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You are hiring for low level airport security and have to choose between these two men. Their resumes look very similar but are not overly detailed in any way.

all you really know is that they have a high scool education, some work experience in minimum wage jobs, and maybe a year or two of community college each.

The one who does not get hired will be adversely affected, as he will remain unemployed.

Do you still go with the white male, or do you now flip a coin?

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If there was absolutly no way to differentiate the two in terms of who is best for the job, and I found some hard statistical evidence showing that middle eastern men similar to the guy I am hiring (have been living in the country for about X years, came from country Y, etc...) have a higher density' of terrorists then white men similar to the guy I am hiring, then yes, I'd go white male. Conversely if statistically the white male was more likely to be a terrorist, I'd go the middle eastern guy.

Yes, I believe that racial stereotypes may be justified if there is unbiased statistical data showing a high likelyhood of some kind of correlation

At the moment I hold no sterotypes because I have seen any data that could support one. But I haven't actively looked for any such reserch.