From Planet Money
Given a choice between $50 now and $100 in a month, many people would
take the money
now. But offered $50 in a year, or $100 in 13 months,
they'd wait the extra month to double
their money.
Another example from This Wikipedia page
In the experiment, subjects of the study were offered free rentals of
movies which were classified into two categories - "lowbrow" (e.g. The Breakfast Club) and "highbrow" (e.g. Schindler's List)
- and researchers analyzed patterns of choices made. In the absence of
dynamic inconsistency, the choice would be expected to be the same
regardless of the delay between the decision date and the consumption
date. In practice, however, the outcome was different. When subjects had
to choose a movie to watch immediately, the choice was consistently
lowbrow for the majority of the subjects. But when they were asked to
pick a movie to be watched at later date, highbrow movies were chosen
far more often. Among movies picked four or more days in advance, over
70% were highbrow.[3]
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