From Karl Dickey at The Examiner:
A Florida Constitutional amendment initiative is being circulated for signatures called the “All Voters Top-Two Primaries Amendment” being put forward by All Voters Vote, Inc. Last night, October 4, 2015, the Libertarian Party of Florida (LPF) Executive Committee voted to not support the initiative. All Voters Vote is working to collect enough signatures for the initiative to be placed on the 2016 general election ballot for Florida voters to consider. Top-Two has been adopted in California, Washington, and Louisiana and the results are that there has been an increase in voting back in incumbents as well as a decrease in third-party candidates making it on the general election ballots for consideration.
The LPF Legislative Review Committee did not support Top Two elections and the state party’s executive committee agreed for the following reasons:
•Only big money candidates will end up in the general election
•Libertarians will be unlikely to appear on a general election ballot
•Although the initiative claims that government subsidized primaries for the purpose of nominating candidates is eliminated, parties will bear the cost of a ‘pre-primary”, there will still most likely always be two elections (a primary and a general election) for each election cycle
•Voter turnout and voter engagement will be severely reduced in the general election resulting in a candidate selected by a small percentage of the electorate
•Incumbents rarely lose
If passed by over 60 percent of Floridians, the initiative would allow registered Florida voters to vote in primaries for Congress, State House, State Senator, Florida Governor, and the governor’s cabinet, as well as it would eliminate government funded party nominations for those offices. How Top-Two works is the most popular two candidates for each elective office will move forward to be the only individuals on the general election ballot regardless of political affiliation, except state office candidates obtaining a majority of votes in primary is elected;. The amendment would provide that the election of majority winners in a congressional primary should federal law change.

Yes, this “top two” primary system is a very bad thing for not merely the Libertarian Party, but also for any third-party. It is clearly an attempt to lock in the “two party system”, and I suspect it does so quite effectively.