Given a society consisting of N people, there will be (N2-N)/2 possible dialogue pairs (i.e. subsets of cardinality 2) and 2N-N-1 possible multilogue groups (i.e. subsets of cardinality greater than or equal to 2).
| N | (N2-N)/2 | 2N-N-1 |
|---|---|---|
| 10 | 45 | 1013 |
| 100 | 4950 | 1.27x1030 |
| 1000 | 499,500 | ... |
| 10000 | 49,995,000 | ... |
The dialogue inclusion of society S is defined as the proportion of the possible dialogue pairs which are communicating pairs (i.e. the two members have a common language). The multilogue inclusion of society S is defined as the proportion of the possible multilogue groups which are communicating groups (i.e. all members have a common language).
In order for a society to have a multilogue inclusion of 1, there must be a universal language which is common to all members - although it may still be possible for particular subsets to have 'private' conversations in non-universal languages. However this is not true for dialogue inclusion - imagine a society of 3 (groups of) people A, B and C where A speaks English and French, B speaks English and German, and C speaks French and German. Thus, multilogue inclusion appears to be a better measure of conversational inclusion.
NB: Can we come up with models which penalise private languages? Or models which reward them? Multilogue exclusion - the proportion of the multilogue groups which have a private language wrt the society as a whole? How many languages for a society S whose multilogue exclusion is 1? 2|S|-|S|-1. In other words, 1030 for a society of 100 people! Note that if multilogue exclusion is 1 then so is multilogue inclusion. However, in a monolingual society (or even a perfectly multilingual one where everyone speaks every language) multilogue exclusion will be 0.
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