Non-conservative kinetic exchange model of opinion dynamics with randomness and bounded confidence
Abstract
The concept of a bounded confidence level is incorporated in a nonconservative kinetic exchange model of opinion dynamics model where opinions have continuous values
∈[−1,1]
. The characteristics of the unrestricted model, which has one parameter
λ
representing conviction, undergo drastic changes with the introduction of bounded confidence parametrised by
δ
. Three distinct regions are identified in the phase diagram in the
δ−λ
plane and the evidences of a first order phase transition for
δ≥0.3
are presented. A neutral state with all opinions equal to zero occurs for
λ≤
λ
c
1
≃2/3
, independent of
δ
, while for
λ
c
1
≤λ≤
λ
c
2
(δ)
, an ordered region is seen to exist where opinions of only one sign prevail. At
λ
c
2
(δ)
, a transition to a disordered state is observed, where individual opinions of both signs coexist and move closer to the extreme values (
±1
) as
λ
is increased. For confidence level
δ<0.3
, the ordered phase exists for a narrow range of
λ
only. The line
δ=0
is apparently a line of discontinuity and this limit is discussed in some detail.