Abstract In social insects, workers perform a multitude of tasks, such as foraging, nest construction, and brood rearing, without central control of how work is allocated among individuals. It has been suggested that workers choose a task by responding to stimuli gathered from the environment. Response-threshold models assume that individuals in a colony vary in the stimulus intensity (response threshold) at which they begin to perform the corresponding task. Here we highlight the limitations of these models with respect to colony performance in task allocation. First, we show with analysis and quantitative simulations that the deterministic response-threshold model constrains the workers' behavioral flexibility under some stimulus conditions. Next, we show that the probabilistic response-threshold model fails to explain precise colony responses to varying stimuli. Both of these limitations would be detrimental to colony performance when dynamic and precise task allocation is needed. To address these problems, we propose extensions of the response-threshold model by adding variables that weigh stimuli. We test the extended response-threshold model in a foraging scenario and show in simulations that it results in an efficient task allocation. Finally, we show that response-threshold models can be formulated as artificial neural networks, which consequently provide a comprehensive framework for modeling task allocation in social insects.