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Aggregation of noisy observations involves a difficult tradeoff betweenobservation quality, which can be increased by increasing the number ofobservations, and aggregation quality which decreases if the number ofobservations is too large. We clarify this behavior for a protypical system inwhich arbitrarily large numbers of observations exceeding the system capacitycan be aggregated using lossy data compression. We show the existence of ascaling relation between the collective error and the system capacity, and showthat large scale lossy aggregation can outperform lossless aggregation above acritical level of observation noise. Further, we show that universal resultsfor scaling and critical value of noise which are independent of systemcapacity can be obtained by considering asymptotic behavior when the systemcapacity increases toward infinity.

Universal Behavior in Large-scale Aggregation of Independent Noisy Observations