Normative properties of multi-criteria choice procedures and their superposition: II

TL;DR

This paper analyzes two-stage superposition choice procedures, examining their normative properties, how they adapt to preference changes, and their computational complexity, with theoretical proofs and empirical evaluations.

Contribution

It provides a comprehensive analysis of normative conditions satisfied by various two-stage choice procedures and evaluates their complexity and runtime on real data.

Findings

Certain two-stage procedures satisfy specific normative conditions.

The complexity and runtime of these procedures are characterized.

Theoretical results are supported by empirical data analysis.

Abstract

Two-stage superposition choice procedures, which sequentially apply two choice procedures so that the result of the first choice procedure is the input for the second choice procedure, are studied. We define which of them satisfy given normative conditions, showing how a final choice is changed due to the changes of preferences or a set of feasible alternatives. A theorem is proved showing which normative conditions are satisfied for two-stage choice procedures based on different scoring rules, rules, using majority relation, value function and tournament matrix. A complexity of two-stage choice procedures as well as its runtime on real data are evaluated.