Cherry picking, literally meaning harvesting cherries, is used metaphorically to accuse someone of pointing at individual cases which seem to confirm his or her position, while ignoring a significant portion of related cases that may contradict it.
For example, opponents of safety belts often cite rare cases in which car accident victims were strangled, or trapped, by a safety belt, whereas accident statistics suggest that they much more commonly save the life of the passenger (unless used improperly).
In each case, we are integrating information differently, weighing different pieces of evidence differently. But cherry-picking would be represented by the last, where one weighs many relevant pieces of information (that one possesses) at zero and favors the information that is preferred. So there is a large difference between weighing information differently based on its quality to come to a conclusion and outright ignoring information that is not preferred.
To prevent auto insurance companies from cherry picking only the good drivers and leaving poorer drivers without any insurance, most states in the U.S.A. require auto insurance companies to insure a certain number of drivers with poor records.
In the 1970s and early 1980s in Australia, cherry picking was a tax avoidance scheme based on tax deductions for company contributions to a superannuation fund. Such a fund was notionally for the benefit of employees, but the benefits (the "cherries") were picked by the company or its owners.
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"Cherry picking".
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