The history of third Parties … in Presidential races … is (1) that they allow the Democrat to roll up an electoral college landslide without winning a majority of the vote and (2) they have no staying power. The most recent example was Ross Perot.
Perot allowed Bill Clinton to win 370 electoral votes with only 43 percent of the popular vote in 1992:
By 1996, Perot was an irrelevancy:
Theodore Roosevelt and his Bull Moose Party were much more successful than Perot in 1912, but the Democrat, Woodrow Wilson, still won in a landslide:
Going on memory here, but I believe the Bull Moose Party was no more by 1916.
While the foregoing examples involved Presidential politics, I see no reason to believe that the result would be any different in State and local races. The Patriot Party would be competing exclusively with the Republican Party for votes and would likely lead to Democrats winning races with as little as 40 percent of the vote.
The far better approach is to attack the Republican Party from within. As I wrote in THIS IS THE WAY:
No getting fooled again. Primary all the Biden-Republicans in 2022. Do NOT support Biden-Republicans that make it through the primary. From U.S. Senators all the way down to the Statehouses. This is the way.
This approach prevents the scenario where the Patriot Party and the GOP get a combined 60 percent of the vote in a “safe” district … for example, 39 percent to Patriot Party and 21 percent to GOP … but the Democrat nonetheless wins (with 40 percent). As more real Republicans win in “safe” districts and more Biden-Republicans lose to Democrats (because we don’t support them if they win the primary) in purplish districts, we will wrest control of the Party from the Biden-Republicans. At that point, we can focus on becoming a majority without compromising our principles as the present iteration of the NH-GOP has.
In other words, we need to fight a guerrilla war not a conventional war against the GOP. This, not a 3rd-Party, is the way.