Suppose I place work I publish under two licenses.
If the two have conflicting attributes which property should be used.
Can you specify which properties you want two be applied from the two licenses?
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No, the two licenses don't have to be compatible.
If you are legally allowed to dual license something, usually because you are the copyright holder, you can pick any two licenses, even if they conflict. As a matter of fact, dual licensing is usually used to get around license conflicts, that is, by offering something under two conflicting licenses. One of the most notable examples is Mozilla Firefox, which is tri-licensed under MPL, GPL and LGPL. This was done because MPL, the original license it used, is incompatible with GPL.
When you dual license, it doesn't mean users must follow both licenses, especially if the licenses conflict, this would be impossible to do anyway. Instead, you may choose the license under which to receive the software. When you redistribute in turn, it is courteous (although not legally required) to pass on that dual licensing, as doing so does not limit the options of your users.
Also, you cannot "pick and choose" clauses within the two licenses, as you are creating a third license that the original author never agreed to.
This is a different situation to sublicensing or relicensing.