Online Appendix: Sensitivity of the Rate of Exchanging Negative Evaluations to Status Differentiation of a Group
For analytic tractability in the analysis to follow, a case in which there is a group leader and a set of other members of approximately equivalent status will be considered. The super- or subscripts L and G will refer to the high status member and other lower status members, respectively. In this binary case, the sensitivity of the equilibrium rates to status differentiation in the group is obtained as follows:
where
![]()
![]()
![]()
(A.1)
Where, ![]()
The initial rates of sending negative evaluations as a function of the member's status can be written as:
= c
and
= c
, 0 £ q £ 1.
where sq is a form for the rate of sending evaluation as a function of sender status that keeps sL and sG within (0,1) and SsI=1.
For the sensitivity of the initial rate of sending evaluations in the team to status differences:
Let ∆ = sL - sG
= c1
= c
,
= c1 (1-sL ) θ = c
,
so
= c
< 0, since
< ![]()
for 0 < ∆ < 1 and 0< q <1
This implies that the initial rate of sending negative evaluations in the team will be decreasing with increases in status differentiation.
Considering the sensitivity of the total equilibrium rate of sending negative evaluations to status differentiation,
is first expressed as a function of
and
:
b(
-
) = -a(β
)
(b + aβ)
= a
+ b![]()
so:
= ![]()
Therefore:
= (β + 1 )![]()
= c2
> 0,
where c2 =
c1 provided that a > b
, which is only a serious restriction when D is close to 1 (i.e., when, sL = 1.0, sG = 0).
This implies that the equilibrium rate of sending negative evaluations in the team will be increasing with increases in status differentiation.
The sensitivity of the equilibrium rate of negative evaluations to the initial rate can be given by:
= c2
> 0
and:
= (β - 1)
> 0
with: a1 > b1 ![]()
Therefore,
> 0 ∎