previous-order
preorder
Usually, economics and game theory assume that preferences are pre-ordered - [Game Theory 3rd ed.]. The relation a=b, in which the elements a and b are identical, and the similarly preferred relation a~b are different, and the former is derived a posteriori from the relation given and the latter is pre-ordered
It is easy to forget that there are two different relationships and confuse them because they are often represented by the same symbol when they match
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