I wasn't sure if I should start a new thread on this or just post here, but here are a couple opposing links:

Guerardist Difficulties: http://www.geocities.ws/prakashjm45/guerardistdifficulties.html

"The Cassiciacuм Thesis"—The Apostolic See 'Occupied'
OR The Case Of A Schizophrenic Theology!
A Commentary By Dr. Eberhard Heller
On Rt. Rev. Guerard des Laurier's
"Papa materialiter, non formaliter" Theory
http://www.geocities.ws/prakashjm45/einsicht12.2003.html

Material/Formal Crowd attacks cuм ex... again:
http://betrayedcatholics.com/wpcms/materialformal-crowd-attacks-cuм-ex-again-2/

I have been trying to clean up these various trad positions, as they are mutually exclusive and cannot all simultaneously be correct and be contradictory. I was a sede for the last few years and then thought that I should go about organizing a new conclave, assuming that people thought pope Michael's and others' elections were invalid. That resolved to me supporting pope Michael. However, I realized that sedeprivationism was one of the 4 possible solutions beyond sede vacantism, which prevented a conclave from happening. Hence, I needed to find a refutation to it, because it claimed that somehow the cardinals were "locking up" the papacy, so to speak, and preventing an alternative election.

One comment from the second link: "According to the conception of des Laurier, as published in the Review, Cassiciacuм, Monsignor Wojtyla was legitimately elected pope, pars minor y sanior, because about 10 cardinals created under Pius XII were present".

This states that clearly the first kind of sedeprivationism died out with the last cardinal, and here we might drop considering this theory any further. However, it seems like in a sense there is a "sedeprivationism 2.0" circulating which claims that the novus ordo cardinals materially designate pope elects.

The simple refutation as I otherwise posted was cuм ex Apostolatus Officio which states that elections of heretics shall be null and void, and then one just needs to review the case that these V2 papal claimants were pre-election heretics by their actions. The canon about heretics being automatically deposed is another alternative to show that elections of heretics do not produce material popes but are invalid and a new election is needed.

A third kind of sedeprivationism, I have seen: someone said that Francis is not a material pope, but upon renouncing his Vatican 2 errors, he would become pope. The only sense in which this has merit is in light of, "Cardinal Billot speaks of the principle of convalidation of a papal election, which means that, no matter what defects or cloudiness should exist concerning the pope-elect, he would be pope if the whole Church should recognize him as pope." from: http://www.traditionalmass.org/articles/article.php?id=40&catname=10

I haven't thought of this at much length, because it seems like an extreme hypothetical: Everyone would have to renounce Vatican 2 as a whole, because heretics who believe in Vatican 2 couldn't convalidate a Catholic into a pope. Also, no cardinal, bishop, or Church Universal election could have happened, and we affirm that the latter happened to elect pope Michael. Actually, this would really be sedevacantism-to-conclavism, a kind of spontaneous election by the Church Universal, in a sense, to create a pope in this way. I was just reading an article that indicated that there were three methods of election of a pope: https://en.wikipedia.org/wiki/Acclamation_(Papal_elections)

"... three methods of election were valid. These were, namely, by scrutiny, by compromise, and by acclamation (or 'quasi-inspiration'). This last form of election consisted in all the electors present unanimously proclaiming one of the candidates Supreme Pontiff, without the formality of casting votes. As this was required to be done without previous consultation or negotiation it was looked on as proceeding from the Holy Spirit and hence was also designated 'quasi-inspiration'."

So, that third kind of "sedeprivationism", I think of as such in a sense, because there are "sedevacantists" who will not support a conclave or hold one because they are holding on to this idea that the novus ordo has something to do with Catholicism, when it is a non-Catholic sect that is totally non-Catholic.

Also, I wanted to note that it seems inconsistent for sedeprivationists and sedevacantists to work together. If Francis were to become pope tomorrow for the sedeprivationists, sedevacantists would not accept him as pope, and so as there would be a schism then, there is in a sense a schism now. Sedeprivationism is promoted as a kind of sedevacantism, but it is really in a position of its own, as the SSPX believes that Francis is both formally and materially pope, and sedevacantists believe that he is both not materially nor formally pope. "Sedevacantism" resolves to a conclave, as all prior sede vacantes did.

There are other problems with sedeprivationism (or sedevacantism), which Lucio notes in the first link, like invoking epikeia for "supplied jurisdiction" and for consecrating without papal mandate. This warps the incentive to elect a pope for ordinary jurisdiction and permission to consecrate, and also allows numbers of clergy to multiply which makes a future conclave among these people more difficult. Sedeprivationism is promoted as a "theory", but it's a serious enough theory when it prevents a conclave and clear Restoration of order under a true pope.

Last note: The four possible solutions I've seen to sedevacantism which I will analyze in another post:
1. Sedeprivationism
2. Sedevacantism until the world ends.
3. Hold or support a conclave.
4. "Mysticalist" conclave (a pope is designated as pope by God)
(5. A miraculous unknown unpredictable solution is implemented by God)

I welcome any feedback, but please remind and ask for charity.

Under NO theory whatsoever would Bawden's "conclave" be considered legitimate.  I believe that the vote was decided by his parents and girlfriend.

That's where you are wrong, Ladislaus.  His "conclave" is most definitely legitimate under the theory that the Church is limited to Bawden, his parents, and his girlfriend.   :roll-laugh2: :roll-laugh2:

You could make a more convincing argument that the freaking Archbishop of Canterbury has any claim to anything than His Midwesternness. Bawden has NOTHING to support him.

David Bawden has about as much credibility as Gregory XVIII the current palmarian pope.