Multi-Expert Consensus in Strategic Portfolio Evaluation using Discrete Choquet Integral for Analytical Network Process Weights

Customer profiling tools have been introduced in recent years to protect investors against the increasing complexity of financial instruments. Advisor experts have to combine measures of finance and behavioural finance studies in their evaluation. The need to integrate different competences and compare complex criteria naturally leads to the modelling of the portfolio selection problem as a group decision problem. The Analytic Network Process (ANP) is a useful technique that helps decision-makers evaluate the available alternatives and aggregate their professional knowledge. In this context, the Reaching Consensus Process (RCP) is crucial for the validity of choices due to the strong sensitivity of the ANP to the decision maker's judgement. However, the RCP may be affected by the behavioural characteristics of experts, the vulnerability of judgements and the uncertainty that characterises the decision-making context, leading to unbiased judgements that are not based on different expertise. Similarly, without the involvement of more experts, the process could be inefficient due to the sensitivity of the ANP decision-maker’s judgement. In order to maximise the aggregation of experts' knowledge, to minimise the influence of the individual in quantifying the relationships between criteria and alternatives, and to preserve the impartiality of evaluations, the present paper discusses RCP through Choquet’s discrete integral. This aggregation captures the non-linearity of preferences and includes the fuzziness of judgments. Thus, there is no need to reach a consensus when evaluating the criteria: each expert manages a single ANP whose synthesis are aggregated using Choquet’s discrete integral. In this sense, the aggregation defines an unbiased consensus which mitigates the sensitivity of the ANP to the preferences of the decision-maker. The methodology is applied to a case study in which several experts evaluate investment alternatives of an individual, simultaneously incorporating behavioural criteria and Markets in Financial Instruments Directive (MiFID) client profiling criteria.