Animal groups can gather disproportionately more information and often outperform solitary individuals in ecologically important activities. Collective decisions, however, may involve costly mechanisms for reaching a consensus. Nest building is a prime example. In a previous study on foraging for building materials by the ant Temnothorax albipennis, we showed that colonies prefer larger building blocks (bigger sand grains) at all distances but always collect some smaller building blocks too. Walls made of mixtures of big and small grains are stronger and more compact. Here we study colonies with marked individuals to look at the foraging decisions of individuals that underlie the collective outcome for the colony. We found that at short distances some foragers preferred big grains and others small grains. However, at longer distances the proportion of foragers preferring big grains increased, whereas no foragers preferred small grains at the greatest distance. We found no evidence of an effect of individual morphology or foraging experience on preference. At all three distances foragers assessed grains before making a choice and were more likely to choose a big grain as a consequence. This likelihood increased with increasing distance. However, even at the greatest distance ants included small grains in the final wall after their initial preference for big grains. Therefore, we conclude that individual decisions to retrieve small grains are not simply errors. Instead, the construction itself may provide cues for the organization of the foraging activity of individuals into the collective building of an approximately optimal mixed wall by the colony.