The Florida Democratic Party and the Republican Party of Florida don’t agree on much, but they will be united on a new ballot proposal that aims to increase voter turnout, pull candidates away from the political fringes and keep pace with registration trends.

They’re going to hate it.

The Democrats and GOP don’t have a real duopoly on state government and congressional seats. You can still register as an independent — in fact, a whole bunch of people do — or you can still join the Green Party or some other splinter group. There’s nothing in the law that gives the Republicans two-thirds of the Legislature and the Democrats one-third, it just works out that way because those who made the law belong to those parties.

Every two years, both parties and all the candidates loudly say they hope everyone will vote. That’s not quite true. They want everyone who agrees with them to vote.

A bipartisan group of very experienced political operators last week filed a constitutional amendment petition that will be known as “All Voters Vote.”

If they can round up nearly 700,000 voter signatures by next February, and get 60 percent of the voters to support it, their constitutional amendment would open the state’s “closed” primaries. The way it is now, only registered Republicans can vote in GOP primaries, only Democrats in Democratic heats, and all the rest have to wait until November – when we pretty much get to choose from what the parties offer us.

There is one little exception in current law. If only Democrats or only Republicans seek an office, everyone can vote in that race because the primary is going to determine who serves in the office. But if an unknown, unserious write-in candidate signs up, the primary is closed, under a legal interpretation by the Division of Elections.

Under an All Voters Vote arrangement, all of us — even independents or minor-party amendments — could vote in the first round. If somebody gets more than 50 percent, they’re home free. If not, the top two contenders would duke it out in November.

There would be some technical difference for Congress, to comply with federal requirements.

The petition campaign was begun by Gene Stearns, a Miami lawyer who was chief of staff to former House Speaker Dick Pettigrew and campaign manager for the late Gov. Reubin Askew. Jim Smith, a former attorney general and secretary of state who served in statewide office and ran for governor in both parties, is on board, along with former FSU President Sandy D’Alemberte, a former Democrat legislator.

The Miami Herald, which first reported on the amendment drive last week, said the sponsors cited a poll of 1,007 voters by Clearview Research. Last year, an average of 55 percent of net new voters chose neither major party. Currently, about 27 percent of voters are not Democrats or Republicans. By 2022, that’s expected to be one-third.

Meanwhile, older voters, who are more likely to choose one of the big parties, are dying off and being replaced by young ones who are increasingly independent.

State legislators would never pass such a constitutional amendment. Why would they willingly give up their shared ability to limit our choices — and to reward or discipline their members?

Smith told the Herald to just look at the regular 2015 legislative session, to see how polarized – paralyzed – partisan politics can get. The Democrats are regimented into a liberal orthodoxy, and the Republicans are rigidly conservative, and anyone who varies from the party line will get a more obedient opponent in the next primary.

That means you have to work hard all summer and raise a ton of money, and you still might not beat back your party’s chosen challenger. On the other hand, you can play along with the bosses and have a pretty much free ride to re-nomination and, probably, re-election.

The result is, if you’re a Republican, you vote for tax and budget cuts (which are always referred to as “for working families”), against Medicaid expansion and for anything labeled family values. If you’re a Democrat, you vote for Medicaid expansion, against tax cuts (which are always referred to as “for the rich”) and for anything labeled gay or women’s rights.

Independent thinking is allowed, but you’d best keep it to yourself.

Under an All Voters Vote system, candidates could still appear on the ballot as Democrats or Republicans – or as Independents or Socialist Workers or whatever. The parties could endorse candidates and everyone would run their own races. And then the voters, not the parties, would choose the winners.

Which is why the parties will hate this thing.