Isn't the ultimate socially-optimal answer for the "guess 2/3rds of the average" game be to convince everyone to answer 0? Because 2/3rds of 0 is 0, so everyone

Isn't the ultimate socially-optimal answer for the "guess 2/3rds of the average" game be to convince everyone to answer 0? Because 2/3rds of 0 is 0, so everyone wins.