Expected utility analysis of infinite compound lotteries

ABSTRACT

Lotteries can be used to model alternatives with uncertain outcomes. Decision theory uses compound ordinary lotteries to represent a structure of lotteries within lotteries, but can only rank the finite compound lottery structure. We expand upon this approach to introduce solutions for infinite compound ordinary lotteries (ICOL). We describe a novel procedure to simplify any ICOL as much as possible to a maximum reduced ICOL, which is not a unique representation. We limit our discussion to ICOLs of first order, which are defined as maximum reduced ICOLs with a single maximum reduced ICOL in their direct outcome. Two special cases of ICOLs of first order are discussed. These are recursive and semi-recursive ICOLs. We provide an analytical approach to find the expected utility of recursive ICOLs, and a numerical algorithm for semi-recursive ICOLs. We demonstrate our solution methods by evaluating example decision problems involving: a randomizing device with unsuccessful trials, the St. Petersburg paradox, and training with virtual reality.

KEYWORDS:

• ICOLs of first order
• recursive ICOL
• semi-recursive ICOL
• expected utility
• generalized St. Petersburg paradox

Acknowledgments

The authors acknowledge the support of Serco Defense Asia-Pacific, the Research Training Centre for Naval Design and Manufacturing (RTC-NDM) and the University of Tasmania in the study design, conducting the research and supporting the publication of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the RTC-NDM and Serco Defence Asia-Pacific under the Australian Research Council Industry Transformation grant scheme [ARC IC140100003], to train the next generation of Naval Manufacturing and Design personnel and provide the Naval manufacturing industry with supporting research.

Notes on contributors

Jane Cullum

Jane Cullum is a PhD student with the National Centre for Maritime Engineering and Hydrodynamics of the Australian Maritime College, University of Tasmania (Australia). Her thesis is in risk-based maintenance of naval ships, doing experimental work with support of SERCO Defence Asia-Pacific. She has a background in engineering and her PhD studies are funded under the Research Training Centre for Naval Design and Manufacturing of the Australian Research Council Industry Transformation grant scheme.

Natalia Nikolova

Natalia Nikolova is a professor in decision sciences and risk analysis. She is affiliated with the National Centre for Ports and Shipping of the Australian Maritime College, University of Tasmania (Australia) and with the Nikola Vaptsarov Naval Academy – Bulgaria. She holds a PhD in data analysis and decision support systems. Natalia has expertise in computational intelligence with specific focus on decision support systems, risk analysis, econometrics and simulation modelling. Those areas of research expertise were implemented in transport management, environmental modelling, port management, business planning, medical science. Her publication output counts to 132 works whose total impact factor is 10, with some 195 citations (Google Scholar) and h-index 8 (Google Scholar). Most of her research links to international grants from the European Union's framework programmes, Japanese education and research fund, Eurocontrol grants, etc.

Kiril Tenekedjiev

Kiril Tenekedjiev is a professor in systems engineering, affiliated with the National Centre for Maritime Engineering and Hydrodynamics of the Australian Maritime College, University of Tasmania (Australia) and with the Nikola Vaptsarov Naval Academy – Bulgaria. He holds a PhD in statistical pattern recognition, as well as a doctor of sciences degree in decision support systems and data analysis. Kiril has expertise within the broad area of intelligent systems and computational intelligence with specific focus on quantitative decision-making, simulation modelling, risk analysis, technical diagnostics and statistical pattern recognition. His research and activities as academic were applied to areas spanning from complex machine analysis and technical diagnostics, to economic analyses and business planning, to energy efficiency procedures, transport management, environmental modelling, biochemistry and medical science. He is an IEEE senior member and fellow of Engineers Australia, as well as Fulbright Visiting scholar to SUNY Binghamton (2007). His publication count is 220 whose total impact factor is 80, and with 788 citations (Google Scholar) and H-index of 12 (Google Scholar).