3 research outputs found
Two opinions dynamics generated by inflexibles and non-contrarian and contrarian floaters
We assume a community whose members adopt one of two opinions or .
Each member appears as an inflexible, or as a non-contrarian or contrarian
floater. An inflexible sticks to its opinion, whereas a floater may change into
a floater of the alternative opinion. The occurrence of this change is governed
by the local majority rule: members meet in groups of a fixed size, and a
floater then changes its opinion provided it is a minority in the group.
Subsequently, a non-contrarian floater keeps the opinion as adopted under the
local majority rule, whereas a contrarian floater adopts the alternative
opinion. Whereas the effects of on the one hand inflexibles and on the other
hand non-contrarians and contrarians have previously been studied seperately,
the current approach allows us to gain insight in the effect of their combined
presence in a community. Given fixed proportions of inflexibles for the two opinions, and fixed fractions of contrarians
among the and floaters, we derive the update
equation for the overall support for opinion at time , given
. The update equation is derived respectively for local group sizes 1, 2
and 3. The associated dynamics generated by repeated local updates is then
determined to identify its asymptotic steady configuration. The full opinion
flow diagram is thus obtained, showing conditions in terms of the parameters
for each opinion to eventually win the competing dynamics. Various dynamical
scenarios are thus exhibited, and it is derived that relatively small densities
of inflexibles allow for more variation in the qualitative outcome of the
dynamics than higher densities of inflexibles.Comment: 45 pages and 13 figure