Which sense does a social animal actually run its social life on?

Their own approaches, and only in the wild. Blinded crabs initiated significantly fewer social contacts with other crabs than controls did on the beach, while other crabs did not single them out for different treatment. In captivity the effect vanished: blinded and control animals behaved alike. The setting, not the sense, is what decided whether the difference showed up at all.

Animals usually carry several senses and do not use them evenly. For social behavior in particular, one channel may be carrying almost all the load, and the only decisive way to find out is to take that channel away.

Few studies have done it and then followed the animal into its own habitat. Steele and Laidre worked with social hermit crabs, Coenobita compressus, applying opaque material over the eyes to blind individuals temporarily. They then released experimentally blinded animals and non-blinded controls both onto the beach and into captive social settings.

In the wild the blinded crabs initiated significantly fewer social contacts with conspecifics. The asymmetry is the interesting part: they were not differentially targeted by other crabs, so the change is in what the blinded animal does rather than in how it is treated.

In captivity none of it appeared. Blinded and control crabs showed no differences in social behavior at all, which argues that experiments in natural settings are essential to seeing what the loss of a sense actually costs. For a social animal leaning heavily on vision, losing it changes the social life dramatically, and a tank is the wrong place to notice.