A lot of major social and political institutions these days are what we are calling “deliberately adversarial.” In fact, so many are — to varying degrees — that we have to search harder for good examples of “deliberately non-adversarial institutions.”
Take the criminal justice system. Some parts of it are fairly adversarial, most notably the highly regulated competition between prosecutors and defense attorneys. And some parts of it are relatively non-adversarial: for example, as the narrator at the beginning of Law & Order always put it, “the police who investigate crime.” A police force is largely bureaucratic service agency. Policies and orders are conveyed hierarchically. Employees are trained and hired to carry about the basic tasks, like investigating crimes and handing out parking tickets. We could imagine a deliberately adversarial alternative to this way of “keeping the peace.” There could be private firms that individuals and firms contract for security, to investigate crimes, to make arrests, and so on. (These services obviously exist in the market now to supplement the work of the police.) But in all civilized societies, we now rely heavily on bureaucratic police forces, not vigilantes and hired goons.
Another part of the criminal justice system involves coroners and medical examiners. And that is also, surely, a non-adversarial system where highly trained medical experts are hired to determine the causes of all deaths (in order to decide if the death was possibly caused by a criminal activity that needs to be investigated).
That’s how it always is on TV. But not, it transpires, in all parts of the US:
In a joint reporting effort, ProPublica, PBS Frontline and NPR spent a year looking at the nation’s 2,300 coroner and medical examiner offices and found a deeply dysfunctional system that quite literally buries its mistakes.
Blunders by doctors in America’s morgues have put innocent people in prison cells, allowed the guilty to go free, and left some cases so muddled that prosecutors could do nothing…
More than 1 in 5 physicians working in the country’s busiest morgues—including the chief medical examiner of Washington, D.C.—are not board certified in forensic pathology, the branch of medicine focused on the mechanics of death, our investigation found. Experts say such certification ensures that doctors have at least a basic understanding of the science, and it should be required for practitioners employed by coroner and medical examiner offices….
And here’s the kicker:
In many places, the person tasked with making the official ruling on how people die isn’t a doctor at all. In nearly 1,600 counties across the country, elected or appointed coroners who may have no qualifications beyond a high-school degree have the final say on whether fatalities are homicides, suicides, accidents or the result of natural or undetermined causes.
The NPR report on the radio included interviews with two rival candidates for the office of coroner in Colorado (I believe). One has held the job for a while and is a medical doctor. He has run as a Democrat, and just barely won the last election against a Republican tide where many voters vote for the entire ticket (i.e. vote for every Republican running for every office on the ballot). His rival for the office is a businessman, not a doctor, and his platform was based on a complaint that the “sitting” coroner was wasting too much money by performing too many autopsies.
In many cases, it is a relatively easy call whether an institution should involve a deliberately adversarial element — like an election or the use of a market — and in these cases are main issues are about how the competition should be regulated and how the individuals occupying special roles should negotiate various ethical dilemmas.
But in the case of coroner or medical examiner, surely there is a good case for saying that the selection procedure should be non-partisan and based on expertise. No? Especially in the relatively unusual (by international standards) American case where police chiefs, district attorneys, and judges are elected and usually affiliated with political parties. In the case of suspicious deaths (say, someone who dies in police custody) we wouldn’t want to also be suspicious of whether the coroner was protecting these political allies… would we?
Ethics for Adversaries 
It’s worth noting, of course, that meritocracies are adversarial too — it’s just that when people are selected based on merit, they’re competing with each other to win the approval of some higher-up or a selection committee, rather than competing for the approval of the electorate. That’s not to blur the distinction you point out, which is clearly important.
Judges are sometimes elected in the US, too. Is there a requirement that they be lawyers? I assume so. If so, that seems a reasonable constraint on an adversarial system, one the coroner-selection process could imitate.
I suspect judges don’t have to be lawyers in most jurisdictions (indeed, many appointed judges in other countries are not lawyers — esp. justices of the peace, for small-claims court, etc).
But your main point is important. It’s still not clear to me exactly HOW to conceptualize the distinction between adversarial and non-adversarial institutions. Most major institutions have various components of both types, and use competitive selection procedures of various kinds. We want to capture something important about holding a competition to get a task or service accomplished rather than doing it “directly” so to speak. But it’s still not obvious how to think about this. I suspect there’s room for a major philosophical paper.