  Social intelligence in natural and artificial systems is usually measured by
the evaluation of associated traits or tasks that are deemed to represent some
facets of social behaviour. The amalgamation of these traits is then used to
configure the intuitive notion of social intelligence. Instead, in this paper
we start from a parametrised definition of social intelligence as the expected
performance in a set of environments with several agents, and we assess and
derive tests from it. This definition makes several dependencies explicit: (1)
the definition depends on the choice (and weight) of environments and agents,
(2) the definition may include both competitive and cooperative behaviours
depending on how agents and rewards are arranged into teams, (3) the definition
mostly depends on the abilities of other agents, and (4) the actual difference
between social intelligence and general intelligence (or other abilities)
depends on these choices. As a result, we address the problem of converting
this definition into a more precise one where some fundamental properties
ensuring social behaviour (such as action and reward dependency and
anticipation on competitive/cooperative behaviours) are met as well as some
other more instrumental properties (such as secernment, boundedness, symmetry,
validity, reliability, efficiency), which are convenient to convert the
definition into a practical test. From the definition and the formalised
properties, we take a look at several representative multi-agent environments,
tests and games to see whether they meet these properties.
