The geometry of voting power: Weighted voting and hyper-ellipsoids

The geometry of voting power: Weighted voting and hyper-ellipsoids

In cases where legislators represent districts that vary in population , the design of fair legislative voting rules requires an understanding of how the number of votes cast by a legislator is related to a measure of her influence over collective decisions. We provide three new characterizations of weighted voting, each based on the intuition that winning coalitions should be close to one anot...

Voting Power in Weighted Voting Games: A Lobbying Approach by

We report experiments on the following lobbying game. Two lobbyists have identical budgets and simultaneously distribute them across voters in a legislature. Each voter votes for the lobbyist who pays them most and the lobbyist who receives most votes wins a prize. Taking the share of the budget distributed to a voter as a measure of the voter‟s voting power we investigate how voting power vari...

Computing voting power in easy weighted voting games

Weighted voting games are ubiquitous mathematical models which are used in economics, political science, neuroscience, threshold logic, reliability theory and distributed systems. They model situations where agents with variable voting weight vote in favour of or against a decision. A coalition of agents is winning if and only if the sum of weights of the coalition exceeds or equals a specified...

Mathematics of Voting – Weighted Voting Systems

Geometry, Voting, and Paradoxes

What could be easier than “voting?” After all, to vote we just count how many people favor each candidate. What can go wrong with something so elementary as this? Actually, a lot. As mathematicians and others have shown over the last two centuries, once there are at least three candidates—not an atypical situation—the winner need not be whom the voters really want. Such bad outcomes may occur n...