"Top 2 primary systems definitely have weaknesses, as Benjamin noted, but the issues you're describing are not voter suppression. If that '20% of the electorate' isn't able to get a candidate on the ballot in the primary, it's more likely that it's just due to inferior numbers (e.g. the following vote split: D1 - 50%, D2 - 30%, R1 20%), and in that case, it's actually more democratic. It could completely cut the other way, however, as it has in CA and WA in recent elections where two Rs are on the final ballot in majority-D area due to vote-splitting in the primary. The votes of your '20% of the electorate' are just as valid in the general election as the other 80% of the electorate, and could easily swing the vote towards one candidate or the other (e.g. the more conservative candidate) if they were to vote as a bloc. Voter suppression is things like closing or reducing hours of polling places in certain areas, mandating stricter rules for voting (perhaps shaped in such a way to affect classes of people that typically vote for one party or the other), etc. You know, tactics usually employed by the Republican party."