The common element among Rajagriha, Vaishali, and Pataliputra is that they are all places where Buddhist Councils were held.

Option 1 suggests that the Pali canon of the Sthaviravadins was compiled in these places. However, this is incorrect as the compilation of the Pali canon happened at a different location called the First Buddhist Council held at Rajagriha, not in all three places mentioned.

Option 2 implies that Ashokan Major Rock Edicts were found in these places. Although Ashokan Major Rock Edicts were found in various locations across India, it does not establish a common element between Rajagriha, Vaishali, and Pataliputra.

Option 4 states that these places are associated with the compilation of Buddhist canons of the Mahasanghikas. However, this is not accurate as the Mahasanghikas were a different Buddhist sect and were not directly involved in the compilation of canons at these places.

Therefore, the correct answer remains option 3, which states that all three places are where Buddhist Councils were held. These councils were significant events in the development and spread of Buddhism, where Buddhist teachings and texts were discussed and compiled.