Funtowicz and Ravetz say that science becomes post-normal when it examines serious risks in a context of high scientific uncertainty and in a situation where the public opinion is divided ("stakes are high, facts uncertain, values in dispute"). Usually this is a risk analysis commissioned by policy makers to determine policy measures.
Therefore post-normal science exists in the gray area between science and politics. Sometimes there is a political pressure to underestimate the risk, when the politician does not want to take responsibility.
For example in Chernobyl. And sometimes there is a political pressure to exaggerate the risk, so they could be blamed on political opponents.
For example Club of Rome. Public opinion is mostly defined by the political attitude to the proposed measures - some people welcome regulations and high taxes, some don't.