While the Internet has revolutionized many aspects of our lives, there are still no online alternatives for making democratic decisions at large scale as a society. In this talk, we will describe algorithmic and market-inspired approaches towards large scale decision making that our research group is exploring. We will start with a model of opinion dynamics that can potentially lead to polarization, and relate that to commonly used recommendation algorithms. We will then describe the algorithms behind Stanford's participatory budgeting platform, and the lessons that we learnt from deploying this platform in over 70 civic elections. We will use this to motivate the need for a modern theory of social choice that goes beyond voting on candidates. We will then describe ongoing practical work on an automated moderator bot for civic deliberation (in collaboration with Jim Fishkin's group), and ongoing theoretical work on deliberative approaches to decision making. We will conclude with a summary of open directions, focusing in particular on fair advertising.