We propose an opinion model based on agents located at the vertices of a regular lattice. Each agent has an independent opinion (among an arbitrary, but fixed, number of choices) and its own degree of conviction. The latter changes every time two agents which have different opinions interact with each other. The dynamics leads to size distributions of clusters (made up of agents which have the same opinion and are located at contiguous spatial positions) which follow a power law, as long as the range of the interaction between the agents is not too short; i.e., the system self-organizes into a critical state. Short range interactions lead to an exponential cutoff in the size distribution and to spatial correlations which cause agents which have the same opinion to be closely grouped. When the diversity of opinions is restricted to two, a nonconsensus dynamic is observed, with unequal population fractions, whereas consensus is reached if the agents are also allowed to interact with those located far from them. The individual agents' convictions, the preestablished interaction range, and the locality of the interaction between a pair of agents (their neighborhood has no effect on the interaction) are the main characteristics which distinguish our model from previous ones.