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In this work we study the opinion formation in a voter-like model defined ona square lattice of linear size $L$. The agents may be in three differentstates, representing any public debate with three choices (yes, no, undecided).We consider heterogeneous agents that have different convictions about theiropinions. These convictions limit the capacity of persuasion of the individualsduring the interactions. Moreover, there is a noise $p$ that represents theprobability of an individual spontaneously change his opinion to the undecidedstate. Our simulations suggest that the system reaches stationary states forall values of $p$, with consensus states occurring only for the noiseless case$p=0$. In this case, the relaxation times are distributed according to alog-normal function, with the average value $\tau$ growing with the latticesize as $\tau\sim L^{\alpha}$, where $\alpha\approx$ 0.9. We found a thresholdvalue $p^{*}\approx$ 0.9 above which the stationary fraction of undecidedagents is greater than the fraction of decided ones. We also study theconsequences of the presence of external effects in the system, which modelsthe influence of mass media on opinion formation.

Role of noise and agents' convictions on opinion spreading in a three-state voter-like model