Papers in Physics, vol. 6, art. 060004 (2014)

Received: 3 August 2014, Accepted: 3 August 2014
Edited by: G. Martinez Mekler
Licence: Creative Commons Attribution 3.0
DOI: http://dx.doi.org/10.4279/PIP.060004

www.papersinphysics.org

ISSN 1852-4249

Commentary on “Critical phenomena in the spreading of opinion
consensus and disagreement”

Franco Bagnoli1∗

The authors of Ref. [1] study a variation of the
voter model in which the neighbors of a cluster of
agents agree or disagree with the nearest member
of the group according with the agreement inside
the group.

The article is interesting and well written. The
authors show that the phase transitions towards the
full consensus obey definite scale relations.

I have some points that I think should be consid-
ered by the authors. The first one is about Fig 1 in
their paper. For pD = pC = 1, the system presents
three absorbing states: full consensus “black”, full
consensus “white” and maximal disagreement, i.e.,
staggered “black-white”. It seems from the figure
that the system reaches the “black” absorbing state
at a time about 2300 and 4700, and the staggered
one at time about 7500. However, in all these cases
the presumed absorbing state is abandoned. This
is surely due to the fact that what is shown is only
a portion of the lattice; the figure is misleading and
should be replaced with a picture of the whole lat-
tice, where the “annihilation” of the random walk-
ers corresponding to the boundaries of the clusters
could be observed.

The second point is about the correspondence
with annihilating random walks. It seems to me
that in one dimension for pC = pD = 1, the dynam-

∗E-mail:franco.bagnolI@unifi.it

1 Department of Physics and Astronomy and CSDC,
University of Florence, via G. Sansone 1 50019 Sesto
Fiorentino, Italy.

ics of the model corresponds to that of annihilat-
ing random walkers, like in the voter model, except
that in this case there are two types of walkers that
do not annihilate among themselves. Let me call
these two walkers types L and R. The portion of
the lattice between two L corresponds to the pat-
tern (10)* (odd rows black, even-rows white), that
between two R is a pattern (01)* (even rows black,
odd-rows white), that between one L and one R is
0* and that between one R and one L is 1*. R
and L can cross, two L or two R annihilate. If this
correspondence is true, one should be able to inter-
pret the scaling laws in the context of annihilating
random walks. For pC = pD different from 1, one
might find some correspondence with branching an-
nihilating random walks and directed percolation.

The final concern is about the generalization of
the rule to non-regular lattices. Social networks
are surely not regular, and often show a broad dis-
tribution of connectivity. How could the rule be
generalized to these cases?

[1] A Chacoma, D H Zanette, Critical phenom-
ena in the spreading of opinion consensus and
disagreement, Pap. Phys. 6, 060003 (2014).

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