Let us assume a group divided into two sub-groups in conflict. We also assume that each combination of two members of the group has friendship if they belong to the same sub-group, while it has hostility if they belong to the different sub-groups. Let $N$ be the number of all members in the group. Let $x$ be the number of all members belonging to a sub-group. Then, the total number of hostility between the members in the group is $x(N-x)$. Let $y$ be the hostilities ratio to all the “relations” in the group, then
y=¥frac{x(N-x)}{_{N}C_{2}}=¥frac{2x(N-x)}{N(N-1)}
Only when $¥frac{N}{2}-¥sqrt{N}<x<¥frac{N}{2}+¥sqrt{N}$, $y$ is more than 1/2. If $N$ is 10,000, $y$ is more than 1/2 only when 4,900<x<5,100. That is to say, if $N$ is sufficiently large, $y$ is more than 1/2 only when the group is divided into almost right halves. We may expect that in most cases there are the majority and the minority when a group is divided into two sub-groups. Thus, we assume that $x$ will emerge with equal probability between 0 and $N$. Let $P$ be the expected ratio of hostilities of the relations, then,
P=¥frac{1}{N+1}¥sum_{x=0}^N ¥frac{2x(N-x)}{N(N-1)}=¥frac{1}{3}.
Therefore, we may assume that in most cases we will find more friendship than hostilities in a social group.
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