It is most useful to consider speed of action as a proxy for secrecy, and address the question of the need for secrecy in terms of the need for speed.

The opposite of speed in governance is obviously slowness, which is associated with deliberation in larger groups.

This gets you to the basic tradeoff in governance: the larger the group that gets involved, the slower the decision process, BUT the more representative the decision that emerges.

If you had all the time in the world, all decisions should be made with full participation. Let's pseudo-mathematize this question (I am going to ignore a LOT of complexity here in the interests of getting to just this "secrecy" aspect):

Let V be the obtainable maximum value from a decision, and T the maximum time available before the value of the option degrades to nothing. Let's say the decision affects n decision makers, of whom ONE, call him [math]\alpha[/math], recognizes the option first. He has to choose how big to make the group m<n, that is to be involved in the decision.

Let the value of the decision, if made at time t be:

[math]V'(t)=\lambda (t)V[/math],
[math]t<T,[/math]
[math]\lambda(0)=1[/math],
[math]\lambda(T)=0[/math]

The rest should be obvious: the more time [math]\alpha[/math] spends generating a consensus, the lower the ultimate value realized. But the LESS time he spends, the greater the risk that the outcome of the decision will be unpopular and/or incorrect with respect to some useful notion of ground truth (more precisely, incorrect AND unpopular, correct BUT unpopular, correct AND popular and incorrect AND unpopular are the four possible cases... I am ignoring the special complexities of the second case).

Assuming the decision is actually correct and popular, the time required to drive a consensus involve m individuals will be [math]\tau (m)[/math], and the relative speeds of the two functions [math]\lambda, \tau [/math], along with the expected value computation of the decision being popular/unpopular with the whole body, tells you the exact shape of the tradeoff (I am being lazy here, but trust me, the mathematical model isn't very hard to derive, I just am not interested enough to do it without being paid :)

[math]\alpha[/math] is faced with what is basically a Bayesian decision. From his prior knowledge, he may have some sense of the probability that the decision will be acceptable/appreciated. He can choose to spend anywhere between 0 and T increasing that probability through a sampling+persuasion exercise, while being aware that the value of the decision is falling all the time.

The faster the decision, the more value added, but the greater the rejection risk later. So a very enlightened decision maker or secret cabal, steering by a strong instinct of what the "people" want can gain a lot more value for the people they dictatorially choose to represent by gaining speed advantages. Completely clueless but well-intentioned dictators will be wrong or right at random, and would be better off with more democracy, since the unpredictability will erode trust (a great example is a medieval Indian emperor, Muhammad bin Tughlaq). Those operating with fundamentally malicious or predatory instincts will usually make decisions that nobody would have voted for.

How does all this abstraction work out in practice. A few examples should suffice.

During the time of Colbert (not Stephen, but the famous French Jean-Baptiste, the finance minister of Louis XIV), he rapidly and systematically built up the French navy and trade capability. While he was autocratically pushing the process, France raced ahead in technology, to the awe of visiting Englishmen. But when he lost favor, the whole thing collapsed, at least until Napoleon. This was because the French effort had no real depth, in terms of a deep-rooted naval tradition and industry and a citizenry deeply tied to the sea.

By contrast, both the Dutch and the British built up their navies in a slower sort of bottom up way with a lot more implicit consultation and representation. Through competent and incompetent leadership, the system kept getting stronger overall.

But you cannot draw the facile lesson that the latter were "better." Due to Colbert's more autocratic driving, France DID develop genuine naval capacity and skill, and contributed to the world's naval knowledge. France just evolved on a more volatile path of naval development with more booms and busts than the British or the Dutch.

It is NOT a case of tortoise vs. hare. Unlike the tortoise/hare scenario, the race of governance never ends, and depending on how smart and prescient secretive decision-makers are, their autocratic decisions on behalf of a larger disenfranchised majority may help or hurt. Democracy and broad consultation are the safe, risk-averse path, and sacrifice potential value attributable to speed, in the interests of making consistently safer decisions.

Ataturk and Lee Kuan Yew are examples where it worked well. Colbert is a middling level example. Most evil dictators are examples of how it fails.

More recently, China and India offer the same distinction. The former is racing ahead driven by backroom processes/secrecy, while the latter is constantly mired in public, democratic consultative processes.

In general, any real governance process is necessarily a live, dynamic balancing act between secrecy and openness, based on a case by case assessment of the value/popularity/time limits of individual decisions, by whichever decision-makers FIRST encounter them.