Weighted voting is built around the idea that voters have differing amounts of influence in elections, with familiar examples ranging from company shareholder meetings to the United States Electoral College. We examine the idea that each voter has a uniquely determined weight, paying particular attention to how voters leverage this weight to get their way on a specific yes/no motion (for example, by forming coalitions). After some more background on weighted voting, we describe a natural partial order relation between these coalitions of voters. This ordering can be modeled by a partially ordered set (poset), which we call a coalitions poset. Using this poset, we derive another important poset via a natural ordering on collections of coalitions. Our results begin by detailing a method for counting the number of maximal chains in the derived poset. After employing this method to find the number of maximal chains in the derived poset with 5 voters, we extend our method for use in the coalitions poset. Finally, we conjecture a formula for the number of maximal chains in the coalitions poset with n voters.
Prof. Jason Parsley, Associate Professor of Mathematics, Wake Forest University
"Counting Maximal Chains in Weighted Voting Posets,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 14
, Article 12.
Available at: https://scholar.rose-hulman.edu/rhumj/vol14/iss1/12