The issue of episcopal collegiality is one of the most misunderstood teachings of the Second Vatican Council. It is hard for many to Catholics understand why this question was the most controversial of all the topics discussed at the Council; it was debated in nine General Congregations and can be viewed as the heart of the conciliar debates. What could be so controversial about collegiality? Isn't collegiality only the rather common-sense teaching that bishops are successors to the apostles? Does it not simply mean that each bishop is the rightful authority in his own diocese, and that taken together, this body of bishops, of whom the pope is Head, constitutes the hierarchy of the Church and governs it according to the will of God? What Catholic could possibly oppose this?
There is much debate today on the meaning and implications of the Second Vatican Council's teaching on collegiality. We will attempt to sketch here the origin of the debate, the motivations of its supporters in the Council halls, and its implications in the modern Church. The topic is complex, and we are poor of understanding. We do not claim our opinion is authoritative and welcome other contributing or clarifying comments by those more knowledgeable than ourselves.
The Teaching of the Church on Papal Primacy
According to the traditional teaching of the Church, the Church is governed by the Pope and the bishops in union with him, and this hierarchical arrangement is iure divino, by divine law.  The bishops are successors of the Apostles, and form the principle of the hierarchy.  As successors of the Apostles, the bishops perpetuate the "Apostolic mission" . The episcopal ministry has a two-fold character, one sacramental, the other jurisdictional. The sacerdotal character of the bishop is conferred by his ordination, and it is through the exercise of this sacramental ministry that the mission of the Apostles is perpetuated. The right of a bishop to exercise jurisdiction, however, is not conferred by ordination but is granted by the Roman Pontiff, who alone has the fullness of jurisdiction in the Church, "complete primacy" and "fullness of power", which has always been understood in terms of an absolute monarchy . Apart from union with and submission to the Roman Pontiff, a bishop has no jurisdiction whatsoever.  The power of the Roman Pontiff is not simply a primacy of honor or of direction, but entails a true and proper jurisdiction over the universal Church .
This is the faith of the Church. Before moving on, it is extraordinarily important to have a proper understanding of the distinction between a bishop's sacerdotal authority and his jurisdictional authority. To keep these concepts clear, we could illustrate the privileges that flow from a bishop's sacerdotal and jurisdictional powers like this:
While each bishop has true and proper jurisdiction within his own diocese, as well as a capacity to wield it by virtue of apostolic succession, he can only enter into the exercise of jurisdiction if he is granted it by the Pope, who alone has plenary and unlimited jurisdiction in the Church. Much was given to the Apostles including Peter, but there was also authority given to Peter that was not given to the others. Because Peter is the Church's unity, it is only in unity with Peter that jurisdiction can be legitimate. This is why St. Cyprian calls the See of Rome "the root and matrix" of the Catholic Church and states that:
"Upon him, being one, He builds His Church, and although after His resurrection He bestows equal power upon all the Apostles, and says: 'As the Father has sent me, I also send you. Receive ye the Holy Spirit: if you forgive the sins of anyone, they will be forgiven him; if you retain the sins of anyone, they will be retained,' yet that He might display unity, He established by His authority the origin of the same unity as beginning from one. Surely the rest of the Apostles also were that which Peter was, endowed with an equal partnership of office and of power, but the beginning proceeds from unity, that the Church of Christ may be shown to be one. This one Church, also, the Holy Spirit in the Canticle of Canticles designates in the person of the Lord and says: 'One is my dove, my perfect one is but one, she is the only one of her mother, the chosen one of her that bore her.' Does he who does not hold this unity think that he holds the faith? 
The Magisterium has echoed this traditional teaching, stating that the whole government of the Church was entrusted to Peter. For examples, Leo XIII taught, "[Peter] was preeminent among the Apostles: He was the mouthpiece of the Apostles and the head of the Apostolic College....at the same time showing him that henceforth he ought to have confidence, and as it were blotting out his denial, He commits to him the government of his brethren..."  The pope's government has been traditionally called "monarchical."
All of this obviously rules out any sort of democratic concept of Church governance, whereby the bishops could have any sort of authority apart from the pope.
Modern Origin of the Theory of Collegiality
Essentially, in taking up the question of collegiality, the Second Vatican Council was asking the bishops to define their own power in relation to the Roman Pontiff. At Vatican II, those in favor of collegiality argued that the doctrine of Papal Primacy as taught at Vatican I needed to be "balanced" by the principle of collegiality in governance. The essential doctrine of collegiality is that the power of jurisdiction had been entrusted, not to Peter alone, but to "the Twelve"; while not denying that Peter had the primacy, the innovators suggested that it was by virtue of his presidency of the apostolic college that Peter held this rank, not by the special, direct commission of Christ. Authority is entrusted to the Twelve, and Peter has authority by virtue of being head of the Twelve. Thus the Twelve is the true body of authority. This is the heart of collegiality.
