I suspect that one part of why hearing half a conversation is more annoying has to do with the intermittent nature of half a conversation. Whenever someone starts talking near me, particularly if they are using a loud voice, I listen for a moment to see if they are talking to me. If they are in a conversation where I an hear both parts it's easier to ignore as it's easy to tell that they are not addressing me. With the stop/start pattern of half a conversation, I think most people are subconsciously triggered to pay attention to see if someone wants to talk to them, every time the local speaker makes a remark.
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I suspect that one part of why hearing half a conversation is more annoying has to do with the intermittent nature of half a conversation. Whenever someone starts talking near me, particularly if they are using a loud voice, I listen for a moment to see if they are talking to me. If they are in a conversation where I an hear both parts it's easier to ignore as it's easy to tell that they are not addressing me. With the stop/start pattern of half a conversation, I think most people are subconsciously triggered to pay attention to see if someone wants to talk to them, every time the local speaker makes a remark.