A new model for evaluating subjective online ratings with uncertain intervals

We formalize the information acquisition and choice structure of a decision maker (DM) when the main characteristics defining the alternatives are not directly observed but numerical evaluations of unknown quality are provided by external raters. The DM observes the overall numerical value assigned by the raters to an alternative and defines an uncertain interval within which the evaluation observed is contained. The width of the interval is determined by the subjective perception and evaluation differences existing between the DM and the raters transmitting the information. We analyze the incentives of the DM to improve upon an evaluation contained within an uncertain interval by retrieving further information from the raters of other alternatives. Different scenarios will be developed based on the ability of the DM to fully assimilate uncertainty and the introduction of heuristic approximations to account for the potential frictions arising from uncertainty. One of the main qualities of the current framework is its capacity to formalize interactions among alternatives determined by interval width differences across their characteristics, providing an analytical advantage over the operational complexity involved in the use of fuzzy and intuitionistic fuzzy sets. The same remark applies to the formalization of the interactions across attributes that must be considered when defining sequential decision processes or dynamical systems while dealing with multiple sources of uncertainty. Numerical simulations are provided to compare the different scenarios developed and describe the main consequences derived from ignoring the uncertainty inherent to the evaluations received. In particular, we illustrate the ranking consequences derived from increasing the spread of the evaluation uncertainty, an effect that can be easily combined with the risk attitude exhibited by DMs. The inclusion of both these features bridges the gap between economics, psychology and multiple criteria decision making, whose techniques do not generally account for these differences among DMs. © 2019 Elsevier Ltd. All rights reserved