Degrees of fairness.
I will advance the philosophy that nearly all differences in people's success in life are not a result of choices but of blind chance; and thus a meritocracy is just unfairly (lopsidedly) rewarding good luck.
For example, consider somebody with extraordinary good luck: Me. The following may sound like braggadocio; but it is not: Keep in mind I am arguing against merit, and I do not believe I deserve much credit for what I say next.
I have a perfect academic record through 14 years of college, and 5 college degrees in STEM fields, including a PhD. Yet I worked far less than most people around me to achieve that; in fact I mostly wandered into most of it.
In some way I was born to take classes. I can memorize a textbook (and have done so three times, all to "test out" of various history classes). It is short term, and gone from my memory completely within a day or so; but I can do it. Unlike other students, if I pay attention in class (front row, near the center) I do not need to study. A standard "full time" academic load is four classes per semester (12 hours per week attending class). That allows room for study. I have (after signing exemption releases) taken 9 classes, in four different semesters, and aced all of them.
I never struggle with recalling terminology; and I very seldom struggle with understanding the analysis of professionals in any subject; from art analysis to physiology to psychology to all of the sciences. Again, it is short term; once the class is passed, if I don't need it for a subsequent class, my mind seems to discard it. I've taken a dozen classes that I passed with wall to wall 100's, and now can remember almost nothing about, or remember perhaps fifteen minutes worth of ideas that interested me.
I also say it isn't magic; there is an amount of work I must do: Attending class, copying board notes, executing the graded assignments. A great deal of showing up on time.
But many students do all that work plus study for double the class hours, and those are hours I never put in. So when I crush them all in class, and as a result I am given opportunity, jobs, recognition and receive invitations to join various elite organizations, I have to wonder: For what exactly am I being rewarded?
Because I did not work as hard, I put in a third of the effort of my most diligent fellow students. I passed spelling tests in grade school by reading the list of words, once. For the first few my father would test me; without a failure. He gave up on that, and after that I was lucky he told me to read my list, or I might have forgotten! I may not remember those words days later, but during the tests I could "see" full pages of them in the order given.
This is an ability I was born with: I was also born white and male in a white-male dominated society, also as an American citizen, and raised from infancy on an extraordinarily low pollution island (my family was military). I grew taller than most people, a proven advantage in job seeking. I have symmetrical features, I am nearly never sick, and I have good teeth due to good medical and dental care.
I personally did not choose those mental or physical traits or my environment; I don't think I did anything intentionally to make a life change until I was 15. My mental and physical traits are not a result of any practice: My inherent memorization skill was evident by the age of three.
So again, what am I rewarded for? Traits I was born with.
Whatever merit my work and abilities may have (and they have helped many people, and helped make products, businesses and other more scientific efforts quite successful), the secret sauce is not hard work or painful exercise or dedication: I did far less of that than hundreds of others people that were rewarded with a tenth of what has come to me.
This is the central difficult question for any form of meritocracy: Isn't rewarding and respecting somebody for a born trait just as misguided as persecuting or punishing somebody for a born trait?
I am personally happy to live in comfort and be respected, I certainly do not want to give it up. Nevertheless, it is patently unfair that others live in poverty and misery because, through no choice of their own, they were born with disabilities instead of abilities, with dark skin instead of light, as homosexuals instead of heterosexuals, with poor immune systems instead of robust ones, in polluted environments instead of crystal clear paradises. Or born to irresponsible or abusive parents instead of attentive ones, or in poverty instead of wealth or even the middle class: Or as a result of being born thusly, for those whose potential was squandered because the only schools available to them were crappy derelicts, understaffed by the dregs of the teaching profession, making them miss all the crucial learning opportunities during the development of their intellect and brains, which are then gone forever: Adults simply cannot learn like children, and such children are left permanently disadvantaged, through no fault of their own.
The vast majority of "merit" is luck. Millions of kids pour their time into practicing some sport, but only some hundreds in any given sport will ever become professionals.
