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Consortium imperii is a Latin term dating from the Roman dominate, denoting the sharing of imperial authority between two or more emperors, hence designated as consors imperii, i.e. "partner in (exercizing) imperium" - either as formal equals or in subordination (the junior is then often the senior's designated heir -not necessarily the natural one- and successor). The purpose can be either to share the burden of government and/or to ensure smooth succession, as rivalry at these moments was a major threat to the stability of the Empire.

Although in political reality adoption was an alternative technique to aim for the same result in terms of succession (succeeding to produce one -genealogically 'false' but politically satisfactory dynasty of so-called adoptive emperors), constitutionally this was a horror as the republic had never been abandoned in law, so monarchical succession in the principate, however realistic, was officially out of the question, regardless of the trappings during the dominate - designation could at least be justified by qualitative criteria.

• An early case of one emperor, remaining 'sole sovereign' in charge, but designating one junior and successor, was Marcus Aurelius (reigned 161-180AD) who designated Lucius Verus - but on his death his son Commodus, which he justly wanted to pass by, managed to seize the throne.
• Emperor Diocletian attempted an elaborate system with four emperors (two seniors styled Augustus, each with a junior styled Caesar), called the Tetrarchy. Revolutionary was the notion that each was to be simultaneously in permanent charge of one quarter of the empire, not just sharing in central government. The experiment did not live up to its promise, as succession was not smoothened but contention multiplied, so the quadruple emperorship was abandoned - not the quarters, which remained as administrative and military divisions called praetorian prefecture, as did the lower level, called diocese, and the smaller size (and larger number) of provinces.
• The Roman empire was soon to be split for good, but in TWO halves, West (declining) and East (richer, so ascending), each under a sovereign emperor, in charge of two praetorian prefectures each, with or without a partner in his government.
• Both the notion of 'partnership' (often described as 'associate rulers') and Diocletian's titulature, but mainly versed in Greek (Sebastos for Augustus, a literal translation), became quite common is the eastern empire, i.e. Byzantium, which lasted a further millennium after the fall of the western ('true' Roman) empire.

However, the August titles were to lose their imperial meaning in Byzantium, as there was an 'inflation' (as with court ranks, usually not reserved for the imperial family) through multiplication of incumbents, mainly within the imperial dynasty; in time an impressive scala of pseudo-imperial titles developed, variations on the Diocletian theme, such as protosebastos, pansebastos.

Indeed, such titles were even bestowed as a reward or other diplomatic manoeuvre on princes of allies - even grugdingly conceded on proud enemies to be kept at distance at any cost. Obviously none of these had a real association with the imperial throne of the second Rome, but the awarding of the (meanwhile very devaluated) title caesar to invaders -mainly on the Balkans, Slavonic and Bulgarian- gave rise to its corruption to czar, a style thus better rendered by king than by emperor, hence logically abandoned in official use -in favor of imperator and autocrat, both expressing their claim to be the 'third Rome' as heir to the Byzantine leadership of orthodoxy- by the very Russian monarchs (formerly grand dukes of Moscovia) who in common language are generally named Tsars, who in fact only used this style for lesser principalities merged into the imperial Russian crown.

• Pauly-Wissowa (in German)

• Co-dictatorship