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Background: During the global pandemic of A/H1N1/California/07/2009 (A/H1N1/Cal) influenza, many governments signed contracts with vaccine producers for a universal influenza immunization program and bought hundreds of millions of vaccines doses. We argue that, as Health Ministers assumed the occurrence of the worst possible scenario (generalized pandemic influenza) and followed the strong version of the Precautionary Principle, they undervalued the possibility of mild or weak pandemic wave. Methodology: An alternative decision rule, based on the non-extensive entropy principle, is introduced, and a different Precautionary Principle characterization is applied. This approach values extreme negative results (catastrophic events) in a different way and predicts more plausible and mild events. It introduces less pessimistic forecasts in the case of uncertain influenza pandemic outbreaks. A simplified application is presented using seasonal data of morbidity and severity among Italian children influenza-like illness for the period 2003–10. Principal Findings: Established literature results predict an average attack rate of not less than 15% for the next pandemic influenza [Meltzer M, Cox N, Fukuda K. The economic impact of pandemic influenza in the United States: implications for setting priorities for interventions. Emerg Infect Dis 1999;5:659–71; Meltzer M, Cox N, Fukuda K. Modeling the Economic Impact of Pandemic Influenza in the United States: Implications for Setting Priorities for Intervention. Background paper. Atlanta, GA: CDC, 1999. Available at: http://www.cdc.gov/ncidod/eid/vol5no5/melt_back.htm (7 January 2011, date last accessed))]. The strong version of the Precautionary Principle would suggest using this prediction for vaccination campaigns. On the contrary, the non-extensive maximum entropy principle predicts a lower attack rate, which induces a 20% saving in public funding for vaccines doses. Conclusions: The need for an effective influenza pandemic prevention program, coupled with an efficient use of public funding, calls for a rethinking of the Precautionary Principle. The non-extensive maximum entropy principle, which incorporates vague and incomplete information available to decision makers, produces a more coherent forecast of possible influenza pandemic and a conservative spending in public funding. [ABSTRACT FROM PUBLISHER]