Do Vague Laws Foster Authoritarian Regimes?
Do authoritarian countries in general have more vague laws on the
books?
The classic fictional statement of this hypothesis, which have elevated it to conventional wisdom to some extent, is as follows, from a play set in the brief period of English history in the 1600s when the monarchy had been deposed and had not yet been reinstated:
William Roper: “So, now you give the Devil the benefit of law!”
Sir Thomas More: “Yes! What would you do? Cut a great road through the
law to get after the Devil?”
William Roper: “Yes, I'd cut down every law in England to do that!”
Sir Thomas More: “Oh? And when the last law was down, and the Devil
turned 'round on you, where would you hide, Roper, the laws all being
flat? This country is planted thick with laws, from coast to coast,
Man's laws, not God's! And if you cut them down, and you're just the
man to do it, do you really think you could stand upright in the winds
that would blow then? Yes, I'd give the Devil benefit of law, for my
own safety's sake!”
― Robert Bolt, A Man for All Seasons
There Are No Such "Objective" Studies
But, there is no such objective data on the books, largely because operationally, defining "authoritarian" is hard, and defining "vague laws" in a relevant way, is much, much harder to do objectively.
One of the issues when it comes to thinking about how you should define "vague laws" for this purpose, is that a small number of vague laws can profoundly impact the overall usefulness of vague laws to advancing authoritarian ends.
For example, while much of the Uniform Code of Military Justice (which governs courts martial in the U.S. military) is quite specific, one section in particular, 10 U.S.C. 933 - Art. 133. Conduct unbecoming an officer and a gentleman, has so potentially expansive in application and vague, that it overshadows the specificity of many other provisions of the Uniform Code of Military Justice. Another singular feature of many of the provisions of the Uniform Code of Military Justice which adds vagueness is the qualification of many UCMJ offense such as adultery, that it is only punishable if the trier of fact in the case finds that the conduct was "in violation of good order and discipline."
The point of this example is not to criticize the UCMJ for fostering authoritarianism (we generally want military personnel to be governed in an authoritarian manner that would not be appropriate for civilians in a democratic society), but to point out that definitionally, the right way to characterize vagueness is to identify particular provision which are both salient to lots of people and have "peak vagueness" rather than trying to quantify some sort of "average vagueness" of an entire body of law.
This means, in practice, that someone trying to evaluate a legal system for vagueness that could be exploited by an authoritarian regime needs to be intimately familiar with how that legal system is implemented on the ground in order to meaningfully rate the system, which makes it hard to be objective, since few evaluators have that depth of practical working knowledge of how a legal system is implemented in order to make an accurate evaluation.
Indeed, "vagueness" per se, is not really the issue. The issue is whether particular authoritarian regimes have found a way to use one or more particular laws in an abusive or oppressive fashion, which can be done through vagueness, but can also simply be "in your face" oppressive and unfair.
A law interning a particular group of people in concentration camps, or openly prohibiting speech critical of the ruling regime can be a powerful tool of an authoritarian regime even if the law is very detailed and precisely defined.
The Hypothesis Is Probably False
Nonetheless, there is still good reason to think that the empirical reality is that "authoritarian countries" do not "in general have more vague laws on the books."
One reason to think this is that there are many newly independent countries which have statutory laws which are almost verbatim identical apart from foreign language translation, to the domestic laws of either a former colonial power that previously ruled the country, or to the statutes of some well functioning democratic capitalists nation used as a model for creating a new legal code, which was not authoritarian at the time that country was used for a model. For example, many French colonies in Africa, quite a few of which later developed authoritarian regimes, more or less copied verbatim the statutory laws of France at around the time they gained independence (often in the 1960s) when France's political system was not particularly authoritarian.
Similarly, there are a number of examples of countries that had almost identical generally applicable statutes on a wide variety of topics that went unchanged during periods when more authoritarian and much less authoritarian regimes where in place.
Germany, which retained the lion's share of the statutes in force during the authoritarian Nazi era in the much less authoritarian post-WWII era.
Japan, which has had a great deal of continuity of statutes from the Meiji era (starting in the late 1800s) to the present (many of which were copied from those of Germany), and South Korea (which also copied most of its Western style statutes from Germany and retained them in an initial post-Korean War authoritarian period and subsequent periods) also illustrate this historical pattern.
