Ants are commonly found on peony buds. The buds secrete a sweet liquid that attracts ants. This has led to the false notion that the presence of ants is necessary for peonies to bloom. There is no truth to this urban legend. Peonies consistently bloom in controlled environments where ants are not present.
Is it advantageous for peonies to attract ants? Possibly. The scientific literature contains many examples of mutualism between ants and plants. In typical plant-ant mutualisms, plants provide ants with food or shelter. In return, ants may attack herbivores that feed on the plant, attack competing plants nearby or perform other services for the plant. However, I am not aware of any scientific study of the relationship between peonies and ants.
The typical method of determining the benefit that plants derive from ants is to compare plants with ants and plants with ants removed. However, Removal of ants from peonies in American gardens does not clearly have a negative effect. Why?
The peony most commonly planted in American gardens is the Chinese Peony, Paeonia lactiflora. Garden peonies have been cultivated and bred for their horticultural characteristics. Associations between ants and peonies could be an artifact of selection for horticulture traits, or the association between ants and peonies could have more relevance to wild peonies in their native habitat with the full complement of native pests. Perhaps studies of peonies in their native habitat will offer clues to their interactions with ants.