 We have proposed three new measures of shared information between two random variables, y, z, and a third random variable, x. These measures are based on the idea of unique information, which states that shared and unique information should depend solely on the marginal distributions of the pairs x, y, x, z, and y, z. In addition, these measures satisfy an invariance property, meaning they are bounded by any other measures that also satisfy this property. We then compared these measures to other candidate measures of shared information. This article was authored by Nils Burtzginger, Johannes Rau, Eckhart Ulbricht, and others.