Three studies

Jaimie Krems and Jason Wilkes
Four people maximum
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Nicolas Fay, Simon Garrod, and Jean Carletta
Five people maximum
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David Gurteen
Four people maximum; five at a push
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Jaimie Krems and Jason Wilkes

Research conducted by Jaimie Krems, an assistant professor of psychology at Oklahoma State University, and Jason Wilkes, a graduate student in evolutionary cognitive psychology at the University of California, reveals that the maximum number for a conversation is four people.

Here is an abstract of their paper, Why are conversations limited to about four people? A theoretical exploration of the conversation size constraint, published in Evolution and Human Behavior:

It is genuinely difficult to sustain a casual conversation that includes more than four speakers. Add a fifth speaker, and the conversation often quickly fissions into smaller groups.
Termed ‘the dinner party problem,’ this four-person conversation size limit is believed to be caused by evolved cognitive constraints on human mentalizing capacities. In this view, people can mentally manage three other minds at any one time, leading to four-person conversations. But whereas existing work has posited and empirically tested alternative accounts of what drives the conversation size constraint, to our knowledge, no work has explored the question of why this capacity is specifically four.
In this theoretical paper, we (a) review research demonstrating this cognitive constraint in sociality, (b) review the relevant working memory literature, which has explored the “why four” question at some length, and (c) we begin to pose possible answers to our specific social “why four” question. Using simple mathematical models of small-scale sociality, which we imbue with evolutionarily-relevant content, we present one novel possible explanation for the four-person conversation size constraint.

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Why four?

Pairs (or “dyads,” in psychology research parlance) are the essential building blocks of a society. Let’s imagine a conversation between four hypothetical humans: you, Chris, Pat, and Taylor. In a four-person conversation, there are six possible pairs of people who can be talking to one another at once. you and Chris, you and Pat, you and Taylor, Chris and Pat, Chris and Taylor, and Pat and Taylor. That’s three pairs you’re part of, and three pairs you’re not. Essentially, you have a role in influencing half of the possible conversations that could be happening in that group.
If there are three people in the conversation, there are three possible pairs, only one of which excludes you. If there are five people, there are 10 possible pairs, and the majority—six—don’t include you, which makes it harder to get your point across.

Source: Why can’t more than four people have a conversation at once? by Corinne Purtill, on Quartz, citing Krems’ and Wilkes’ research

Nicolas Fay, Simon Garrod, and Jean Carletta

Current communication models draw a broad distinction between communication as dialogue and communication as monologue. The two kinds of models have different implications for who influences whom in a group discussion.
The experiments reported in this paper show that in small, 5-person groups, the communication is like dialogue and members are influenced most by those with whom they interact in the discussion.
However, in large, 10-person groups, the communication is like monologue and members are influenced most by the dominant speaker.
The difference in mode of communication is explained in terms of how speakers in the two sizes of groups design their utterances for different audiences.

Source: Group Discussion as Interactive Dialogue or as Serial Monologue: The Influence of Group Size, by Nicolas Fay (University of Glasgow), Simon Garrod (University of Glasgow) and Jean Carletta (University of Edinburgh).

David Gurteen

David Gurteen
David Gurteen (pictured) is a professional speaker and conversational facilitator. He is the founder of the Gurteen Knowledge Community, a global learning community of more than 22,000 people in 160 countries; the author of Conversational Leadership, an online book; and the originator of the Knowledge Café, in which people come together for unfacilitated conversations on a topic of mutual interest. Over the course of 15 years, David has facilitated Knowledge Cafés in more than 30 countries.
The Knowledge Café process
In his article Interactive Dialogue or Serial Monologue: The Influence of Group Size on conversation, David reveals that the ideal group size for unfacilitated interactive conversation is four people. If not four, then five is OK but three is better.

Best: four people.
Second best: three people.
Maximum: five people.

David has discovered that the conversation does not work so well when the group consists of more than five people. One or two people are likely to dominate; the conversation will probably break into two, even three; someone may be excluded from the conversation, and group energy will be low.

To be continued as further information comes to light.