Have Christians in communion with the Bishop of Rome been always in the majority since St. Peter?

Question

Demographics-wise, has the number of global Christians in communion with the Bishop of Rome (called "Catholics" for convenience in this Q) been always the majority in every generation since the church in Rome was established, compared to the number of Christians of all "Great Church"-compatible denominations?

Criteria for the accepted answer:

• References to scholarly estimates / reputable statistics are needed in the answer.
• If the answer is no, then the statistics need to include a historic trend line with a point showing the years when the number lost majority.
• If the answer is no, then please consider answering a related question of whether the "Catholic" percentage has always been greater than the percentages of other 4 major groups: Protestants, Eastern Orthodox, Oriental Orthodox, and Churches of the East + Nestorian Asian churches.

Method of calculation and the rationale

"Majority" is defined as more than 50% share of all Christians who subscribe to the key doctrines of the Great Church.

The purpose for this answer is to figure out whether in light of post-Nicene schisms, the numbers of adherents that remained in communion with Rome from the time of the Great Church until today ("Great Church" understood as the mainstream that survived various pre-Nicene heresies) can be interpreted to indicate that the Holy Spirit also assisted the ecclesial leadership of the Bishop of Rome by numerical strength. That is why the criteria below excludes Christian movements that are outright incompatible with the key doctrines of the Great Church.

This question may not be as straightforward to answer because at one point in the history of global Christianity, the Nestorian Eastern churches were very active in evangelism, widespread, numerous, and consisted of hundreds of bishoprics that mostly have perished and forgotten (except in the academia). See a fascinating 2009 book by historian Philip Jenkins The Lost History of Christianity: The Thousand-Year Golden Age of the Church in the Middle East, Africa, and Asia--and How It Died.

Criteria for group inclusion

For the sake of identifying who ARE "Catholics" (the numerator of the ratio):

• The only criteria is the number of Christians in full communion with the Bishop of Rome throughout history. In the modern period, a good starting point would be all the churches listed in the Pontifical year book.
• Protestant congregations who started afresh OR who broke communion with Rome (such as the Church of England) should NOT be counted.
• Eastern Orthodox adherents are counted before the 1054 Great schism, but not afterwards.
• Oriental orthodox churches churches (such as the Armenian Church) are counted before they broke off from the Great Church.
• Eastern Catholic churches in communion with Rome (both Eastern / Oriental Orthodox) such as the Armenian Catholic Church SHOULD be counted starting at the year of their recognition by Rome, so should ex-Protestant churches who are recognized by Rome such as parishes wishing to be part of Personal Ordinariate of the Chair of Saint Peter.
• Church of the East are counted, but not after the Nestorian schism.
• Ancient churches in Asia (some of them Nestorian) are counted, but not after losing contact with the Great Church since after the AD 325 Nicene council.
• Historic Arian factions (before 8th century) SHOULD be counted because (as far as I know) the centuries-long dispute was resolved without schism (see Wikipedia). Similarly, during the 4th-5th century Donatist controversy Donatist dioceses should also be counted because (as far as I know) Rome never break communion with them (but they were the ones who broke from Rome because of their stricter doctrine).
• A rough historical schema of the major schisms and reconciliations is shown below. Only the solid gray and red lines are counted, plus those not in the picture such as the Personal Ordinariate.

For the sake of identifying who ARE "Christians": (the denominator of the ratio):

• All of the numerator (Christians in full communion with either the Great Church or the Bishop of Rome)
• All Nicene and Chalcedonian Protestants
• All Eastern Orthodox churches
• Historic Non-Chalcedonian Christians (such as Coptics, Syriac, other Oriental Orthodox churches, Nestorians, etc.) who trace their roots to before c. AD 500 ARE included because:
  • they were organic schisms of the Great Church: they affirmed the common heritage except certain aspects of Christology
  • they never denied the divine hypostasis of Christ but disagreed only on the relation between the divine nature and the human nature of Christ (see Christological comparison chart)
  • they baptized in the name of the Father, the Son, and the Holy Spirit
• Non-Nicene or non-Chalcedonian restorationist movements that started after c. AD 500 such as LDS, Jehovah's Witnesses, Unitarians, Oneness Pentecostals, are NOT included because unlike Protestants (who also started after AD 500), they repudiated the core beliefs of the Great Church in one or more of the following ways:
  • deny the orthodoxy of the Great Church by labelling it the "Great Apostasy" which they dated to happen very early (1st to early 2nd century): LDS reason, JW reason
  • deny the divine hypostasis of Jesus (see the Unitarian narrative)
  • baptize only in the name of Jesus (Oneness Pentecostal)

Criteria for individual inclusion

Considering this congregation involvement statistics (thanks to @OneGodTheFather for the discussion), why are non-practicing Catholics included while the high-involvement JW/LDS members do not even count in the denominator?

This is because the purpose of this Q is to measure whether the Latin Church (later known as the Roman Catholic Church) has always been the church which most orthodox Christians choose to teach the most "correct" doctrines about Christianity compared to other valid descendants of the Great Church. The numbers should approximate the number of those who would answer "Yes" to this survey question:

Regardless of your level of faith in Jesus, your participation in church, the church in which you were baptized, how certain you are of the correctness of your church's doctrines, or the church you are attending (eg. if you are attending the church for family reason, not out of conviction), which denomination would you choose as the one that teaches the most correct Christianity?

Most non-practicing Catholics and C & E Catholics don't go to church more often out of laziness, backsliding, or agnosticism. They don't outright deny the authority of the Catholic church to teach the right doctrines even though they may not agree 100%. That is why they are included in the numerator.

Most non-practicing Christians and most of the "Nones" also don't go to church for the same reason, but when asked "which denomination would you most trust to teach the right doctrines of Christianity should you be a practicing Christian again" would STILL be able to choose one of the denomination as the one they would most likely trust over the others, even though they could be in the process mulling over whether to go to another religion. Until they decide to practice a non-orthodox form of Christianity (by going LDS, for example) or to practice another religion, they are still included in the denominator.

Answer 1

Your question assumes that the church founded in Rome was the Roman Catholic Church that it is now. During at least the first 400 years of Christianity, the Bishop of Rome was just another bishop - the universal church was not governed by one person (ie the bishop of Rome or the bishop of anywhere else), but instead by consensus among the different bishops (ie the Church Fathers) in the different cities of the empire. The Roman church, because of its size and resources, but also because of its preeminence as the capital of the empire, slowly took on more authority.

By the time Christianity was legalized by Constantine in the late 4th century AD, the catholic church (that is the "universal church", which is what catholic means) was governed by the churches thought to have the most importance, namely: Jerusalem, Alexandria, Rome, Antioch, and Constantinople. This is attested to by the Nicean council and the following general church councils in the next 200 years.

We can say safely that therefore, at least for the first 400 years or so, the Roman church only shared rule over the church, and people would not have considered themselves to be 'Roman Catholic', as the nomenclature wasn't in use yet, and the idea of an exclusively Roman run church was anachronistic.