[Pontiac]

The concept calls for 300 reflective balloons, each 150 metres across, arranged side-by-side to create a 1.5-kilometre-wide mirror in orbit around Mars.

Somehow I just don’t get the concept of balloons in space. Why would you use balloons in space?

If the mirror is in space it does not need to be buoyant.

It also seems to me a balloon would have a convex shape which would disperse light rather than focus it on a specific area.

[verum ago]

maybe they aren't balloons per se, but just inflatable foil mirrors. but right -- why bother with anything inflatable when you can just unfold a big framework/foil mirror

[The_Reader_David]

Unfurling a mirrored surface by filling a balloon with gas is easier and more reliable than unfurling or building a rigid frame to hold a mirrored sheet in
orbit.

Also, the amount of pressure needed to keep the balloon up is miniscule: the balloons could be assembled by fusing flat panels of flexible but relatively inelastic material, so the minimal energy surface would not need to be highly convex as is the case with a balloon made of a single piece of highly elastic material.