What rules? Nicea said a bishop should be elected by other bishops. That fell into disuse. Even laymen voted at times.Anti-Popes are false claimants to the Chair of Peter. Their election as “Pope” is not recognized as canonically valid and hence they are what we might call “pretenders”, and practically anyone can always claim to have been “elected”. They always try to exercise their “office” as “Pope” in defiance of the legally and validly elected Pontiff. Since they were never validly elected, and Papal elections are governed by rules and procedures which must be followed to be legitimate, hence they are not Popes in any real sense of the word. Hence, there is no conflict with the unity and apostolicity of the Catholic Church, simply because the Church can produce a complete list of all legitimate, validly elected Popes from St. Peter to the present.
Antipope Ursicinus - Wikipedia
Liberius died on 24 September 366. The upper-class partisans of Felix threw their support to Damasus, but the opposing supporters of Liberius, the deacons and laity, supported Ursicinus; the two were elected simultaneously, in an atmosphere of rioting. Supporters already clashed at the beginning of October. Such was the violence and bloodshed that the two praefecti of the city were called in to restore order, and after a first setback, when they were driven to the suburbs and a massacre of 137 was perpetrated in the basilica of Sicininus (as cited in Ammianus Marcellinus), the prefects banished Ursicinus to Gaul. There was further violence when he returned, which continued after Ursicinus was exiled again.
Church historians, such as Jerome and Rufinus, took the part of Damasus. At a synod in 378 Ursicinus was condemned and Damasus exonerated and declared the true pope. The former antipope continued to intrigue[vague] against Damasus for the next few years, and unsuccessfully attempted to revive his claim on Damasus's death. Ursicinus was among the Arian party in Milan, according to Ambrose (Epistle iv).
A decree of 502 under Pope Symmachus ruled that laymen should no longer vote for the popes and that only higher clergy should be considered eligible.
Things got quite crazy in the Crescentii era when Popes and Antipopes were installed using irregular methods.
Papal selection before 1059 - Wikipedia
Otto I's successor, Otto II, was impelled to conquer Rome in 980 to depose Antipope Boniface VII and install his preferred candidate Pope John XIV (983-4), without even feigning an election.[20]
Pope John XV, the candidate of the Roman nobles upon the death of Otto II, did not survive long enough to be deposed by Otto III, who engineered the election of Pope Gregory V upon reaching Rome in 996.[20] However, Gregory V could not remain on the throne once Otto III headed back for Germany, and the Romans replaced him with Antipope John XVI temporarily until Otto III could return.[20] Otto III reinstalled Gregory V and secured the election of Pope Sylvester II (999-1003) upon his death, only to die himself shortly thereafter, allowing the Roman nobles to choose 3 popes of their own.
Things were not always as orderly as we might like to think. Whoever had the bigger army seems to be who got to decide who the Pope was and who the Antipope was. It looks to me that whoever won got to declare the loser an Antipope -- and what the rules were.
In 1119 most of the Cardinals were in Rome, but 10 Cardinals (6 Cardinal-bishops and 4 Cardinal-deacons) in Cluny voted anyway, with the idea they'd ask the whole College of Cardinals later.
1119 papal election - Wikipedia
The cardinals attending the death Mass of Gelasius II in Cluny in late January 1119 were divided over whether his successor should be elected on the spot (as was permitted by In Nomine Domini) or whether they should return to Rome and hold the election with the full College of Cardinals; although the cardinals proceeded with the election immediately, they agreed that they would submit their choice to the entire College thereafter.[3] The cardinals who accompanied Gleasius II to Cluny are known from the Liber Pontificalis associated with "Pandulphus" (either Pandulf of Pisa or Pandulf of Lucca), from the charter from Cluny, and from the chronicle of Ordericus Vitalis.[3]
Although the contemporary accounts diverge on many points, it is clear across them that the two candidates who emerged were Guy and Pontius of Cluny, both named as candidates by the late pontiff.[4] The account of Gaufrid, prior of Vigois, relates that Gelasius II had preferred Pontius and predicted his election; Pontius was a far more conciliatory candidate, likely to negotiate a solution to the Investiture Controversy.[4] Two accounts in particular—those of Bernard of Carrion and Gaufrid of Vigois—detail the election of Guy, emphasizing the importance of his known confrontational stance towards Henry V (having previously excommunicated him) and his powerful family, the Salian dynasty.[4]
At the time of his election as Callixtus II, Guy was in the company of his militia, which began rioting when it learned of his election, breaking into the election chamber and violently disrobing him, according to the Historia Compostelana.[5] Callixtus II proceeded to Sutri, the location of his opponent, Antipope Gregory VIII, appointed by Henry V, and laid siege to the city for eight days until Gregory VIII was handed over to him; Callixtus then imprisoned Gregory VIII in the Septizodium, from which the papal claimant was moved from monastery to monastery before his death in 1137.
I've little doubt if Antipope Gregory VIII had had a better army, it would have been Callixtus II who got the title Antipope, and Gregory could have pointed out how the election was irregular.