We will examine the implications of this doctrine momentarily, but first let us look at its history. We have already examined the traditional teaching, reaffirmed at Vatican I and in Leo XIII's Satis Cognitum. Where and when and among whom did the push for collegiality get its origin? If we are seeking for the ultimate origin of the concept, it can be found in 15th century Conciliarism; but, if we are looking for a more modern source, we can trace collegiality to the work of Dom Lamber Beauduin (1873–1960), a Belgian Benedictine who was also one of the pioneers of the ecumenical movement. In 1925 he founded a monastery at Chevetogne in Belgium dedicated to promoting Christian unity, particularly with the Anglicans. A series of talks with the Anglicans were held under Beauduin's auspices throughout the 20's. We do not know the precise content of these talks, but the Catholic hierarchy of England protested that the nature of the unity Beauduin envisioned was contrary to the principles of Apostolicae Curae. The Vatican, then under Pius XI, subsequently ordered the talks terminated.
The work of Beauduin was perpetuated, however, through the journal Irenikon, published by the Chevetogne community beginning in 1926. Christian unity was the theme of the publication. Beauduin, through his work with the Anglicans and discussions with the Eastern Orthodox, became convinced that the major stumbling block to the reunion of Christendom was the Papal Primacy. Thus Beauduin and those under his influence, sought to find an ecclesiological model that would be more palatable to Protestants and Orthodox while still retaining a place for the papacy - a via media on papal authority.
It was in the pages of Irenikon in 1951 that Fr. Yves Congar, a disciple of Beauduin, first coined the term "collegiality" to describe this ideal relationship between the pope and the bishops.  The context in which Congar employed this term merits close attention. He is discussing the Russian concept of sobornost, which was a philosophical-religious idea put forward by the Russian Hegelians Ivan Kireevsky (d. 1856) and Nickolay Lossky (d. 1956). Sobornost was the Hegelian dialectic applied to religion as a model for a pan-Slavic Christianity; opposing tendencies within different ecclesial circles could be played down and even subsumed in favor of what was shared in common between the groups. The term sobornost means unity based on like-minded interest. Kireevsky's concept of the Church was pan-Christian; he wrote that the Church consisted of "the sum total of all Christians of all ages, past and present, comprise one indivisible, eternal living assembly of the faithful, held together just as much by the unity of consciousness as through the communion of prayer" . Sobornost was a theory that these diverse Christian groups could be held together in a sort of real spiritual unity based on those minimum principles they held in common; a kind of "mere Christianity."
Needless to say, the religious concept of sobornost is not consonant with Catholic teaching. Pope Pius XI addressed the issue of pan-Christianity in his 1928 encyclical Mortalium Animos, saying:
"These pan-Christians who turn their minds to uniting the churches seem, indeed, to pursue the noblest of ideas in promoting charity among all Christians: nevertheless how does it happen that this charity tends to injure faith?...since charity is based on a complete and sincere faith, the disciples of Christ must be united principally by the bond of one faith. Who then can conceive a Christian Federation, the members of which retain each his own opinions and private judgment, even in matters which concern the object of faith, even though they be repugnant to the opinions of the rest? And in what manner, We ask, can men who follow contrary opinions, belong to one and the same Federation of the faithful?... How so great a variety of opinions can make the way clear to effect the unity of the Church We know not; that unity can only arise from one teaching authority, one law of belief and one faith of Christians. But We do know that from this it is an easy step to the neglect of religion or indifferentism and to modernism, as they call it." 
Having highlighted the dangers of pan-Christianity and its tendencies towards indifferentism, he reminds the faithful that they are forbidden from participating in non-Catholic assemblies and restates the traditional understanding of Christian unity in terms of the principle of unity: return to the Church whose head is the successor of Peter:
"So, Venerable Brethren, it is clear why this Apostolic See has never allowed its subjects to take part in the assemblies of non-Catholics: for the union of Christians can only be promoted by promoting the return to the one true Church of Christ of those who are separated from it, for in the past they have unhappily left it... Furthermore, in this one Church of Christ no man can be or remain who does not accept, recognize and obey the authority and supremacy of Peter and his legitimate successors" 
To return to Congar: In his 1951 article in Irenikon, Fr. Congar coined the term "collegiality" as a translation of the word sobornost. Applied to problems of Christian unity in the West, Congar hypothesized that the one factor that the Eastern Orthodox, Catholics and Anglicans held in common was an episcopacy. Applying the principle of sobornost, he reasoned that a reaffirmation or strengthening of the Catholic episcopacy could provide firmer grounds upon which to effect reunion with the Anglicans and Orthodox. This theory of the ecumenical value of a strengthened episcopacy he called "collegiality."
Thus, the push for collegiality was founded on an application of the Hegelian dialectic, originally utilized in a pan-Christian Slavic context, for the final end of diminishing the emphasis on the papacy for the purposes of ecumenism.
