OOAD clarification on multiplicity or cardinality

I am confused about the cardinality/ multiplicity when designing class diagrams. My main confusion is when to represent 1---* relationship. For ex in case of passenger and seat classes, passenger will be allotted to one seat, where as the seat can be allotted to one passenger at A POINT IN TIME but over a period of its existence it can be allotted to many passengers.

So should the seat--->passenger be 1-1 or 1-*?

Let's summarize:

• At one precise moment in time:
  • each Passenger will be allocated to exactly one Seat (1). Open question: does the Passenger exists already before the allocation (i.e. 1 or 0..1) ?
  • each Seat can have one allocated Passenger but it may remain empty (so 0..1)
• Over their lifetime:
  • each Passenger can have been allocated to many seats (one per flight)
  • each Seat can have had many Passenger allocated.

Conclusions: the relation between Seat and Passenger is *-* (many to many)