The simple answer
Any balloon can be pumped once, twice, or zero times, and there is no limit to the number of balloons you can pump up.
Why we designed it that way
Balloon's pump system was designed with elements from the multivoting decision making method (reduce and prioritize a list of ideas) and the approval voting system (no limit on the number of pumps).
Flight participants have no limit on the number of balloons they can pump up. Limiting pumps would potentially prevent flight participants from expressing their support for alternatives across all balloons (responses) submitted on a flight. This would limit the group's understanding of the true distribution of sentiment, which may be important in some contexts.
We do, however, limit the number of pumps per balloon, to two. This limitation was designed to allow participants to be more expressive in the way they show approval while ensuring the approval scale stays simple.
Here are a few resources on the voting systems mentioned above.
Tague, Nancy R. (2005) What is Multivoting? Retrieved from https://asq.org/quality-resources/multivoting
Burgman, Mark A., & Regan, Helen M., & Maguire, Lynn A., & Colyvan, Mark, & Justus, James, & Martin, Tara G., & Rothley, Kris. "Voting Systems for Environmental Decisions" Conservation Biology, 28(2), 326. doi: 10.1111/cobi.12209
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