Arguments in Favor of Collegiality
We have seen that the origin of the phrase was based in the ecumenical work of Dom Beauduin and Fr, Congar. Moving forward to Vatican II, ecumenism was one of the main arguments offered in favor of collegiality. Since the primacy of the pope was a stumbling block to ecumenical dialogue, it was necessary to minimize its importance by highlighting the "collegial" nature of the Church's government. If it could be shown that the bishops around the world retained a power to govern collectively as a "college", Catholicism would be more palatable to non-Catholics who objected to the primacy of Peter. Besides Fr. Congar, then a peritus at the Council, the other major proponent of collegiality was Bishop Charue of Namur, vice-president of the Theological Commission. Charue's talking points were taken from the book The Primacy of Peter (1960), a book authored by Chevetogne monk Oliver Rousseau in which the "juridical" notion of "power" was contrasted with a more "collegial" ecclesiology based on "love." As we can see, a dangerous dualism was being introduced into the ecclesiological thinking of the Council Fathers - a Church of the "spirit" opposed to a rigidly inflexible hierarchy.
We could also cite a separate but parallel trend in theology towards rehabilitating the condemned doctrines of Conciliarism, the 15th century heresy that had sought to limit papal authority by subsuming under the authority of a Council and a sitting "parliament" of bishops. While Conciliarism proper was soundly condemned , a popular series of essays were published in 1959 by the Benedictine Paul de Vooght, also a Belgian, in which an appeal was made to a "moderate Conciliarism" as a balance to the doctrines defined at Vatican I.
Finally, we could also cite the changing political thinking in progressive circles. The model of the Church as "absolute monarchy" was no longer appropriate given the democratic nature of the modern age. This democratic approach was first expressed in the Council chambers of Vatican II, when the bishops of the Rhine "revolted" against Cardinal Ottaviani and demanded new elections for the commission seats. In Roberto de Mattei's The Second Vatican Council: An Unwritten Story, he states that "The progressives saw the council as a representative assembly analogous to modern parliaments, and the bishops as the agents of 'the will of the people of God'." 
Of course, pure innovation has no place in Catholic theology. If collegiality were to become accepted, it must be presented as the Church's tradition, something that was being "rediscovered". Yet Congar and the others knew that this theology was in fact an innovation. Congar's journal reflects that he knew the program he was pushing went against the current of a millennium of theological development. He wrote in his journal:
"For a thousand years everything among us has been seen and constructed from the papal angle, not from that of the episcopate and its collegiality. Now THIS history, THIS theology, THIS canon law needs to be done." 
Congar was clear that "THIS theology" was contrary to over a thousand years of theological development.
The Conciliar Debates and Vote of October, 1963
Because of its far-reaching implications, collegiality actually occupied more discussion in the Second Vatican Council than any other topic. Even if modern Catholics do not understand the controversy surrounding collegiality, the Council Fathers realized it was a striking departure from the theology of papal primacy, at least as it had developed since Vatican I. The major debates on collegiality in the schema that would become Lumen Gentium occurred in October, 1963. The progressives, led by Cardinals Meyer, Leger, König, Alfrink and De Smedt, argued in favor of collegiality, and for the establishment of permanent national episcopal conferences, which were held to be the appropriate structural expression of collegiality. The theory was bitterly contested by Cardinals Siri, Ruffini and Archbishops Staffa and Sigaud.
The interventions of the latter-named bishops are interesting because they demonstrate that the Council Fathers, far from viewing collegiality as the simple affirmation that bishops succeed the apostles, saw it as a fundamental reordering of the Church's structure. Archbishop Sigaud, for example, stated that the schema gave the impression that new doctrine was being taught. He also stated that he believed that collegiality would imply that the Church would be ruled "by means of a sort of permanent council."  Archbishop Lefebvre also argued that the authority of episcopal conference would not only weaken papal authority, but the authority of individual bishops.
One of the most pivotal arguments in favor of collegiality came from the auxiliary Bishop of Bologna, Luigi Bettazzi. Bettazzi's intervention is notable because it highlights the confusion between the juridical and sacerdotal elements of the episcopacy, as noted above. He maintained that the college of bishops possessed an ecclesiastical jurisdiction that was collective, and argued that this was in continuity with theological developments of the 18th and 19th century, although these "developments" he mentioned were mainly in circles affected by Gallicanism. We see in Bettazzi's comments a confusion between the juridical and sacerdotal realities; the episcopal college does enjoy a collective jurisdiction, but only an extraordinary one; i.e. in the context of an ecumenical council. Bettazzi was positing the existence of an ordinary collective jurisdiction of the episcopate, something that was completely novel, unless one includes the propositions of the 15th century Conciliarists. We have already noted a revival of "moderate Conciliarism" was popular in the circles of Chevetogne.
The argument was also fueled by an unhealthy dualism introduced between the Church's hierarchical and charismatic dimensions, or between the "juridical" and "pneumatic", as Cardinal Suenens put it in his intervention of October 22nd, which was in fact written by none other than Hans Küng.  Suenens argued that the essential characteristic of the Church is pneumatic - a charismatic, "prophetic" reality. The Church's hierarchical structure was peripheral and not part of the Church's essential structure. Any Catholic with even a modicum of ecclesiological knowledge should be uncomfortable with this dualistic relegation of the Church's hierarchy to the sidelines. We should also call to mind the recent words of Pope Emeritus Benedict XVI, who said that "every dualism is negative in the Christian sense." 
