Hm, can you say more about information? I believe you should get the most direct information (in the information-theoretic sense) out of running tests where the outcome is most in doubt (i.e. where your prior is approximately 50%, although I think this might budge a bit depending on the FP/FN rates of the test if they are different.) You also get information about their contacts—if their contacts have a lower-than-50% base rate of exposure, then it seems like you get more of that “secondary information” from a positive than from a negative. (I’m not too confident about that, but certainly at worst it’s equal, right?)
Hm, can you say more about information? I believe you should get the most direct information (in the information-theoretic sense) out of running tests where the outcome is most in doubt (i.e. where your prior is approximately 50%, although I think this might budge a bit depending on the FP/FN rates of the test if they are different.) You also get information about their contacts—if their contacts have a lower-than-50% base rate of exposure, then it seems like you get more of that “secondary information” from a positive than from a negative. (I’m not too confident about that, but certainly at worst it’s equal, right?)