 In many situations, a voter can cast multiple votes on the same measure. For example, in publicly-held companies, every share owned by a shareholder entitles them to one vote. In a faculty senate, a faculty member might have one vote for each position they hold in the college. Now, remember for this analysis we're assuming there are only two alternatives, yes and no. And in principle, a voter could cast simultaneous, yes and no votes. But only a mathematician would consider this a possibility, and so it's convenient to treat all votes a person can cast as a single weighted vote. We can describe a weighted voting system by identifying the quota, q, the number of votes necessary to pass a measure, and the weights, w1, w2, and so on, the weight of each voter. And we'll use the notation. So let's interpret the weighted voting system 10, 8, 7, 3, 1. So remember the first number gives us the quota, the total number of votes required to pass a measure, and so 10 total votes are needed to pass a measure, since there are four weights, there are four voters. We could call them voter 1, voter 2, voter 3, and voter 4, but we'll be creative and call them, in order, a, b, c, and d, okay maybe that's not that creative. But since the weights are 8, 7, 3, and 1, these are the number of votes cast by each of the four voters. And so the four voters, a, b, c, and d, will cast the following numbers of votes, a will cast 8, b cast 7, c cast 3, and d cast 1. For example, suppose that at a certain university there are five professors, Xavier, Moriarty, Octavius, Challenger, and Stein. Xavier is also the university president and a department chair, Moriarty is department chair. Approval requires a majority of the votes cast, and if each professor is entitled to one vote plus one more vote for each position they hold, describe the system. So Professor Xavier has one vote for being a faculty member, one vote for being a university president, and one vote for being department chair for a total of three votes, and so he has a weight of three. Professor Moriarty has one vote for being a faculty member, and one vote for being a department chair for a total of two votes, and so Professor Moriarty has a weight of two. And Professor Octavius, Challenger, and Stein don't have any additional positions, so they each have one vote. All together the faculty cast a total of eight votes, since approval requires a majority, and a majority is any amount more than 50%, half of these would be four, and so a majority would be more than four votes, so quota is five votes. And so we describe the system as, where the faculty are in the order Xavier, Moriarty, Octavius, Challenger, and Stein. In a weighted voting system some voters cast more votes than others. So common sense tells us the more votes someone cast, the more power they have. But mathematicians don't use common sense, we use math. And in fact the Banzai Findex was created to analyze power in weighted voting systems. So let's see how important the number of votes that you cast actually is. We'll take a look at that next.