Speaking of Benedict XVI, it is interesting that as it became apparent the Council was moving in the direction of understanding itself in a collegial sense, some members of the Theological Commission proposed adding clear affirmations of the teaching of Vatican I to the schema to highlight the continuity with the doctrine of papal primacy, but the proposal was blocked by commission members Rahner and Ratzinger. 
The voting on collegiality took place on October 29 and 30, 1963. In order to understand how this happened, we will present the actual language of the ballot the Council Fathers were asked to vote on:
Does it please the fathers that the Council should affirm:
(1) That episcopal consecration is the highest degree of the sacrament of Holy Orders.
(2) That each bishop who is legitimately consecrated in communion with the bishops and the pope, their head and principle of unity, becomes a member of the Episcopal College.
(3) That this Body or College of Bishops succeeds the College of the Apostles in the mission of evangelizing, sanctifying and governing, and that this College of Bishops, united with its head, the Roman Pontiff and never without this head-it being understood that the primatial right of head remains whole and entire-possesses a supreme and plenary authority in the universal Church.
(4) That this power belongs, by divine right, to the Episcopal College united with its head.
(5) That the revival of the diaconate as a distinct and permanent grade of the sacred ministry is opportune.
The questions were approved by a solid (though not unanimous) margin, around 75% overall. The key question here is question three, because it introduces a legal entity unknown in the entire history of the Church - the Episcopal College as a whole, which is attributed "supreme and plenary authority."
If the Episcopal College has supreme and plenary authority, what of the "fullness of power" Lyons II attributed to the person of the Roman Pontiff, or the "full power was given to him in blessed Peter by our Lord Jesus Christ, to feed, rule, and govern the universal Church" spoken of at Florence? What about the teaching of Vatican I that "the Roman Church possesses a superiority of ordinary power over all other Churches, and that this power of jurisdiction of the Roman Pontiff, which is truly episcopal, is immediate; to which all, of whatever rite and dignity, both pastors and faithful, both individually and collectively, are bound, by their duty of hierarchical subordination and true obedience"?  Somehow, previous Magisterial pronouncements about the power of the Roman Pontiffs needed to be squared with the new teaching on collegiality, beyond the disclaimer included in the text of the question.
The Problem of Jurisdiction and the Roman Pontiff
This brings us to the question of the Roman Pontiff and his place vis-à-vis the bishops. People often look at the texts on collegiality and, seeing the careful reaffirmation of the pope's authority, cannot understand why this teaching could be construed as a threat to papal supremacy, or why it is hard to reconcile with tradition. It is important to note that the concept of collegiality does not deny that the Roman Pontiff possesses the powers traditionally ascribed to him, but states that he derives these powers by virtue of his headship over the Episcopal College. This appears to be a divergence from the traditional teaching. The statement affirmed by the Council Fathers says that the College of Bishops possesses "supreme and plenary authority in the universal Church", and the pope, by virtue of being the head of that college, exercises this supreme power in its name. Let us compare this to the traditional teaching:
As we can see, the definition of collegiality voted on by the Council Fathers introduced several innovations:
First, it derived the bishops' powers of jurisdiction from their ordination rather than to papal prerogative. It has always been understood that the bishops are the successors of the Apostles, and that they have their own proper authority, and that this authority is recognized in the monarchical government of a bishop in his diocese; Leo XIII taught as much in Satis Cognitum.  Yet, as we see from the language the Council Fathers voted on, the "supreme and plenary authority" attributed to the Episcopal College is derived from their status as being successors of the Apostles - i.e., from episcopal ordination, not from the permission of the Roman Pontiff for them to enter into the exercise of their jurisdiction. The sacerdotal and the juridical are confused. 
Second, rather than understanding the successor of Peter as the source of supreme and plenary authority, and the bishops as exercising jurisdiction only insofar as they do in union with Peter, the Episcopal College itself is said to possess supreme and plenary authority, and that the Roman Pontiff wields his authority by virtue of being head of this College. The Church seemed to be replacing its monarchical structure with a democratic structure guided not by the pope individually but by the bishops as a whole. Papal primacy is not denied, but its source is changed. The wording emphasizes the need for bishops to be united with their head for their acts to have legitimacy, but they retain collectively the fullness of power. Just like - to use an American analogy - the Congress needs the President to sign off on legislation for it to become binding, but ultimately the Congress retains full legislative authority. Similarly, the pope is needed to sign off on episcopal initiatives or exercises of collegial power, but if the pope possesses his authority by virtue of his headship of the College, then it is ultimately the College, not the Pope, who has supreme power, notwithstanding the qualifications to the contrary.
