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8.2.3 Social entropy 8 Multi-agents
The above examples show how different heterogeneous teams can be. One
SOCIAL ENTROPY rough measure of the degree of heterogeneity is the social entropy metric cre-
ated by Tucker Balch. 16 (Entropy is a measure of disorder in a system, espe-
cially in the sense of the Third Law of Thermodynamics. It was also adapted
by Shannon for use in information theory to quantify the amount or quality
of information in a system.) The point of social entropy is to assign a numeri-
cal value for rating diversity (or disorder) in a team. The number should be 0
if all team members are the same (homogeneous). The number should have
the maximum value if all the team members are different. The number of
team members which are different should make the overall number higher.
To compute social entropy, consider a marsupial team R with a mother
robot and three identical (hardware and software) micro-rovers. The formula
for the social entropy, H (R),is: e t

c
X
(8.1) H (R) = e t p i log 2 (p i )
i=1

CASTES There are two types of robots in the team, called castes or c:the mother and
the daughters. Therefore c = . The term p i is the decimal percent of robots 2
1
belonging to caste c i .If i = for the mother, and i = for the daughters: 2

1
(8.2) p 1 = = :25 0
4
3
p 2 = = :75 0
4

Substituting into Eqn. 8.1 (and remembering that log 2 n = log log 10 n ), the so-
2
cial entropy is: 10

c
X
(8.3) H (R) = e t p i log 2 (p i )
i=1
0
= (0 :25log 2 0:25+ :75log 2 0:75)
= (( 0:50)+ 0:31))
(
= 0:81