the local market for wheat. They find hundreds of independent farms selling wheat to numerous buyers. The wheat from one farm is indistinguishable from the wheat from any other farm. Prices are publicly quoted and change based on overall supply and demand, with no single farm able to set its own price. However, the economist discovers that a new government program provides exclusive, non-public reports on future weather patterns to a small, select group of the largest farms. How does this new information asymmetry affect the market's alignment with the ideal conditions described in economic theory?

The Park Location Paradox

A political reform group is designing a new ranked-preference voting system for their city council elections. Their stated goal is to create a system that is perfectly fair and always translates the individual preferences of voters into a clear, consistent group decision. According to the fundamental conclusions of social choice theory, what is the most likely outcome of their endeavor?

An individual's indifference curve, which illustrates their trade-offs between consumption today and consumption in the future, has a slope of -1.05 at their current consumption level. Based on this information, what is this individual's discount rate (ρ)?

A society discovers its current ranked-voting system sometimes fails to produce a transitive group preference (e.g., A is preferred to B, B is preferred to C, but C is preferred to A). According to the fundamental principles of social choice theory, this is a correctable design flaw, and a different ranked-voting system can be implemented that guarantees both rational group outcomes and adherence to all standard fairness conditions.

Identifying a Flaw in a Voting System

The Elder's Edict Voting System