A relational operator indicating "succeeds or is similar to" in ordered sets and preference relations.
Examples
Comparing sequences or series
a_n \succsim b_n \text{ for all } n \geq N
Ordering relation in partial orders
x \succsim y \text{ implies } f(x) \geq f(y)
Preference relation in economics
A \succsim B \text{ means A is preferred to or indifferent to B}