Joint aggregation of cardinal and ordinal evaluations with an application to a student paper competition

TL;DR

This paper introduces a robust method for aggregating both ordinal and cardinal evaluations in decision-making contexts, especially when evaluations are incomplete and subjective scales vary among judges.

Contribution

A novel aggregation methodology that jointly combines ordinal and cardinal evaluations, addressing challenges of incomplete data and subjective scoring in decision processes.

Findings

Effective aggregation of mixed evaluations demonstrated

Method performs well with incomplete and subjective data

Applicable to managerial decision-making scenarios

Abstract

An important problem in decision theory concerns the aggregation of individual rankings/ratings into a collective evaluation. We illustrate a new aggregation method in the context of the 2007 MSOM's student paper competition. The aggregation problem in this competition poses two challenges. Firstly, each paper was reviewed only by a very small fraction of the judges; thus the aggregate evaluation is highly sensitive to the subjective scales chosen by the judges. Secondly, the judges provided both cardinal and ordinal evaluations (ratings and rankings) of the papers they reviewed. The contribution here is a new robust methodology that jointly aggregates ordinal and cardinal evaluations into a collective evaluation. This methodology is particularly suitable in cases of incomplete evaluations -- i.e., when the individuals evaluate only a strict subset of the objects. This approach is potentially useful in managerial decision making problems by a committee selecting projects from a large set or capital budgeting involving multiple priorities.