T cells orchestrate pathogen-specific adaptive immune responses by identifying peptides derived from pathogenic proteins that are displayed on the surface of infected cells. Host cells also display peptide fragments from the host’s own proteins. Incorrectly identifying peptides derived from the body’s own proteome as pathogenic can result in autoimmune disease. To minimize autoreactivity, immature T cells that respond to self-peptides are deleted in the thymus by a process called negative selection. However, negative selection is imperfect, and autoreactive T cells exist in healthy individuals. To understand how autoimmunity is yet avoided, without loss of responsiveness to pathogens, we have developed a model of T-cell training and response. Our model shows that T cells reliably respond to infection and avoid autoimmunity because collective decisions made by the T-cell population, rather than the responses of individual T cells, determine biological outcomes. The theory is qualitatively consistent with experimental data and yields a criterion for thymic selection to be adequate for suppressing autoimmunity.