Third, by connecting the authority of the College with ordination rather than papal appointment, it made the collegiality of the Church a matter of divine right (iure divino); as demonstrated on our chart at the top of this post, the jurisdictional authority of any bishop is not a matter of divine right, but must be conferred by the Roman Pontiff.
Fourth, and most importantly, a new juridical, legal entity is created - the Episcopal College as a permanent, ordinary source of universal authority. Of course, the Episcopal College has always existed. Leo XIII references it many times in Satis Cognitum. What is new is not the Episcopal College, but the College as a juridical entity exercising "supreme and plenary authority in the Universal Church." A bishop can have two sorts of jurisdiction: ordinary-individual, and extraordinary-collective. A bishop's ordinary-individual jurisdiction is that which he exercises as supreme pastor of his own diocese. A bishop's extraordinary-collective jurisdiction is that which is exercised by all of the bishop's gathered in an ecumenical council as the Episcopal College. These are the only forms of episcopal jurisdiction recognized by Tradition. But the ballot on collegiality called into existence an unheard of third type of jurisdiction: ordinary-collective, by which the Episcopal College is understood as a kind of permanent, ordinary source of jurisdiction.
Responses and Implementation
Again, lest we think the progressives were not aware of what a major victory this vote was, we can note that Hans Küng elatedly called this vote "the peaceful 'October Revolution' of the Catholic Church", referring to the Bolshevik Revolution of 1917 . Cardinal Suenens declared, "October 30 is a decisive date in the history of the Church. The battle of the Twelve has been won!" and even Paul VI, when meeting Cardinals Dopfner, Lercaro and Suenens the day after the vote, greeted them with the words, "So we have won!"  Had the teaching on collegiality been merely a reaffirmation of something the Church had always taught, would Suenens and the others have been so elated? Would Hans Küng have had occasion to liken it to the Bolshevik Revolution?
Of course, the ballot language was not definitive. It would remain for the Council to put the will of the bishops into final form. Some, such as Cardinal Felici, attempted to go right to the pope to protest the dangerous features of the teaching, but as we have seen, Paul VI was firmly on the side of the progressives in this matter.
It only took a single day to see what the implications of this vote were. On October 31st, Cardinal Alfrink and the Dutch bishops stated that if collegiality was a divine right, then the College of Bishops ought to take priority over the Roman Curia, which was certainly not of divine right. Furthermore, they argued that the Roman Curia had no authority to interpose itself between the College and the Pope. On November 6, the Maronite patriarch Maximos IV Saigh attacked the College of Cardinals and argued that if collegiality were a divine right, the Church ought to be governed by "a sacred college of the Universal Church" made up of representatives of the episcopal conferences of each country.  Cardinal König, meanwhile, invoked the principle of subsidiarity in expanding the role and authority of episcopal conferences as an expression of the Church's collegial nature.  All around, the progressives echoed König's support for episcopal conferences "by divine right" as an expression of the Church's collegiality, and as a way to undermine the College of Cardinals and the Roman Curia and to democratize the Church. Pandora's Box had been opened.
The conservative response over the coming weeks was concise, even profound, but ultimately ineffective. Nevertheless, the conservative objections merit examination, because they are just as relevant today as they were in 1963. Part of this ineffectiveness, as noted by Roberto de Mattei, was the inability of the conservatives to realize that what was happening was an event, a progressive coup - not just a debate about theological language.
One objection was that the devotion due to the pope is necessarily filial, and that collegiality was fatal to traditional Catholic love for the pope because it destroys his fatherhood. Fr. Berto, the peritus working with Archbishop Lefebvre, expressed this concern masterfully:
"The father-son relation is a relation between two physical persons who are directly conjoined. If the pope is the head of the Church only because he is the head of the Collegio Episcoporum, then the true sovereign of the Church is that college; i.e., a moral person...Now let the 'collegialists' tell me: who would ever love a moral person? Who would ever love a college with a filial love while thinking in his heart: This college is my father and I am its son?...and who could ever believe that the Fatherhood of God 'from whom all paternity on heaven and on earth is named' should be represented, symbolized, or shared by a collegial entity, precisely in the highest order of created things, namely, His Church?" 
Another objection was that, even assuming episcopal collegiality by divine right would be adopted by the Council, it would not follow that permanent national episcopal conferences should be established as an expression of that collegiality. For one thing, a national episcopal conference could never exist by divine right because it lacks the union of all bishops and the participation of the Head of the College; i.e., the Pope. Hence, there is no theological necessity of national episcopal conferences as the expression of collegiality by divine right.
Furthermore, as Archbishop Lefebvre as pointed out, the authority of a bishop in his diocese is said to be monarchical. This power would in fact be limited by the existence of national episcopal conferences. No bishop would want this usurpation in his own See, not even those who wax eloquent about collegiality in the sees of other bishops. It would fundamentally alter the relationship of a bishop to his own flock.
