Origen of Alexandria's writings on Election and Predestination must be read while keeping his teachings on Universalism and Resurrection in mind. Origen's doctrine of ἀποκατάστασις (apokatastasis or apocatastasis) is famous for supporting Universalism (or Universal Reconciliation), that is that all people will eventually saved and possibly including fallen angels and finally the Devil. Although ἀποκατάστασις only occurs once in the New Testament (Acts 3:21), it was later developed into a robust dogma, especially by Gregory of Nyssa. In First Principles, (Book I), Origen teaches that our current material bodies are temporal and will be resurrected as eternal spiritual bodies, and anything that is temporary will be brought to an end so that God will be All-In-All (1 Cor 15); this includes the emptying of hell and salvation of all souls, and even including the liberation of the Sun and the Moon. Origen speculates that the spiritual resurrected bodies may be more similar to flames of fire, because fire exists without a body.
Gottschalk of Orbais was the first to consider and affirm Double Predestination as a dogma in the sense of John Calvin's decretum absolutum (absolute decree, ie. Double Predestination) as now receive it in the Reformed Church. Before Gottschalk's writings, the question of decretum absolutum was not fully or formally stated like it is in Calvin's Institutes. So, it would be an anachronism to say Origen was either for or against the decretum absolutum. Additionally, with Origen's ἀποκατάστασις, decretum absolutum did not have the same foundational meaning. Origen saw predestination and election as only positive, such that even when God foreordains evil, it is only so that good will eventually come to that being. The election of individuals as "vessels of wrath" (cf. Romans 9) wasn't a sensical statement due to ἀποκατάστασις.
In Book III, Chapter I (and especially Sections 17, 18 and 19), Origen exegetes Romans 9, and affirms that God does the hardening, but not in the sense of Calvin's Decretum Absolutum (Decretum Absolutum).
We asserted also, when investigating the subject of Pharaoh, that sometimes a rapid cure is not for the advantage of those who are healed, if, after being seized by troublesome diseases, they should easily get rid of those by which they had been entangled. For, despising the evil as one that is easy of cure, and not being on their guard a second time against falling into it, they will be involved in it (again). Wherefore, in the case of such persons, the everlasting God, the Knower of secrets, who knows all things before they exist, in conformity with His goodness, delays sending them more rapid assistance, and, so to speak, in helping them does not help, the latter course being to their advantage. It is probable, then, that those “without,” of whom we are speaking, having been foreseen by the Saviour, according to our supposition, as not (likely) to prove steady in their conversion, if they should hear more clearly the words that were spoken, were (so) treated by the Saviour as not to hear distinctly the deeper (things of His teaching), lest, after a rapid conversion, and after being healed by obtaining remission of sins, they should despise the wounds of their wickedness, as being slight and easy of healing, and should again speedily relapse into them. And perhaps also, suffering punishment for their former transgressions against virtue, which they had committed when they had forsaken her, they had not yet filled up the (full) time; in order that, being abandoned by the divine superintendence, and being filled to a greater degree by their own evils which they had sown, they may afterwards be called to a more stable repentance; so as not to be quickly entangled again in those evils in which they had formerly been involved when they treated with insolence the requirements of virtue, and devoted themselves to worse things. Those, then, who are said to be “without” (manifestly by comparison with those “within”), not being very far from those “within,” while those “within” hear clearly, do themselves hear indistinctly, because they are addressed in parables; but nevertheless they do hear. Others, again, of those “without,” who are called Tyrians, although it was foreknown that they would have repented long ago, sitting in sackcloth and ashes, had the Saviour come near their borders, do not hear even those words which are heard by those “without” (being, as is probable, very far inferior in merit to those “without”), in order that at another season, after it has been more tolerable for them than for those who did not receive the word (among whom he mentioned also the Tyrians), they may, on hearing the word at a more appropriate time, obtain a more lasting repentance. But observe whether, besides our desire to investigate (the truth), we do not rather strive to maintain an attitude of piety in everything regarding God and His Christ, seeing we endeavour by every means to prove that, in matters so great and so peculiar regarding the varied providence of God, He takes an oversight of the immortal soul. If, indeed, one were to inquire regarding those things that are objected to, why those who saw wonders and who heard divine words are not benefited, while the Tyrians would have repented if such had been performed and spoken amongst them; and should ask, and say, Why did the Saviour proclaim such to these persons, to their own hurt, that their sin might be reckoned to them as heavier? we must say, in answer to such an one, that He who understands the dispositions of all those who find fault with His providence—(alleging) that it is owing to it that they have not believed, because it did not permit them to see what it enabled others to behold, and did not arrange for them to hear those words by which others, on hearing them, were benefited—wishing to prove that their defence is not founded on reason, He grants those advantages which those who blame His administration asked; in order that, after obtaining them, they may notwithstanding be convicted of the greatest impiety in not having even then yielded themselves to be benefited, and may cease from such audacity; and having been made free in respect to this very point, may learn that God occasionally, in conferring benefits upon certain persons, delays and procrastinates, not conferring the favour of seeing and hearing those things which, when seen and heard, would render the sin of those who did not believe, after acts so great and peculiar, heavier and more serious.
Origen of Alexandria, On First Principles, Book III, Chapter I, Section 17, trans. Rev. Frederick Crombie, D.D. (from Greek text)
Related: apocatastasis, Apokatastasis, Decretum Absolutum, Double Predestination, First Principles, Frederick Crombie, Gottschalk, Gottshalk of Orbais, Gregory of Nyssa, John Calvin, Origen of Alexandria, Resurrection, Universalism