Two New Measurements of Voting Power

The analysis of voting power in elections has been playing an important role in many traditional social choice problems, where the voting power of an agent is measured by whether the agent is pivotal. In this paper, we introduce two new extensions of such pivotality to measure agents’ voting power in a given profile. The first extension, called hierarchical pivotal sets, captures the voting power for an agent to make other agents pivotal. The second extension, called coalitional pivotal sets, captures the voting power for a group of agents to change the winner by voting differently in collabo-