The public funds a large number of projects in the arts, humanities and sciences. How this funding is distributed is decided by a small group of people who given the power to make a decision on behalf of the population at large.

Generally speaking, the existence of this funding is justified by the projects being for the public good, whether this is in terms of economic or cultural value, the populations wellbeing, or something else. 

It seems that the power to make decisions about who gets this money is granted by the people in a very indirect way, elected representatives choose bodies, which then use a rather complex system of panels to make decisions. Whilst things like economic value might be addressable in a fairly objective way, decisions about scientific merit or cultural value are much more tricky. It seems that such things can only be judged by experts, for example, we wouldn't give scientific papers to some random person and expect them to make a good decision.

But a panel of experts is always going do differ in their mode of valuing to non-experts. An arts panel can always be accused of snobbery, and a scientific panel valuing useless things of interest only to an insular community.

How can such a panel ever escape such a criticism and be considered to legitimately represent the interests of the population? If considering values other than economic value is necessary for this problem to exist, perhaps the less-than-preferable option of using economic value exclusively is the only way to be properly representative?

*This is a refinement of [this](https://philosophy.stackexchange.com/questions/11426/legitimacy-of-peer-review) question.*