Existing Political/Social Sciences
Sociology and 'political science' (also economics, I suppose) are both social sciences which aim to develop theories about large groups of people and their political organisation based on, like you say, observation and measurement. As it stands, these kinds of studies impact and influence actual politics but perhaps not enough.
It's Can't Just be Science
The problem is, you can't have politics just be about observation and measurement. As someone else here mentions, there has to be some discussion about what our aims are as a group (whether that group be a city, nation, some alliance of nations etc). Once aims are well defined, scientific investigation regarding how to achieve those aims is extremely necessary. But, I would argue, one cannot define aims through the use of scientific inquiry. This is an example of Hume's is/ought distinction. Statements about goals (or values, which are essentially the same thing) are inherently distinct from descriptive claims about the world. You simply have to have some assumed value or aim to work from. Sam Harris might disagree but I think he is terribly mistaken. And much of politics can be thought of as moral debate about our values or aims.
Difficulties With Social Sciences
One problem, however, with social sciences in general is that they're dealing with extremely complex systems. As much as physics seems complex when the equations are stuck up on a board, the systems studied by physicists are very simple either in their nature or because their enormous scale allows certain approximations to be made that are still very accurate. E.g. The Earth is no where near perfectly spherical. There are mountains, rivers, cities, bulges. However, if one 'zooms out' far enough, the earth can be modelled as a perfect sphere which makes computation and theoretical development easier. If you zoom out even further a planet (or even a galaxy!) can be modelled as a point with no spatial dimensions, making computation even easier. It turns out that the only reason physicists are able to be so mathematically precise with their work (such that they can develop very precise mathematical models) is that these systems are simple.
Social sciences and economics, however, may be dealing with very large groups of people. A volatile environment in which patterns and quantitative relationships between variables are difficult to find. What happens if I invest X amount of money in to this certain kind of industry? Answering those kinds of questions accurately requires extreme care and consideration of many different factors including the state of consumers within that industry, the interactions of this industry with others and perhaps it could even be the case that the actions of key individuals in the industry really matter. In some ways, this may make things even harder since with large populations you might be able to make certain assumptions or approximations (like physicists do) to make your model more simple but you can't really 'approximate' the behaviour of individuals- there's an innumerable amount of important variables involved in our decision making processes that some extreme advances in neuroscience must be made before we can hope to 'model' the behaviour of an individual. It's typical in science that the more complex a system of study becomes, the less mathematical formalisation is present. For example, mathematical modelling is used in biology but not as much as in physics or chemistry and for this exact reason.
To make things worse, you have this kind of 'measurement-effect' where simply observing some population or designing a model of their behaviour may actually change their behaviour. For example, if you have been observing some specific market's behaviour and created a model which is predictively successful in seeing the rise and fall of value in shares (or whatever it is), you or someone else who knows about your model may use it and invest loads of money which would alter the "natural" behaviour of the market. Therefore, we have to wonder if we will ever be able to model the behaviour of these kinds of systems when the model itself effects the system. It may be the case that it's literally impossible for a model to be able to predict its own effect on the system being modelled (seems kind of circular, doesn't it?).
Further development of mathematical and observation tools are simply required before this can be made a reality. The complexity problem seems to be the largest hurdle to jump (obviously)