Tuesday, February 10, 2009

Science and Politics (and Religion)

I have been meaning to write on this for sometime now, but not until reading Pure Pedantry's response to the "Rightful Place Project" was i finally motivated to do so. This is not yet a completed version so i am still taking constructive criticisms and will be doing some editing but here it is so far:

Science isn't about separating facts from non-facts. A fact is something that is *known* to be true. Unfortunately, as Laplace said, "One may even say, strictly speaking, that almost all our knowledge is only probable; and in the small number of things that we *claim* to know with certainty, the principles means of arriving at the truth, i.e. induction and analogy, are based on probabilities."

Experimentation produces facts which take the form of raw data, D, or observations. Science then is the art of generating and the means of comparing various hypothesis, H, which might have given rise to observations. The conclusions of science can, in principle, take two forms: (1) the probability distribution on the hypothesis space given your data, p(H|D), or, more usefully, (2) a posterior predictive model,

p(D'|D,{H}) = sum_H p(D'|H)p(H|D),

which gives the relative likelihood of future observations, D'.

Now, one might be tempted to say that, if a particular hypothesis is much more probable than all others under consideration, then it is true. However, this ignores one of the most important features of the scientific process: the possibility of newer and better theories (and also novel domains of measurement). As such, I fell that it is best say that a hypothesis is never true, only better than another competing hypothesis.

But even this statement isn't terribly useful. The utility of science is in the prediction of future outcomes, the p(D'|D,{H}). Latching onto the single, "best" hypothesis can lead one to ignore outliers, "Black Swans" if you prefer, as well as overconfidence in one's predictions. This should be avoided if decisions are to be made. Since this is one of the two functions of policy makers in our society, it is important not that scientists provide "facts" but rather predictions complete with relative likelihood assessments that take into account ALL the data and a broad range of theories.

Which brings me to my view on the exact nature of the relationship between science and politics. As you may have guessed, i see this in a decision theoretic framework. A decision takes into account two things predicted outcome and utility.

a_opt = argmax_a = argmax_a sum_R sum_s R(o,a)*p(o|a,s,D)p(s|D)


a_opt is the optimal action or decision

is the expected reward given an action and all the observational data.

R(o,a) is the Reward or negative cost of a given outcome, o, and action, a, taken with the intent of achieving that outcome.

p(o|a,s,D) is the likelihood of a particular outcome given action a, and state of the world s.

p(s|D) is the likelihood that the world is in a current state s, given all the observational data, D, obtained to date.

Science regulates only the probability functions which are conditioned upon the data.

Politics has two functions: The first is to compute the reward function R(o,a). In a democracy this might be accomplished by averaging over the reward functions of the people, but is most often accomplished by averaging over the reward functions that politicians have, slightly weighted by the reward functions that politicians think that the people "should" have, whatever that means. The second function of politics is then actually make the decision which is simply taking the arg max over the expected Reward.

Now in principle, politicians should not be telling people what they should value, each individuals personal ethic should be doing that. Since there is no normative solution to the problem of objective function selection (sry Rand) and reward starts with, R, I will call this religion, with a small 'r' to separate it from the kind where a clergy man tells you what to value. Thus properly understood and executed, politics should only be implementing the decision based upon an average over objective or reward functions. Thus,

politics = argmax_Decisions religion(a,o) * science(o|a,D)

it couldn't be simpler :P

Anyway, i will fill this out with an addenda regarding the funding loop later.

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