We could of course mention the historical argument, that the relation between the bishops and the pope had never been understood this way before. The Roman pontiffs had recommended episcopal conferences at times and even granted them official status (for example, the Plenary Councils of Baltimore in the United States), but not pope ever taught that such conferences were founded on divine right. Rather, they were always summoned for merely pastoral purposes, such as the famous regional Synod of Whitby in England in 663 that settled disputes between the Roman and Irish practices in England. And none were perpetual.
Finally, to the degree that collegiality was really meant to alter the understanding of where the Roman Pontiff derived his authority, we can cite against the 'collegialists' the teaching of Leo XIII, who asks rhetorically whether it were possible for the Roman Pontiff to derive his power from the College of Bishops, the implied answer being negative. Leo had written:
"...he who is set over the whole flock must have authority, not only over the sheep dispersed throughout the Church, but also when they are assembled together. Do the sheep when they are all assembled together rule and guide the shepherd? Do the successors of the Apostles assembled together constitute the foundation on which the successor of St. Peter rests in order to derive therefrom strength and stability? 
The Definition in Lumen Gentium and Aftermath
The final definition of collegiality the Council adopted in Lumen Gentium is a mixed bag. While some of the more radical concepts of the collegialists were omitted - and while the prerogatives of the Supreme Pontiff are elaborated - the document does contain the statement that supreme and full power over the universal Church resides with the college, and that the college always enjoys this power. Remembering that the real innovation with collegiality is not in that it denies the power of the pope but grounds his authority in a different source, the final wording of the document allows for orthodox interpretation for those primarily interested in preserving the special privileges of the Roman Pontiff while simultaneously allowing room to maneuver for those pushing a greater role for the Episcopal College. Let us examine the language adopted in Lumen Gentium.
The introduction of collegiality begins in LG 22, in Chapter III's discussion on the hierarchy. In introducing the concept, the Council Fathers seemed sensitive to the critique that such a concept was not found anywhere in the history of the Church. Thus, we see in section 22 various attempts to construct a historical pedigree for the teaching. Ecumenical councils and regional synods are cited as "an indication of the collegiate character and aspect of the episcopal order", as well as the practice of having multiple bishops present at an episcopal consecration. 
This is all fine if the purpose is to prove simply that bishops have always had a role in the administration of the Church, but not if we are seeking to establish the permanent juridical reality of the Episcopal College. The practice of bishops attending synods and councils and the discipline of multiple bishops participating in a consecration indicate only that there is an order of bishops, which everybody understands. No one denies that the episcopacy has a collegial nature; but to say the collegial nature is a permanent, juridical reality is something different, and to say it is the subject of supreme and full power even more so. While Lumen Gentium is certainly correct in pointing out that the collegial nature of the episcopacy is manifested in these sorts of actions, it does not follow that the Episcopal College is a permanent, ordinary juridical reality.
The following paragraph goes on to explain that the College must be united to the Pope, the Head of the College, and then we see a reaffirmation of the Pope's authority, which is "supreme and universal power over the Church. And he is always free to exercise this power." But in the very next sentence, we read, "The order of bishops, which succeeds to the college of apostles and gives this apostolic body continued existence, is also the subject of supreme and full power over the universal Church."  How the College can "also" possess supreme and full power" along with the Roman Pontiff is an interesting quandary.
Although bishops taken singly, or even collectively in an Ecumenical Council, possess real authority, it has never been normative to refer to the Episcopal College as the subject of "supreme and full power." The text specifies that this power is contingent upon their unity with the Roman Pontiff, but with one fundamental difference - tradition has always affirmed that the bishops, exercising their judgment through an Ecumenical Council, can make authoritative and infallible pronouncements in union with the Roman Pontiff. However, tradition has not taught, to our poor knowledge, that this equates to possessing a "supreme and full power." It is one thing to say a body may sometimes exercise the charism of teaching infallibly; another to suggest that it is the subject of supreme and full jurisdiction.
As mentioned above, there are many affirmations of the pope's authority in Lumen Gentium, but the conclusions we can draw from them are mixed. This chapter of Lumen Gentium seems to be one of those "compromise formulas" spoken of by Cardinal Kasper, that "open the door to a selective reception in either direction."  Those seeking a traditional reaffirmation of the pope's primacy in Lumen Gentium while certainly find it, whilst those seeking to argue in favor of more episcopal power at the expense of the pope will find support as well.
The key is in the source of the pope's authority. Consider that papal primacy is mentioned eight times specifically in Chapter III of Lumen Gentium; of those eight mentions, only once are the power of the keys or Peter as the "rock" mentioned in connection with Peter's authority. By contrast, papal authority is tied to the headship of the College of Bishops six times. While it is not specifically spelled out, if one were to go by this chapter alone, one would be under the impression that the pope possesses his primacy by virtue of bring head of the Episcopal College.
