Preferences (Partial Pre-Orders) on Complex Numbers - in View of Possible Use in Quantum Econometrics

Songsak Sriboonchitta, Vladik Kreinovich, Olga Kosheleva

Abstract

In economicapplication, it is desirable to find an optimal solution -- i.e.,a solution which is preferable to any other possible solution.Traditionally, the state of an economic system has been describedby real-valued quantities such as profit, unemployment level, etc.For such quantities, preferences correspond to natural orderbetween real numbers: all things being equal, the more profit thebetter, and the smaller unemployment, the better. Lately, itturned out that to adequately describe economic phenomena, it isoften convenient to use complex numbers. From this viewpoint, anatural question is: what are possible orders on complex numbers?In this paper, we show that the only possible orders are orders onreal numbers.