For governments to implement effective adaptation and mitigation policies, they typically require a public mandate, often expressed through voting support. Building on this, we examine how personal experiences with natural hazards translate into voting intentions for politicians who advocate such policies, highlighting the critical interplay between citizen psychology and the political system. First, a 13-week longitudinal study of nearly 2,000 Americans tested whether weekly fluctuations in heatwave experiences drove changes in policy voting intentions. It revealed that while experiences were related to increased climate concern, voting support for both adaptation and mitigation policies remained stable, with support being more strongly related to climate change concern, pre-existing beliefs, and political affiliation. A second cross-sectional study across four countries (N=1,295) and multiple hazards (e.g., floods, storms, droughts) revealed that the relationship between experience and voting intentions was not direct, but mediated by expectations of future severe weather and climate change concern. Together, these findings challenge assumptions that direct experience automatically fuels political demand. Instead, they show that policy support is a function of complex socio-psychological processes, where personal experience is filtered through future expectations, pre-existing concerns, and beliefs. For risk governance, this underscores that simply communicating past events is insufficient. To build the public mandate necessary for societal-level responses, communication must engage with the public's shared vision of the future while taking into account pre-existing beliefs.