The ability to set the voting agenda can often be a powerful...

The ability to set the voting agenda can often be a powerful asset. Assuming that social preferences are decided by pair-wise majority voting and that the preferences given in Table 30.1 hold, demonstrate this fact by producing a voting agenda that results in allocation $y$ winning. Find an agenda that has z as the winner. What property of the social preferences is responsible for this agenda-setting power?

Key Concepts

Condorcet Cycle (Non-transitive Social Preferences)

Condorcet cycles occur when collective preferences are cyclic, meaning that no alternative is universally preferred over all others in pairwise comparisons. This non-transitivity, often illustrated by the Condorcet paradox, enables an agenda setter to exploit the sequential nature of the voting process. Because of these cycles, the final outcome can be manipulated simply by changing the order of the votes.

Sequential Pairwise Voting

This voting system pits alternatives against each other one by one, where the winner of each round goes on to face the next alternative. The sequence of pairwise comparisons is crucial, as the final outcome greatly depends on the order in which alternatives are compared, leaving room for strategic manipulation by an agenda setter.

Agenda Setting Power

Agenda setting power refers to the ability of a decision maker to determine the order in which alternatives are voted upon. By carefully designing the sequence of pairwise votes, an agenda setter can ensure that an otherwise less-preferred alternative ultimately wins. This influence arises from the structure of sequential voting processes, where the path to victory can be engineered.

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