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We study a model of binary decision making when a certain population ofagents is initially seeded with two different opinions, `$+$' and `$-$', withfractions $p_1$ and $p_2$ respectively, $p_1+p_2=1$. Individuals can reversetheir initial opinion only once based on this information exchange. We studythis model on a completely connected network, where any pair of agents canexchange information, and a two-dimensional square lattice with periodicboundary conditions, where information exchange is possible only between thenearest neighbors. We propose a model in which each agent maintains twocounters of opposite opinions and accepts opinions of other agents with a powerlaw bias until a threshold is reached, when they fix their final opinion. Ourmodel is inspired by the study of negativity bias and positive-negativeasymmetry known in the psychology literature for a long time. Our model canachieve stable intermediate mix of positive and negative opinions in apopulation. In particular, we show that it is possible to achieve close to anyfraction $p_3, 0\leq p_3\leq 1$, of `$-$' opinion starting from an initialfraction $p_1$ of `$-$' opinion by applying a bias through adjusting the powerlaw exponent of $p_3$.

Stable target opinion through power law bias in information exchange