many clustered cells and a single large cell: even clonal populations of cells can have highly variable responses to signals, due to many factors, including intrinsic variations in regulatory protein concentrations [@swain2002intrinsic; @niepel2009non; @sigal2006variability]. These cell-to-cell variations (CCV) can be persistent over timescales much larger than the typical motility timescale of the cell [@sigal2006variability]. CCV has not been addressed in models of collective chemotaxis and it is not clear whether collective gradient sensing is limited by CCV or by stochastic receptor-ligand binding [@malet2015collective; @camley2016emergent; @camley2016collective; @varennes2016collective; @ellison2016cell; @mugler2016limits; @cai2016modeling].

Using a combination of analytics and simulations, we show that unless CCV is tightly controlled, collective guidance of a cluster of cells is limited by these variations: gradient sensing is biased toward cells with intrinsically strong responses. This bias swamps the effects of stochastic ligand-receptor binding. Cell clusters may reduce this error by time-averaging their gradient measurements only if the cells rearrange their positions, creating an unavoidable link between the [*mechanics*]{} of the cell cluster and its [*gradient sensing ability*]{}. As a result, surprising new tradeoffs arise: clusters must balance using motility to follow a biased signal with using motility to reduce error, and compromise between reducing noise and increasing cluster 