In the field of People Intelligence, Emotion Analytics is one of the emerging and growing challenges. A prominent study field is analyzing an individual's emotional state from textual data, as well as recognizing emotions from audio and video recordings. Current Artificial Intelligence approaches for Emotion Analytics based on machine and deep learning and neural networks based on classic data science approaches assume rational people's decision-making process. People's decision-making is irrational. As a result of recent quantum cognition advancements, we show that emotional judgments from one modality may be incompatible with judgments from another, and they cannot be assessed together to produce a final judgment. As a result, the cognitive process exhibits "quantum-like" biases that classical AI approaches based on probability models challenged to analyze. As a result, we offer an emotion analytics approach based on the quantum data science method for predicting people's emotions by a fundamentally novel assessment method.