Arbitrating between multiple potentially-responsive electronic devices

A first electronic device comprising one or more processors and memory storing instructions that, in response to execution of the instructions by the one or more processors, cause the one or more processors to:

• detect, at a microphone of the first electronic device, a spoken utterance provided by a user;
• detect one or more outputs emitted by one or more additional electronic devices, wherein each of the one or more outputs encodes a timestamp corresponding to detection of the spoken utterance at a respective electronic device of the one or more additional electronic devices;
• extract, from the one or more outputs emitted by the one or more additional electronic devices, the one or more timestamps;
• compare the one or more timestamps to a local timestamp corresponding to detection of the spoken utterance at the first electronic device;
• and
• based on the comparison, cause the first electronic device to either invoke an automated assistant locally or defer to one of the additional electronic devices.

At least one non-transitory computer-readable medium comprising instructions that, in response to execution of the instructions by one or more processors of a first electronic device, cause the one or more processors to:

• detect, at a microphone of the first electronic device, a spoken utterance provided by a user;
• detect one or more outputs emitted by one or more additional electronic devices, wherein each of the one or more outputs encodes a timestamp corresponding to detection of the spoken utterance at a respective electronic device of the one or more additional electronic devices;
• extract, from the one or more outputs emitted by the one or more additional electronic devices, the one or more timestamps;
• compare the one or more timestamps to a local timestamp corresponding to detection of the spoken utterance at the first electronic device;
• and
• based on the comparison, cause the first electronic device to either invoke an automated assistant locally or defer to one of the additional electronic devices.