Cartels of Mediocrity

Reproducing a sociology simulation paper about social norms and the tendency towards low-quality exchanges and suboptimal outcomes.

The Unaccountability Machine¹ by Dan Davies is broadly about how and why dysfunctional systems produce outcomes nobody seems to want. It also contains a tidy introduction to Cybernetics² and ideas like the viable system model³ and requisite variety⁴.

Reading that got me interested in more systems and sociology topics, eventually leading me to a pair of papers:

1. The LL game: The curious preference for low quality and its norms (Gambetta & Origgi, 2012)⁵
2. Social Norms and the Dominance of Low-Doers (Proietti & Franco, 2018)⁶

Both were approachable and engaging despite my total unfamiliarity with game theory, sociology, and behavioral modeling. After 25 years in industry it was refreshing to see a formal take on corporate clique culture. And the papers were timely with a few things in my life:

• I’d been prototyping some game ideas involving simulated agent populations and emergent behavior with my kid, and the second paper does exactly that
• I’d been looking for a reason to try Clerk⁷, a Clojure visual notebook tool
• It was performance review time at work

So I committed to reproducing the paper’s findings in Clojure and its tables/figures (plus new ones) using Clerk.

This is a draft post. Clerk notebook and source code to follow.

The phenomenon

Professionally, have you ever felt like your hard work wasn’t furthering your career, or even irritating some colleagues? Ever thought maybe things would be easier if you coasted a bit? Maybe you needn’t even feel bad about it if your peers had the same mindset.

The dissonance is reduced by interacting always with the same people, whom one can trust for not challenging one’s standards. L-doers segregate themselves in mutual admiration societies.

This is the mindset from which Gambetta & Origgi’s “cartels of mediocrity” arise. The LL game abstract:

We investigate a phenomenon which we have experienced as common when dealing with an assortment of Italian public and private institutions: people promise to exchange high quality goods and services (H), but then something goes wrong and the quality delivered is lower than promised (L). While this is perceived as ‘cheating’ by outsiders, insiders seem not only to adapt but to rely on this outcome. They do not resent low quality exchanges, in fact they seem to resent high quality ones, and are inclined to ostracise and avoid dealing with agents who deliver high quality. This equilibrium violates the standard preference ranking associated to the prisoner’s dilemma and similar games, whereby self-interested rational agents prefer to dish out low quality in exchange for high quality. While equally ‘lazy’, agents in our L-worlds are nonetheless oddly ‘pro-social’: to the advantage of maximizing their raw self-interest, they prefer to receive low quality provided that they too can in exchange deliver low quality without embarrassment. They develop a set of oblique social norms to sustain their preferred equilibrium when threatened by intrusions of high quality. We argue that cooperation is not always for the better: high quality collective outcomes are not only endangered by self-interested individual defectors, but by ‘cartels’ of mutually satisfied mediocrities.

And later in the LL game:

Our basic point so far can be summed up thus: if you give me L but in return you tolerate my L we collude on L-ness, we become friends in L-ness, just like friends we tolerate each other’s weaknesses. But if you give me H that leaves you free to disclose my L-ness and complain about it. So you are not my friend, I fear and resent you, and if I cannot punish you for producing H, at least I avoid dealing with you. While in an ordinary world it is L-doers who are punished by avoidance and exclusion, in an L-dominated world it is H-doers who are ostracised. Essentially, the L-exchange can be seen as a cartel of mediocrities who pretend to be H.

There seems to be two forces that could contrast our supposed natural inclinations to L-ness and promote quality, one is the passion for a job well-done, the intrinsic pleasure found in employing and testing one’s skills at some task; the other is competition, succeeding at which carries extrinsic rewards. Generically, these forces fail if the algebraic sum of rewards and punishments for H-ness is lower than the sum of rewards and punishments for L-ness. Even H-prone individuals are ultimately driven to choose L (or to become eccentric and isolated ‘perfectionists’ or to migrate) if they systematically fail to gain any reward from their effort. In short, L spreads if it pays off. This remains a tautology, however, unless we can understand the conditions that affect the relative payoffs of H and L.

I recommend reading the LL game just for the examples of different H/L exchanges, their psychosocial underpinnings, and the colorful Italian anecdotes⁸.

Social Norms and Low-Doers takes these ideas further with social agent simulation in NetLogo⁹. After modeling the social corrosion of L-worlds, it tests different regimes of rewards/sanctions to foster high-quality exchange:

Social norms play a fundamental role in holding groups together. The rationale behind most of them is to coordinate individual actions into a beneficial societal outcome. However, there are cases where pro-social behavior within a community seems, to the contrary, to cause inefficiencies and suboptimal collective outcomes. An explanation for this is that individuals in a society are of different types and their type determines the norm of fairness they adopt. Not all such norms are bound to be beneficial at the societal level. When individuals of different types meet a clash of norms can arise. This, in turn, can determine an advantage for the “wrong” type. We show this by a game-theoretic analysis in a very simple setting. To test this result – as well as its possible remedies – we also devise a specific simulation model. Our model is written in NETLOGO and is a first attempt to study our problem within an artificial environment that simulates the evolution of a society over time.

