An alternative approach to quadratic scoring rules using continuous-valued logic

Abstract Following tfhe seminal paper of Offerman et al. (2009), in this study, adaptations constructions continuous-valued logic to prospect theory are presented. Here, we demonstrate that the so-called kappa function and its special cases viable alternatives some elements quadratic scoring rule prospects theory. After, present tau-eta show it may be treated as a generalization prospect. Furthermore, prove if new for an uncertain event is evaluated using specific functions utility functions, then (1) weighting measure optimal value reported probability, (2) inverse latter function, (3) (risk-) corrected probability event, also all have common formula. The parameters formula unambiguously determined by four tuning parameters. Lastly, with our approach, fitting one abovementioned corresponding empirical data, can immediately obtain other two well.