Seven traders, red or blue hats, win seven times in eight

Seven traders each get a red or blue hat decided by an independent fair coin. Each sees the other six hats but not their own. At a signal, every trader simultaneously either says "red," says "blue," or passes. The team wins if at least one person guesses and every guess made is correct; a single wrong guess loses.

If just one person guesses and the rest pass, the team wins with probability $1/2$. That feels like a ceiling.

Devise a strategy that wins with probability $7/8$.