Cherry picking
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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).
Weighing information
For a more involved example, imagine we wish to find the average height of men in the U.S., and we have in hand a sample of average heights of men by state, across years. We could average these heights and call this the right number. We could just average the heights in the most recent year. We could give a weighted average of heights, based on the population of each state. Or we could pick the two states with the highest average height and call this the national average.
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.
Business Policies
Cherry picking is also used to refer to business policies of picking out profitable customers from a large base. For example, by only insuring healthy people and refusing to insure those who were unhealthy or are likely to become unhealthy, a health insurance company can cherry pick the most profitable customers. If an auto insurance company only insured good drivers by cherry picking them from among all drivers this would enable a company to gain an advantage over a company that insures all drivers.
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.