The latter part of Chapter III, Section 22 is the most revolutionary section of the document, for it is in this passage that the teaching of collegiality by divine right is extended to the acts of national episcopal conferences. The passage in questions states:
"The supreme power in the universal Church, which this college enjoys, is exercised in a solemn way in an ecumenical council. A council is never ecumenical unless it is confirmed or at least accepted as such by the successor of Peter; and it is prerogative of the Roman Pontiff to convoke these councils, to preside over them and to confirm them. This same collegiate power can be exercised together with the pope by the bishops living in all parts of the world, provided that the head of the college calls them to collegiate action, or at least approves of or freely accepts the united action of the scattered bishops, so that it is thereby made a collegiate act." .
After affirming the "supreme power" of the College of Bishops, the passage notes that episcopal collegial power is exercised in a "solemn way" in an Ecumenical Council, and then it expands upon the prerogatives of the Roman Pontiff in this regard. But in noting a "solemn" exercise of collegial authority, the stage is set for a "non-solemn" or "ordinary" exercise of collegial authority. Thus, the passage goes on to say, "This same collegiate power can be exercised together with the pope by the bishops living in all parts of the world." This means that, beyond the ordinary jurisdiction exercised by a bishop in his own diocese, and beyond the extraordinary jurisdiction of an Ecumenical Council, there is a mediate form of "collegiate power" that can be exercised by the bishops "living in all parts of the world." This would be the justification for national episcopal conferences, for that is the only type of episcopal body above a bishop's individual diocesan jurisdiction and that of an ecumenical council.
So regional or national conferences of bishops "living in all parts of the world" are expressions of collegial authority. But what is more interesting is the criteria the document lists for when such conferences become expressions of collegiality. Lumen Gentium states that the acts of these bodies are collegiate "provided that the head of the college calls them to collegiate action, or at least approves of or freely accepts the united action of the scattered bishops." If the Head of the College calls them to act, this is one thing; but the document says this is not necessary; it is sufficient for the Pope to simply approve their actions - even more so, for him to "freely accept." The acts of national episcopal conferences express collegiality simply by virtue of the pope "freely accepting" them, or in other words, by not actively stopping or opposing them. It is difficult to see how the acts of "scattered bishops" are collegial since these acts lack the union of all bishops or the participation of the Head. Indeed, they can only be collegial if an ordinary, collective jurisdiction is granted, and if the mere non-intervention of Roman Pontiff is counted as "participation."
This is revolutionary. Step back and consider the line of development we have traced. First, collegiality is noted as a character of the episcopal college, and this is linked to consecration, not jurisdiction. Second, an ordinary, collective, permanent juridical reality ("the Episcopal College") is affirmed, which really has no precedent in the Church's history. Third, this College is said to have supreme and full authority in the Universal Church. Fourth, it is at least inferred that the pope's authority derives from his position as president or head of this college. Finally, the acts of "scattered bishops" throughout the world are said to manifest collegiality so long as the pope does not actively oppose them.
We must not fail to notice what difficult position this put the Holy Father in. While he in theory retains all of his prerogatives, the actions of "scattered bishops" and their conferences are now affirmed as expressions of the Church's collegial nature, so long as the pope doesn't actively oppose them. But since the aforesaid actions are expressions of the Church's collegial structure, if the pope does step in to intervene, oppose, or regulate these "scattered bishops", he is implicitly acting against the Church's collegial structure. It is now the Roman Pontiff who must offer a justification as to why he is interfering. And if such interventions may make one appear to be usurping the Church's collegial character, perhaps it is better not to intervene at all?
This explains the proliferation of national episcopal conferences in the wake of Vatican II, the popes' seeming unwillingness to restrain their excesses, the abdication of the symbols of papal monarchy, the mystifying silence of the papacy in the face of persistent episcopal corruption and incompetence, and the multiplication of regional liturgical "norms" that are at variance with the universal norms of the Church.
It is ironic that, if we look at the schema De Ecclesia, the original document on the Church prepared by Ottaviani's Preparatory Commission - the document which was massively revised by the Council Fathers - we can see that the original document went out of its way to note that there is no ordinary collective jurisdiction of bishops, specifying that the authority of the College of Bishops can only be exercised in an extraordinary manner:
"[Bishops] gathered in great numbers do not have power over the entire Church nor over any Church other than those committed to their charge except by participation in the power of the Roman Pontiff, still they are bound to show a real solicitude for the whole Church; and, although this is not a power of jurisdiction, still, as the powerful support of fraternal communion, it contributes greatly to the benefit of the universal Church...But the power of this College, even its ordinary power insofar as it is inherent in the office, is legitimately exercised only in an extraordinary manner and in devoted subordination to the Vicar of Jesus Christ on earth, when, as, and to what extent he deems it expedient in the Lord. As for the constitution of this august College, all residential Bishops living in peace with the Apostolic See are by their own right members of it, and no Bishop, whether residential or not, can belong to this College unless by direct act or by tacit consent he is admitted into it by the successor of Peter, the Vicar of Christ, and Head of the College." 
Whereas the language voted on at Vatican II suggested that bishops entered the College by virtue of their episcopal consecration, the original language of the schema noted that entrance into the College was reserved to the direct act or tacit consent of the Roman Pontiff; i.e., that it was linked to the entering into jurisdiction, which could only occur with papal approval.
