The only way to erect such a common power, as may be able to defend them from the invasion of foreigners, and the injuries of one another, and thereby to secure them in such sort as that by their own industry and by the fruits of the earth they may nourish themselves and live contentedly, is to confer all their power and strength upon one man, or upon one assembly of men, that may reduce all their wills, by plurality of voices, unto one will: which is as much as to say, to appoint one man, or assembly of men, to bear their person; and every one to own and acknowledge himself to be author of whatsoever he that so beareth their person shall act, or cause to be acted, in those things which concern the common peace and safety; and therein to submit their wills, every one to his will, and their judgements to his judgement. This is more than consent, or concord; it is a real unity of them all in one and the same person, made by covenant of every man with every man, in such manner as if every man should say to every man: I authorise and give up my right of governing myself to this man, or to this assembly of men, on this condition; that thou give up, thy right to him, and authorise all his actions in like manner. This done, the multitude so united in one person is called a COMMONWEALTH; in Latin, CIVITAS. This is the generation of that great LEVIATHAN. Thomas Hobbes, "Of the Causes, Generation, and Definition of a Commonwealth," Leviathan (2:17).
A political transformative experience (hereafter PTE) involves an experience that is both epistemically and politically transformative; PTE arises in situations where collective agents (e.g., social activists or financial regulators) think of themselves as authoritatively controlling their choices by collectively projecting themselves forward and considering possible futures, and their plans are undermined by cognitive and epistemic limitations; thus PTE is -- like Laurie Paul's account of transformative experience (TE) on which it is explicitly modeled* -- a species of epistemic (subjective) true (or Knightian) uncertainty. In particular, PTE is a theory of unforeseen (and, thus, unintended) consequences in which those consequences change political actors in ways they could not have willed. PTE assumes the intelligibility of collective agents (and collective intentionality), but it is compatible with various kinds of methodological individualism (recall this post on Brian Epstein).
A characteristic example (with qualification noted shortly) of such a PTE is the transition during the Hobbesian covenant from a multitude of men in the state of nature to a unity under a common power or commonwealth (see the quote above). The covenant willingly transform the Hobbesian free agent in the state of nature into source of collective agency (the sovereign), which, in turn, makes them into subjects of the sovereign (e.g., "by this institution of a Commonwealth every particular man is author of all the sovereign doth," (Leviathan, 2:18)). The social contract changes the (social) identity of agents. The Hobbesian social contract, the generation of the rule of law, is also a clear response to bad forms of uncertainty (to quote a famous paragraph from L2:13): "there is no place for industry, because the fruit thereof is uncertain, and consequently no culture of the earth, no navigation nor use of the commodities that may be imported by sea, no commodious building, no instruments of moving and removing such things as require much force, no knowledge of the face of the earth; no account of time, no arts, no letters, no society, and, which is worst of all, continual fear and danger of violent death, and the life of man solitary, poor, nasty, brutish, and short."
I noted I would qualify the example. In Hobbes the most important consequences of the covenant are imagined (recall "to defend them from the invasion of foreigners, and the injuries of one another, and thereby to secure them in such sort as that by their own industry and by the fruits of the earth they may nourish themselves and live contentedly,") to be foreseeable. Hume, whose own theory of the origin of law embraces many Hobbesian elements, criticizes Hobbes on this point: "In vain shou’d we expect to find, in uncultivated nature, a remedy to this inconvenience....The idea of justice can never serve to this purpose...[it] wou’d never have been dream’d of among rude and savage men." (Treatise 18.104.22.168) Here, Hume calls to the cognitive and epistemic limitations of agents living under the state of nature So, a (counter-factual) paradigmatic instance of PTE in the liberal tradition combines Hobbesian collective agency in which the agents' social identity is transformed with a Humean understanding of what those very agents could not have foreseen (and, thus, not intended).
The previous paragraph may suggest that PTE is always a mere fiction (like the Hobbesian/Humean story). But this does not follow. For example, let's assume that British voters decide to vote for Brexit the referendum on 23 June. (Here I treat a referendum as an instance of collective action; if you don't like that imagine your own example.) If they vote fro Brexit they intend -- inter alia -- to transform their citizenship and a whole bunch of constitutive relations with other peoples. All of that is clear even if the content of the transformation will be contested before and after the vote. But what is equally clear is that a whole bunch of consequences on their political identity occasioned or caused by Brexit are now shrouded in mystery. (If you think that nothing much will change, that's fine--it's just that you are not in an epistemically superior position to think so.) It's possible, thus, that Brexit will be an instance of PTE, although perhaps an aversion to transformative experiences (status quo bias) may induce the voters to reject Brexit--I don't know.*
*TE is itself a novel analysis – echoing the spirit of Knight (recall), but also distinct from Ellsberg and Allais (Collins 2015) – of the limits of standard decision theory. I have applied it to political theory (here), and have learned since of work by Krishnamurthy (here) and Arvan (chapter 2) very much in the same spirit (theirs is more carefully developed).
**I have benefitted from facebook discussion with Ruth Groff, Mark Lance, Laurie Paul, Annaleigh Curtis, Marcus Arvan, and Meena Krishnamurthy.