Where policy and science intersect, there are always issues of ambiguous and conflicting lines of evidence. Combining disparate information sources is mathematically complex; common heuristics based on simple statistical models easily lead us astray. Here, we use Bayesian Nets (BNs) to illustrate the complexity in reasoning under uncertainty. Data from joint research at Resources for the Future and NASA Langley are used to populate a BN for predicting equilibrium climate sensitivity (ECS). The information sources consist of measuring the rate of decadal temperature rise (DTR) and measuring the rate of percentage change in cloud radiative forcing (CRF), with both the existing configuration of satellites and with a proposed enhanced measuring system. The goal of all measurements is to reduce uncertainty in equilibrium climate sensitivity. Subtle aspects of probabilistic reasoning with concordant and discordant measurements are illustrated. Relative to the current prior distribution on ECS, we show that after 30 years of observing with the current systems, the 2σ uncertainty band for ECS would be shrunk on average to 73% of its current value. With the enhanced systems over the same time, it would be shrunk to 32% of its current value. The actual shrinkage depends on the values actually observed. These results are based on models recommended by the Social Cost of Carbon methodology and assume a Business as Usual emissions path.