We in the United States are deep in the middle of a major national election, and over half of the world’s population also have elections in 2024. This is why Carry the Two is going to focus on the intersection of mathematics and democracy for our new season. In this, the third episode of our mathematics and democracy season, we speak to Andrea Mock, Gunnar Carlsson, Samin Aref, and Zachary Neal. We dig into what mathematics has to say about the stability of political coalitions, how mediators can make coalitions more stable, the ways in which Democrats and Republicans can be clustered together in the House of Representatives based on their votes, and the hidden third coalition of really successful legislators in the House that co-sponsorship data can illuminate.   Find our transcript here: Google Doc or .txt file Curious to learn more? Check out these additional links: Political structures and the topology of simplicial complexes  Andrea Mock & Ismar Volić Gunnar Carlsson The topology of politics: voting connectivity in the US House of Representatives Pek Yee Lum, Alan Lehmann, Gurjeet Singh, Tigran Ishkhanov, Gunnar Carlsson, & Mikael Vejdemo-Johansson Samin Aref Zachary Neal Identifying hidden coalitions in the US House of Representatives by optimally partitioning signed networks based on generalized balance Samin Aref & Zachary Neal Follow more of IMSI’s work: www.IMSI.institute, (twitter) @IMSI_institute, (mastodon) https://sciencemastodon.com/@IMSI, (instagram) IMSI.institute Music by Blue Dot Sessions The Institute for Mathematical and Statistical Innovation (IMSI) is funded by NSF grant DMS-1929348