In Australia or the UK, you can run without being a billionaire, and legislators who aren't members of major parties still have influence (sometimes disproportionate) on who is chosen as head of state.
It sure helps though, for example Clive Palmer in Aus in 2013.
> legislators who aren't members of major parties still have influence (sometimes disproportionate) on who is chosen as head of state.
Australia and the UK still have the same monarch, so the head of state is not chosen by anyone in either country - but if you mean the Prime Minister, then you are correct.
