@Pluto's Republic Alligator Ed's analysis was upon passing bills.

So the third possibility is how many P3 votes will it take to help either P1 or P2 to either block OR pass a measure? Please, let's not let unicorns vote--let's talk about real world.

The point, then, of pompous "realism" backed by Poly-Sci Math, is to prove that there's no alternative to neoliberalism. The passage estimating P3's success, toward the bottom of Alligator Ed's diary, is a non sequitur from that proof:

The answer here is that even with growing voter disenchantment the likelihood of a third party gaining enough vitality would be twenty years or more, assuming no revolution or total societal collapse.

Why the "twenty years or more"? Why not two thousand, or two billion, years? The Republican Party was a "third party" in 1854 which acquired the White House in 1860. So much for Poly-Sci Math.

The point of analyses like this is to "prove" that there's no alternative to the Two-Party System, that the choice between Texas/ Florida/ Midwest elitism and California/ Suburban NYC elitism is an eternal choice, because the elitists are in some magical way "different" and because no nice liberal (you know, the self-proclaimed Great White Hopes of planet Earth) will ever grant P2 a victory by refusing to vote for P1.

Meanwhile, in the real world outside of the world of Poly-Sci Math, the process described in Kees van der Pijl's "The Making of an Atlantic Ruling Class" continues with Internet speed.

It is thus the real world that such Poly-Sci Math analyses ignore. Let's talk about the function of passing bills in the real world, which as readers will recall was the point of the analysis above. The function of passing bills, today, is to introduce refinements of the neoliberal order, the shared function of both P1 and P2. I'm sure that if there's any real conflict between P1 and P2, it can be resolved at the next Trilateral Commission or WEF or CFR meeting. Perhaps P1 and P2 can pretend to be "different" significantly enough to fool the voters, but the common assumption of both P1 and P2 today is that it takes damned little to fool the voters, thus BFFs HRC and DJT can pretend to run "against" each other in the 2016 Presidential election.

The party that ostensibly never ends

As I pointed out a long time ago, what's needed is a realignment. But lacking that, let's go back to the question at the top:

So the third possibility is how many P3 votes will it take to help either P1 or P2 to either block OR pass a measure? Please, let's not let unicorns vote--let's talk about real world.

The point of P3 is not to "help either P1 or P2," otherwise why bother with P3 in the first place?

...for a third party to enter the duopoly-designed election system. It's taken centuries to block every entrance or interface to third-party participants. The ruling cartel does not want to spoil the polarity that divides the People and moves them around the neoliberal game board.

Under a duopoly, voters tend to suffer from a mass delusion. Americans are convinced that the two parties are competing over ideals and ideologies. But nothing could be further from the truth.

The two Parties are colluding. With each other and Wall Street. Both Parties are mesmerized by the siren song of capitalism. They are protecting themselves from communism. And nationalized oil and natural resources, public utilities, infrastructure, and banking. The horror! For over a century the ruling elite has been desperately fighting an anti-communist war. It is the war that keeps us poor.

So, what happens when a third party is added to the mix? The effect is called the Prisoner's Dilemma. The vote becomes even more polarized. Well-intentioned reform turns to vapor, and voters pursue their own immediate self-interests. The heck with the future.

"Short-term self-interest" is the midwife of dystopias.

Click this for a fascinating description of how Americans vote when they are caught in the Prisoner's Dilemma.

Meanwhile, the author does go on to discuss some interesting strategies that can help voters on both sides break free. But it will require a major paradigm shift. Perhaps the looming Dollar crash and a dying Empire is just what we need.

Viewing third-party voting as a "Prisoner's Dilemma" suggests specific strategies for extricating American voters from their current predicament. Several, but not all, of these strategies relate to improving the perception of payoffs so that cooperation, i.e., voting for third-party candidates, is more appealing. Specific strategies include the following:

Accurately perceive costs of non-cooperation. The ultimate problem is that Democrat and Republican voters are not accurately considering the costs of maintaining the two-party hegemony or the benefits of electing third-party candidates. If the true costs and benefits were salient in our minds, we would more eagerly vote against the abusive and arrogant Republican-Democratic party establishment....

Less often considered, but perhaps even more important are the ‘opportunity costs’, i.e., besides these negative things, what positive things are we missing out on because of our dysfunctional and aversive government? Objectively considered, America has sufficient natural and human resources to construct a veritable utopia; we could eliminate poverty, grant free higher education and health-care for all; we have enough land to let everyone live in their own houses on their own property in environmentally friendly and attractive communities. Indeed, the blessings of nature generally, and in our country particularly, are so great that it seems we must make a concerted effort to avoid constructing such a prosperous and congenial society. We need a clearer vision of how good life could be were we only to stop punishing ourselves with the present inimical political system.

How can we gain this vision?

This is probably the most useful article I've read all week.