A more likely hypothesis is this: Liberals elevate the abstraction of “fairness” over the concrete benefits that accrue to both parties under even the most uneven split in the Ultimatum Game because they believe that life is in fact a lot like something somewhere between Dictator Game and Ultimatum Game. The fundamental liberal economic fallacy is that the economy is a kind of pie and that somebody, somewhere, is deciding how to divide it up. Economies do not work that way, of course, which is why the phrase “distribution of wealth” is in fact meaningless in most modern contexts — wealth is the result of a dynamic process of creation and exchange, not something that sits in a bucket waiting to get handed out by The Man. (My guess is that this is a holdover from the liberal land-redistribution project that goes back at least to the Lex Sempronia Agraria, the conflict over which some scholars blame for the destruction of the Roman republic. Unlike modern wealth, land really does exist in fixed amounts in any given political territory, and was in fact handed out by the prince according to his whims. Our liberals: Still bravely fighting the social injustices of 134 b.c.)
Ask a liberal to describe the relationship between employer and employee, and you will very often hear something like Dictator Game or Ultimatum Game: The lordly employer simply proposes to share some of his revenue with his serf, who, as in Ultimatum Game, may have the wherewithal to walk away or may face immediate material privation unless he accepts whatever terms are offered him, even if they are as meager as those that would be dictated to him in the Dictator Game. In the real world, things are of course much more complex — there are lots of employers, lots of employees, lots of options, and lots of negotiation — but the case for (e.g.) labor unions is generally presented as a response to an implied Dictator Game. The nice thing about free markets: You may have some Ultimatum Games, but you never have a Dictator Game.
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