Like me in academics, those that reach the top will not get there by practicing harder than others: The work does matter, but the millions are doing it: The top performers have something extra they did not gain by choice: Some lucky combination of genes, environment, contacts and social circumstances (being in the right place at the right time to take advantage of some unique opportunity). The same goes for acting, for writing, for business, even for inventing.
Merit is over-rated: when thousands compete, the winners are not really working much harder than the best of the rest: Their wins are ultimately due to plain old luck.
You want to classify governments. It really does not matter too much how many people are in charge, or how exactly decisions are made. A dictator can be benevolent or cruel; likewise with a Congress or Parliament or board of Elders. Whether everybody gets to vote, or only certain qualified people can vote, or nobody votes: Makes little difference in the lives of the people.
The government decides how the society will treat its people, what will be rewarded and what will be punished, what wrongs will be ignored and what will be addressed.
So what really matters is how fair or unfair the government is; how much misery and persecution people must endure, and how imbalanced the punishments and rewards are, and how imbalanced the access to resources, courts, schools, medical care, housing and income are.
The important criteria is; where is the floor on misery for those born with the least of natural mental and physical advantages? Is it homelessness, starvation, and dying of an infection that could have been treated with a dollar's worth of penicillin?
A meritocracy is inherently unfair. Nearly everything about life is a roll of the dice, and it will heap rewards on one and misery on another when neither of them chose a thing. Not to mention that the most miserable often has to work many times harder than the lucky one that is richly rewarded.
What matters in a government is degrees of fairness on all these fronts. There is a good argument, from human nature, for rewards to correlate with ability; it is the rewards that encourage the gifted to develop and pursue their gifts, usually to the betterment of society. The work is still a prerequisite to refining the gift. For example it is hard to become a medical doctor; and without the higher pay and prestige and respect and gratitude for lives saved, many of the rare people capable of doing it would not bother.
However, that does not mean such rewards must be unlimited. In business or in professions.
In other areas of society, merit should not matter at all: being famous, or rich, or a politician, or poor, or unintelligent, should not have any effect whatsoever on one's fate in court. Justice should be equal in every respect to all, from how long one must wait, whether one must wait in prison or not, or whether one gets a good lawyer or not. So, for example, it would be more fair in society if all defense lawyers and all prosecutors (tested for competence) but made exactly the same amount of money no matter who they represented. By somehow eliminating the possibility of a lawyer getting rich by having a rich client or negotiating a huge settlement, the lawyers would have fewer incentives to represent the rich over anybody else. The same idea could apply to doctors and other professionals whose decisions routinely have life altering consequences.
Rewarding people for good luck is fine; but to me, government should provide some leveling mechanism so that people do not suffer for lack of luck, or just bad luck. I do not mean there should be no disparity of income or comfort or entertainments: Getting "ahead" in society is a strong motivator to actually put in the hours of work and learning required to develop one's inborn talents, be they athletic, acting, scientific, creative or artistic.
What I mean is better governments do a better job of minimizing human misery for that 49.9% of society born with less luck than most of their fellow citizens, and ensuring that treatment is fair to all: There may be an elite class of businessmen and stars in sport, music, acting and arts: but there should be zero elite when it comes to the courts, prisons, law enforcement, legal representation, education, health care, nutrition, drinking water and other environmental concerns.
A typology based upon Degrees of Fairness in these many categories will tell you far more about a government and a society than how many people are in Congress or whether a governor can pardon a criminal. Those things are really a proxy (and a poor one) for what is ultimately degrees of fairness: An ability of a King, President or Governor to pardon somebody and overturn a decision by a jury is less fair. Prosecutorial discretion, as in the ability of a prosecutor to choose not to prosecute a police officer for a murder-on-tape, is less fair. "Representative" government, as in denying citizens the ability to vote directly on laws and regulations, taxes and decisions to go to war that can have dramatic effects on their lives, is less fair.
Judgment of a government is going to come down to the totality of fairness or unfairness it causes; all other traits are just proxies for how we can expect that will ultimately work out. A robust typology will attempt to measure directly the actual Degrees of Fairness achieved in categories that really matter the most to the people being governed.