The game

A society of agents that collaborate with each other, accumulate payoffs, age, retire, and get replaced by new hires over time. Their collaborations are simply a mutual exchange of abstract “goods”:

Assume for simplicity that goods can be produced at two levels of quality, High (H) and Low (L). H is both more rewarding to receive and more costly to produce than L; H takes more time, effort, skills and organisation.

Agents independently choose how much effort to put in: H (high) or L (low). Neither knows the other’s choice in advance. The four possible outcomes from any agent’s perspective:

Every agent has a type, which describes their ranking of preferred outcomes, e.g. HH > HL > LH > LL. All orderings of those four outcomes yield 24 possible types in all, each classifiable along two axes: a type is selfish when free-riding (LH) is its top choice, and high-minded when it ranks mutual-high (HH) above mutual-low (LL).

Proietti & Franco focus on two canonical types to start. Both are selfish (their top preference is giving L and receiving H) but they differ in their mindedness (which they’d prefer if selfishness isn’t on the table.)

• hs1 (high-minded) prefers mutual-high (HH) over mutual-low (LL). Starts out playing H.
• ls1 (low-minded) prefers mutual-low (LL) over mutual-high (HH). Starts out playing L.

Such agents are arguably likely to be found in a competitive society where individuals are incentivized to participate in many activities (for example improving their CV by publishing, teaching, participating to conferences and research projects) while at the same time economizing their efforts and getting the most out of them.

Payoffs follow the preference ordering:

Agents can reconsider their strategy after an exchange. Each agent tracks two running tallies per partner (which are reset whenever the agent changes strategy):

• Shortfall: cumulative gap between actual payoff and what both playing baseline would have earned.
• Balance: running difference between actual payoff and what the opposite action would have earned with this partner.

When the shortfall crosses a threshold, a negative balance triggers a switch in the agent’s baseline strategy.

The asymmetry for the hs1 vs ls1 collaborations is in their opening play: hs1 starts at H and can fall short, but ls1 starts at L and in an LL exchange already earns its second-best outcome.

sequenceDiagram
    participant hs1
    participant ls1

    Note over hs1: plays H (baseline)
    Note over ls1: plays L (baseline)

    hs1->>ls1: H
    ls1->>hs1: L

    Note over hs1: earns 1 (sucker)
shortfall +2, balance −1
    Note over ls1: earns 4 (free-rider)

    Note over hs1: shortfall ≥ threshold
balance < 0 → switches to L

    loop Every subsequent round
        hs1->>ls1: L
        ls1->>hs1: L
        Note over hs1: earns 2, shortfall grows
but switching back to H
would only earn 1 --- stuck
        Note over ls1: earns 3 (preferred LL)
    end

The simulation

Proietti & Franco implement the model simulation in NetLogo, and I based my reproduction on their published source code¹⁰.

Each simulated year:

1. Reset everyone’s annual earnings
2. Retire the oldest agents and replace them with fresh ones
3. Every pair plays one round; earnings are gated by a collaboration probability
4. Age everyone
5. Mark anyone past the retirement age for mandatory retirement
6. Mark a bottom % earners for early retirement

The institution hires 50/50 from hs1/ls1. The mechanism that tips the balance is in step 6: ls1 agents systematically out-earn hs1 agents over time, so hs1 agents have shorter careers/earlier retirements. Try-hards burn out and low-doers inherit the org: fresh hs1 replacements (hired 50/50) start out playing H, get exploited again, and the cycle repeats.

The agent state is a plain map; the memory map is keyed by partner id and tracks the shortfall/balance running tallies.

(defn agent [id type]
  {:my-id id :type-of-academic type :age 0 :total-payoff 0 :memory {}})

Each round, both agents decide independently whether to offer H or L, then record the exchange:

(defn play-round
  ([a1 a2] (play-round a1 a2 default-params true))
  ([a1 a2 params pays-out?]
   (let [act1 (decide a1 (:my-id a2) params)
         act2 (decide a2 (:my-id a1) params)
         [p1 p2] (typ/payoffs (:type-of-academic a1)
                              (:type-of-academic a2)
                              [act1 act2])]
     [(record-exchange a1 (:my-id a2) act1 act2 p1 pays-out?)
      (record-exchange a2 (:my-id a1) act2 act1 p2 pays-out?)])))

The decide function implements the reconsider rule: an agent plays its baseline until shortfall crosses the threshold, then a negative balance flips it to the opposite action (H-to-L or vice versa.)

