The two American political parties usually select their candidates through open primaries, where ordinary voters not just party members, get to vote. Recently their has been experiments with primaries in Australia. The Labor Party in Kilsyth, Victoria and the Nationals in Tamworth NSW.
I'm open minded n the subject. I can see considerable advantages, more democratic, likely to get a wide range of nominees and a candidate that the electorate will like. However I have concerns over cost and that the opposing party could shaft you by sending its supporters to vote for the worst candidate.
Having said that I will be watching developments with interest and would like to see all parties doing experiments with primaries.