We derive a general form of Tornqvist multilateral (transitive) place to place index numbers and a new variant of regression methodology for imposing transitivity while minimally adjusting the initial system of bilateral index comparisons. We show that when several levels of item aggregation are to be published in a system of Tornqvist interarea parities, the adjusted, transitive Tornqvist parities at each level of aggregation preserve the aggregation rule in the unadjusted data. Finally, the method incorporates characteristics-based, hedonic quality adjustment as an integral feature. We apply the method to a subset of commodity price and expenditure data for the 44 areas of the United States covered by the Consumer Price Index. In closing, we also discuss an application of the method that makes time series and geographical comparisons consistent with one another, and note that it permits decentralization of calculation in a way that may have distinct advantages for compiling international price comparisons.\“