(defn- reconsidering? [baseline shortfall threshold]
  (and (= baseline :H) (>= shortfall threshold)))

(defn decide
  [agent partner-id {threshold :change-of-strategy-threshold
                     :keys [reward-tick? reward-pct sanction-pct reward-maxes]}]
  (let [t    (:type-of-academic agent)
        base (typ/baseline-action t)
        m    (get-in agent [:memory partner-id])
        last (:last-action m base)]
    (if (reconsidering? base (:difference-from-optimal m 0) threshold)
      (let [rb (if reward-tick?
                 (reward-balance t (:recon-exch m {})
                                 (reward-prob (:window-hh agent 0)
                                              (:max-hh reward-maxes))
                                 (reward-prob (:window-ll agent 0)
                                              (:max-ll reward-maxes))
                                 (double (or reward-pct 0))
                                 (double (or sanction-pct 0)))
                 0.0)]
        (if (neg? (+ (:balance m 0) rb))
          (other last)
          last))
      base)))

The reward-tick? branch is used later: when a reward/sanction regime is active, the expected reward/sanction differential (rb) is added to the balance before the switch test.

I think it’s important to note, as in the paper, the experiments below are conducted on a fully-connected network of agents and each connection has a probability of collaboration. Obviously this doesn’t accurately reflect many organizations that may be more hierarchical or siloed. To that end they also model scale-free networks where agents have fewer connections, and they find those conditions more favorable for hs1.

The outcomes

Given a society of 20 agents hired evenly from hs1 and ls1: H actions begin around 20% of exchanges, then collapse to a ~9% steady state within the first decade or two and hold there across 1,500 simulated years.

Career churn

The churn driving that collapse shows up in the career tenures and retirement reasons, by type. Plotting tenure-at-retirement, hs1 (left) piles up at short tenures while ls1 (right) generally lasts longer.

Splitting the same records by why each agent left is more telling. hs1 dominates the early-retirement side (bottom-% earners forced out under sustained low payoffs), while agents that survive to the mandatory retirement age reach it at similar tenures regardless of type. ls1’s longer careers come from rarely capitulating, not from outlasting hs1 once it does.

Robustness

The paper’s finding holds across society sizes and strategy-change thresholds. (See original: 4.3)

Table 4 breaks that asymmetry by raising hs1’s LL payoff above ls1’s, so an hs1 stuck in mutual-low no longer trails its partner as it does under normal payoffs, yet the simulated outcome is mostly the same. (See original: 4.7)

What can be done?

The paper tests two basic strategies for preventing the collapse into low-quality exchanges:

1. Change who you hire (the society’s composition)
2. Change their incentives (rewards for HH, sanctions for LL)

Hiring filters

The first lever is the mix of agent types in the society. The obvious move, hiring more hs1 agents, slows the decline but doesn’t stop it. (See original: 4.10)

As the paper notes:

Furthermore, it is quite challenging for a policy maker or employer to succeed in hiring such a high percentage of high-minded individuals.

Heroes & Saints

What works better is changing the kind of high-minded agent you hire. These two non-selfish, high-minded types protect the H equilibrium:

• hn1 (hero): always plays H, even as the sucker, though it still ranks free-riding (LH) on top in preference.
• hn2 (saint): same behavior as the hero, but goes further and ranks LH below LL, so it wouldn’t even want to exploit.

Both types resist the capitulation mechanism entirely: since they always play H regardless, their shortfall/balance never push them to capitulate. Swap hs1 for either and the H-rate hovers around 50%.

Under such conditions, the efficiency of an institution can be sustained if high-minded people are not selfish, we may call them “heroes” or “saints”.

While reliably hiring heroes (hn1) and saints (hn2) would evidently be more effective than hiring 70-90% high-minded, selfish agents (hs1), it is similarly challenging for most organizations. Mathematically, they cannot all “hire only the best.”

Rewards & Sanctions

The second lever leaves the agent mix alone and changes the incentives (the reward-tick? branch of decide above).

As it turns out, rewarding HH exchanges has little effect, but sanctioning LL exchanges pulls capitulated hs1 agents back to H: the looming penalty enters the reconsider calculation and tips the balance.

Frequency also matters: sanctions every round push H-rates above 65%, while sanctions every three rounds barely help at all. Sanctioning LL is what helps. Frequent sanctions help more (bottom-left), and hiring more hs1 pushes the effect toward ~90% (bottom-right).

Sanctions only fire when an agent is in range of a reconsideration, so the more hs1 agents you start with, the more often the penalty has something to penalize. Hiring 65% hs1 lifts the baseline and reduces the sanction-frequency impact, recovering much of the sanction benefit even at the every-three-years cadence where 50/50 hiring collapses.

With selective hiring and balanced incentives, the H-rate climbs to ~90% (the most effective policy tested in the paper.)

Takeaways

These papers model societies/organizations that tend toward an equilibrium where low effort becomes pro-social behavior despite the undesirable outcomes. They contend “cartels of mediocrity” form against those offering higher quality exchanges.

To my mind, the big insight is that pro-social conformists and disillusioned try-hards (not free-riders) are the true drivers of decay: agents who’d genuinely prefer mutual excellence get captured by a social norm, “rationally” capitulating once sufficiently exploited. The high-minded burn out earlier and churn, and are replaced with new hires, keeping the organization flush with new subjects.

My advice to anyone finding themselves in scenarios resembling the ones above is to take pride in doing high-quality work even if peers do not! (But also, work within your means¹¹. Don’t sacrifice your sanity and burn out.)

Notes