<abstract xmlns="http://www.w3.org/1999/xhtml">
<p>Cancellation conditions play a central role in the representation theory of measurement for a weak order on a finite two-dimensional Cartesian product set <italic>X</italic>. A weak order has an additive representation if and only if it violates no cancellation conditions. Given <italic>X</italic>, a longstanding open problem is to determine the simplest set of cancellation conditions that is violated by every linear order that is not additively representable. Here, we report that the simplest set of cancellation conditions on a 5 by 5 product <italic>X </italic>is obtained.</p>
</abstract>

Cancellation conditions play a central role in the representation theory of measurement for a weak order on a finite two-dimensional Cartesian product set X. A weak order has an additive representation if and only if it violates no cancellation conditions. Given X, a longstanding open problem is to determine the simplest set of cancellation conditions that is violated by every linear order that is not additively representable. Here, we report that the simplest set of cancellation conditions on a 5 by 5 product X is obtained.

A Basic Set of Cancellation Violating Sequences for Finite Two-Dimensional Non-Additive Measurement

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

Cancellation conditions play a central role in the representation theory of measurement for a weak order on a finite two-dimensional Cartesian product set X. A...

A Basic Set of Cancellation Violating Sequences for Finite Two-Dimensional Non-Additive Measurement

Published Online: Dec 13, 2023

Page range: 64 - 77

Received: Sep 18, 2023

Accepted: Nov 17, 2023

DOI: https://doi.org/10.2478/amsil-2023-0023

Keywords
Preference order, Cartesian product structure, additive measurement, cancellation conditions

© 2023 Che Tat Ng, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

A Basic Set of Cancellation Violating Sequences for Finite Two-Dimensional Non-Additive Measurement

Published Online: Dec 13, 2023

Page range: 64 - 77

Received: Sep 18, 2023

Accepted: Nov 17, 2023

DOI: https://doi.org/10.2478/amsil-2023-0023

KeywordsPreference order, Cartesian product structure, additive measurement, cancellation conditions

© 2023 Che Tat Ng, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Preference order, Cartesian product structure, additive measurement, cancellation conditions