We define populism as a platform proposing a policy based on a misspecified model of the world, a simple alternative worldview. Voters’ trust in the traditional/mainstream political class evolves over time and depends on traditional politicians’ performance once in office. Crucially, political distrust behaviourally increases how gullible voters are to the simple alternative worldviews proposed by populists. Traditional politicians are aware of the populist threat and try to prevent it. In this novel framework we study when voters elect populist politicians, how populist and their alternative worldviews survive/recur and their long-run effect on several measures of voter’s welfare. We show that the link between distrust and alt-truth gives rise to a low-trust trap, where trust in the political class never recovers, leading to populists recurring in power. This trap/cycles need not always be detrimental to voters, as the increased pervasiveness of alt-worldviews also has a disciplining effect on traditional politicians.