LetRbe a linear order on a setZ= {x, y,…} ofnobjects. LetDmandD(t) be systems of paired comparisons onZsuch that in every one of the pairs withxRythe systemDmcontains an observed proportionp= 0, 1/m,…, 1 of choices forxoverywhileD(t) contains a probability of choosingxoveryas given by a choice theory (t) which also specifiesR.For systemsD1a circularity index is proposed as an alternative to Kendall's and Slater's consistency indices. Some properties of these three indices are investigated in the sets of all possibleD1for some smalln.If m>1,Dmmay be more or less compatible withD(t) and also give rise to aD1, estimatingR.It is argued that the compatibility ofDmwithD(t) may be regarded as an index of theexternalconsistency of D1, with respect toRwhich is to be distinguished from its circularity orinternalconsistency. This distinction is corroborated by computer simulations of paired comparisons under Thurstone's case V model. The correlations between the three circularity indices and four indices of external consistency are essentially zero. Finally, the bearing of assessing circularity to the assessing and testing of the (in)transitivity of data systems is indica