Chakraborty and Harbaugh (2010) prove the existence of influential cheap talk equilibria

in one sender one receiver games when the state is multidimensional and the preferences of

the sender are state-independent. We show that only the babbling equilibrium survives the

introduction of any small degree of uncertainty about the sender’s preferences in the spirit

of Harsanyi (1973). None of the influential equilibria are robust to this kind of uncertainty.