Abstract
In Wakker (1989b, ‘Additive Representations of Preferences, A New Foundation of Decision Analysis’), a new foundation of decision analysis was given. The main tool was a way to derive comparisons of ‘tradeoffs’ from ordinal preferences, with comparisons of tradeoffs revealing orderings of utility differences. These comparisons of tradeoffs underly the construction of standard sequences in conjoint measurement theory. The restrictive structural assumption (every approach has its restrictive structural assumption) was of a topological nature, requiring continuity. This paper adapts the main results of Wakker (1989b) to the algebraic approach, where a solvability condition is required which is less restrictive than continuity.
The research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences, and a fellowship of the Netherlands Organization for Scientific Research. Two anonymous referees made helpful comments.
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Wakker, P. (1991). Additive Representations of Preferences, A New Foundation of Decision Analysis; The Algebraic Approach. In: Doignon, JP., Falmagne, JC. (eds) Mathematical Psychology. Recent Research in Psychology. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9728-1_4
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DOI: https://doi.org/10.1007/978-1-4613-9728-1_4
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