This is understandable a very intricate matter. Even within the argument laid out here, there are many nuances, disputed questions and interpretations, and legitimate differences of opinion. This question of collegiality was, however, the most disputed topic of Vatican II, and for this very purpose - many of the Council Fathers perceived that this touched on the very constitution of the Church and that the government of the Mystical Body itself was in question. While the pope's authority was certainly not overthrown or called into question, it was set on a different foundation. Pope Benedict XVI himself recognized this when, a few days after his abdication, he spoke about the transfer of power to the episcopate that happened in light of Vatican II, discussing "those who sought a decentralization of the Church, power for the bishops and then, through the Word for the "people of God", the power of the people, the laity. There was this triple issue: the power of the Pope, then transferred to the power of the bishops and then the power of all... popular sovereignty" .
The doctrine, as we have seen, has its remote origin in Conciliar thought, in more modern times in the thought of the Russian pan-Slavic movement, which was in turn inspired by Hegelian historicism. It was promoted by disciples of the Chevetogne ecumenism movement, whose discussions had been sanctioned by Pius XI as opposed to Catholic ecclesiology. The motivation of the collegialists was to downplay the primacy of the Roman Pontiff, and it was championed by the most liberal bishops and periti, including the modernist Rahner and heresiarch Küng. It was utilized as a tool to beat down the Roman Curia and establish the legitimacy of national episcopal conferences, which have been the bane of modern Catholicism. It's guiding ecclesiology is based on an unhealthy dualism between a 'pneumatic' Church and a 'judicial' Church. Its fruits have been chaos and the emasculating of papal power. It is the Pandora's Box of Catholicism.
 Council of Trent, Session XXIII, Can. 6 and Leo XIII, Satis Cognitum, 14
 Council of Trent, Session XXIII, Chap. IV, "The holy council declares that, besides the other ecclesiastical grades, the bishops, who have succeeded the Apostles, principally belong to this hierarchical order, and have been placed, as the same Apostle says, by the Holy Ghost to rule the Church of God."
 Leo XIII, Satis Cognitum, 8
 Second Council of Lyons (1274), Denz. 466 and Council of Florence (1439), Denz. 694
 Leo XIII, Satis Cognitum, 12-13, 15
 ibid., 12
 St. Cyprian of Carthage, Letter 44, De Unitate Ecclesia 4
 Leo XIII, Satis Cognitum, 12
 Yves Congar, "Le peuple fidèle et la fonction prophétique de l'Eglise", in Irenikon #24 (1951), p. 466
 Ninian Smart, John Clayton, Patrick Sherry, Steven T. Katz. Nineteenth-Century Religious Thought in the West. Cambridge University Press, 1988. Page 183.
 Pius XI, Mortalium Animos, 9
 ibid., 10-11
 By Eugenius IV at Florence in 1439 and Pius II in his bull Execrabilis in 1460 (Denz. 1307, 1376)
 The Second Vatican Council: An Unwritten Story by Robert de Mattei (Loreto Publications, 2012), 313
 Yves Congar, Journal, Sept. 25, 1964, quoted in Mattei, pg. 313-314. Emphasis in original.
 Archbishop Proença Sigaud, interview with Divine Word Service, October 10, 1963
 Mattei, 317; see also Hans Küng, My Struggle, 360-361
 The episode is related in the biography of Msgr. Michele Maccarrone, who was on the Commission. Mattei, pg. 317
 Pastor Aeternus, 3
 Leo XIII, Satis Cognitum 14: "But if the authority of Peter and his successors is plenary and supreme, it is not to be regarded as the sole authority. For He who made Peter the foundation of the Church also "chose, twelve, whom He called apostles" (Luke vi., 13); and just as it is necessary that the authority of Peter should be perpetuated in the Roman Pontiff, so, by the fact that the bishops succeed the Apostles, they inherit their ordinary power, and thus the episcopal order necessarily belongs to the essential constitution of the Church."
 In Satis Cognitum, Leo XIII states that the bishops are successors of the apostles in the sense that they continue the Apostolic ministry, not in the sense that they automatically inherit jurisdiction. "For the Apostles consecrated bishops, and each one appointed those who were to succeed them immediately "in the ministry of the word" (Satis Cognitum, 8). It is as ministers of God's word and the primary preachers of the Gospel that they succeed the Apostles.
 Hans Kung, My Struggle, 364
 Mattei, 319
 ibid., 320
 Cardinal Franz König, interview with Divine Word Service, Nov. 7, 1963
Fr. V.A. Berto, "Letter to Bishop Carli", Nov. 6, 1963, cited in Mattei, 321
 Satis Cognitum, 15
 Lumen Gentium, 22
 Cardinal Walter Kasper, L'Osservatore Romano, April 12, 2013
 Schema De Ecclesia, 15-16
 "Pope Benedict's last great master class: Vatican II, as I saw it", Radio Vaticana, February 14, 2013.