Conversely, many quite important areas of law in Western legal systems that are not considered authoritarian, are quite vague.
For example, the law of torts that governs liability for accidents (making up a huge share of all litigated civil cases in the court system), is likewise, exceedingly vague. You can fit the core tort law rules governing these kinds of cases in most civil law systems on a t-shirt.
The standard U.S. jury instructions for a typical personal injury case setting forth the tort law part of those instructions are likewise very vague standards expressed in very few words.
The People Operating A Legal System Matters More Than Its Content
Arguably, countries with a common law legal heritage have tended to be less likely to become authoritarian upon gaining independence, or upon a major electoral upheaval, than those that do not. But see, e.g., Sudan following independence and to a lesser extent, Singapore.
Yet, common law legal systems, if anything, tend to be more, rather than less vague and indeterminate on their face, than countries with a civil law legal tradition (e.g. most of continental Europe, Latin America and Southeast and East Asia).
A better explanation of this discrepancy, however, can be found not in the content of the laws themselves, but in the corps of personnel in place when those laws are applied. It is nearly impossible to conduct a legal system without a large number of legal professionals who have had extensive training in the common law legal system's working and its case law precedents to implement it. But, one can adopt a set of legal codes, widely promulgate them in quite thin volumes to large numbers of people who aren't legally trained, and can create the misleading impression that those non-legally trained people can use this to implement this new legal system right away.
For example, even conservative judges in the U.S. with whom I have spoken and dealt with, are much more skeptical of the weight and credibility of prosecution evidence in criminal cases than the vast majority of judges I've met from Japan and South Korea. Pretty much each of the dozen or so sitting Japanese and South Korean judges I've had conversations with about this subject have told me personally that they start from the assumption that every prosecution witness is telling the truth in a criminal case, and that every defense witness is lying, deviating from that general rule only in very exceptionally weak prosecution cases and very exceptionally strong defense cases. (Many sitting Japanese and South Korean judges pursued graduate studies as part of their civil service career development at my law school while I was enrolled there, and I studied a lot of international law at that time, which is how I came to have these conservations with my classmates.)
In theory, this could lead to an authoritarian system, but in practice, it comes down to the integrity of the law enforcement officers and prosecutors in countries like Japan and South Korea (which often is quite a bit less obtain convictions with maximum sentences, and more do collective community justice oriented than in the U.S.), which can make up for a certain lack of impartiality in the actual trial practice in court in criminal cases there.
The bottom line is that the competence and depth of people with training, education, and experience in carrying on government at the legislative, administrative, and judicial levels, and of the general public, in interfacing with a Western style political and legal system, is far more predictive of the risk that a regime will become authoritarian than the verbatim content and vagueness of its statutes.
In this regard, history has to a significant extent vindicated Confucian era (plus or minus a few centuries) legal philosophers who concluded that a system rooted in having government administered by civil servants who are both moral and competent is more important that focusing on strict adherence to specific provisions of written legal codes, when it comes to producing just government. How these written provisions are applied in practice matters more than the exact wording of what they say.
Footnote On Modern Chinese Law
It is also worth noting that the Chinese legal system mentioned in the question is something of an outlier and unique legal system in the world.
The vast majority of major world legal systems (but not China) are common law legal systems, are based upon a European civil law system, are based upon Islamic law, or are hybrids of one or more of these systems.
While China has some superficial similarities to continental system European legal systems, however, this similarities are really only skin deep, and China's legal system (along with the legal systems of a handful of countries in its sphere of influence in Asia) are both substantively and procedurally unlike either of the main models of Western style legal systems, or Islamic law.
As a result, drawing general conclusions from this outlier somewhat "oddball" example from systemically very different kinds of legal systems, isn't really appropriate.
Put another way, you can't use the scientific method to pin down just one connection between a particular feature of China's legal system and its authoritarian political system, because two many independent variables change simultaneously between it and any other system implicating a wide variety of legal system features, making it hard to pin down any one of them in isolation as being critical to this outcome.
For example, China's judiciary is also not very independent, and like other aspects of the People's Republic of China, is largely an instrument of the will of the Chinese Communist Party.
How much is the problem the inherent vagueness of the laws and how much of the problem is the politically responsive biases of the judges and other legal system officials who implement it?