The underlying scenario of this thesis is the existence and extent of liability to tax on income arising from patent royalties in cross-border transactions. A quantitative method and associated model are developed that compare and contrast the susceptibility of identified legal frameworks, considered in pairs, to jurisdictional arbitrage regarding this income. The jurisdictions of Australia and the United States engaged in cross-border transactions with Ireland are examined. Additional jurisdictions are also examined to showcase “tears” in specific domestic legal fabrics due to international law in the form of bilateral and multilateral treaties regarding unions, specifically regional communities, to which these additional jurisdictions belong. These identifiable “tears” in specific jurisdictions’ domestic legal fabric prove that the principal factor in relocating intellectual property assets to other jurisdictions in order to benefit from jurisdictional arbitrage is not domestic corporate tax rates, as is the generally held position. Novel three dimensional visualization techniques are employed that both compare and contrast the similarities and differences between pairs of jurisdictions in a single operational view. The findings derived from the application of the quantitative method and associated model enable the proactive development and/or modification of both current and future legislation (international treaties, domestic statutes and domestic regulations) based on a quantitative risk/reward analysis. Furthermore, these findings may prescriptively identify jurisdictions that may require treaties to alleviate large, potentially harmful, gaps in jurisdictional domestic tax law regimes.