Upon becoming a colony in 80BC Pompeii adopted and followed the Lex Iulia Municipalis, a law which set regulations for Italian municipalities, including how they were governed. This kept Pompeii in line with the Roman government and therefore the Ordo Decurionem, has parallels with the capital.
WHAT WAS THE ORDO DECURIONEM?
The Ordo Decurionem was the Pompeian local government, it was formed of worthy officials and councilors and these were appointed by the people of Pompeii by public election.
WHO WAS A MEMBER OF THE ORDO?
The Pompeian local government was formed of decuriones who had been elected as magistrates in the past or who had been admitted into the local government by the Ordo for honorary purpose or to make up numbers if the Ordo was lacking members. The electoral positions can be looked at hierarchically; the higher the position one held, the wider their responsibilities were and therefore this greater prestige made them more socially prominent. There were three temporary (yearly) positions which one could be elected as; aedile, duovir or duovir quinquenallis. Other municipalities, such as Capua and Canusium , normally had around 100 decurions in their Ordo. However, the number varies depending on the size of the colonial city and therefore it is estimated that Pompeii had 80 to 100 members.
Aedile was a yearly position. There were two aediles in office at one time and, once aedile, one would have the opportunity to be part of the Ordo, a decurion, for life, assuming that the duoviri quinquenalles deem them worthy to stay in the local government during the census taken every 5 years.
The position of duovir was equivalent to consul in Rome and two of these senior magistrates would be elected per year. In order to become duovir one must have been an aedile previously and therefore there were less people who were eligible.
Every five years the duoviri quinquennales would be elected into office, this was arguably the highest achievable position in Pompeian government. They would take the place of the duoviri that year and, following the pattern for the lower positions, one must been duovir previously and therefore aedile also. It was likely that one would have been duovir multiple times before becoming duovir quinquenallis.
One could be admitted into the Ordo as an honorary member. This was usually the case when someone had done a deed which would make them eligible to enter into the Ordo Decurionem, but were not eligible due to their age or lowly birth. This was usually children, being granted membership for great benefactions. We can see an example of this when looking at the inscription of the temple of Isis
CIL X 846
Numerius Popidius Celsinus, son of Numerius, restored the Temple of Isis from the ground up, after it had been totally destroyed by an earthquake. The Town Council, coopted him into their assembly when he was only six years old, (and) without charge, in consideration of his generosity.
We can see here that a six year old boy was granted membership ‘without expense’ as he had paid for the restoration of the Temple of Isis with his own money, a great benefit to the society of Pompeii. Note that the inscription here states without expense, which confirms that regular members of the Ordo would have been fee paying.
In some circumstances decurions were elected into office in an extraordinary way. For example when a magistrate died during office someone would be elected to take their place. In the republican period these stand-ins were called interreges and this appears in some Pompeian inscriptions, which proves that someone would have taken the deceased’s place during the period between death and the yearly re-election.  In the imperial period, however, the Lex Petronia was been put in place, regulating the elections for extraordinary magistracies and therefore the name for the magistrate became praefectus iure dicundo ex decurionem decreto lego Petronia.
The Emperor and Imperial Family-
There were two cases when an Emperor would be elected into office in Pompeii; an Imperial prince would be elected once they were the apparent heir or, if there was a crisis in the municipality, the Emperor or member of the Imperial family was likely to be appointed. 
23-25BC – MARCELLUS – Patronus Coloniae
AD 20-21 – DRUSUS – Duovir Quinquennalis
AD 23 & 31- NERO (GERMANICUS’ SON) – Duovir
AD 33-34 – CALIGULA – Duovir
AD 54-55 – NERO – (likely to have been) Duovir 
It is worth noting that Caligula while Emperor also officiated as duovir quinquennalis in AD 40. This was the only known time a ruling Emperor appeared as quinquennial duumvir. As he had already appeared in office once he was the established heir, we can assume that this was due to some kind of internal crisis in Pompeii. However, we do not have any evidence for this exactly, or for the details of what the crisis could be. While in office Caligula himself wouldn’t have acted, but a ‘prefect with judicial power’ would have acted on his behalf. Although very uncommon, this position was probably the most desirable.
 Beard,2008: 205