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"...the failure rate is very low..." Got any actual statistics on that?
The guy that taught my Microsoft SQL Server2005 class builds HR databases. He had to add a true "unique" field because there were several matches at one company.
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Find your own statistics, but the last I read a couple years ago was under a tenth of a percent. Most duplication is due to fraudulent use of SS#'s, or clerical error by either the persons putting down the numbers or the ones entering them into databases. The lack of check digits, etc. contributes to this as it is too easy to misenter a SS# and still get a valid one. Byond that, most organizations don't try to validate the ones they have on record. Very few come from the SSA itself issuing the same number to 2 or more different people.
A much higher percentage at about 1% is the number of people with 2 or more SS#'s. This is from the SSA itself in 2007. Most were older, average age around 83. Mostly this was from the early days of the program when the misinformation was going around that people needed to apply for a new number each time they changed jobs. Another source were parents who applied for a number for a child, then reapplied for another if there was an error in the name. There is a form to file to correct such information, some chose what they thought was the "easier" way.
P.S. How big was the company he was creating the database for? If it was big enough, statistical probability would almost guarantee finding such a match even with an occurrence of such a small percentage. Same type of probability calculation applies to the odds of another person in a room having the same birthdate as another. Once you geet past about 20 in number it can be rather higher than most people think,