How can many people (who may disagree) come together to answer a question or make a decision? "Collective response systems" are a type of generative collective intelligence (CI) facilitation process meant to address this challenge. They enable a form of "generative voting", where both the votes, and the choices of what to vote on, are provided by the group. Such systems overcome the traditional limitations of polling, town halls, standard voting, referendums, etc. The generative CI outputs of collective response systems can also be chained together into iterative "collective dialogues", analogously to some kinds of generative AI. Technical advances across domains including recommender systems, language models, and human-computer interaction have led to the development of innovative and scalable collective response systems. For example, Polis has been used around the world to support policy-making at different levels of government, and Remesh has been used by the UN to understand the challenges and needs of ordinary people across war-torn countries. This paper aims to develop a shared language by defining the structure, processes, properties, and principles of such systems. Collective response systems allow non-confrontational exploration of divisive issues, help identify common ground, and elicit insights from those closest to the issues. As a result, they can help overcome gridlock around conflict and governance challenges, increase trust, and develop mandates. Continued progress toward their development and adoption could help revitalize democracies, reimagine corporate governance, transform conflict, and govern powerful AI systems -- both as a complement to deeper deliberative democratic processes and as an option where deeper processes are not applicable or possible.