Interesting framing, speaking of liberals convincing moderates, rather than vice versa:

«So, even though the Republican Party has become thoroughly right-wing, Republicans still have a baked-in edge. Conservatives outnumber liberals in the electorate — and always have — so a left-wing coalition needs to win over a bunch of moderates in order to get to 50% plus one.»

https://www.theargumentmag.com/p/why-centrists-cant-win-the-democratic