This is a genuinely interesting application of Binmore's framework, and the core descriptive thesis (that fairness norms reflect the long-run balance of bargaining power) is well-supported by the specific historical evidence you marshal. But I think that account is incomplete in a way that matters, because it only addresses one of the two recognized components of fairness as a moral foundation.
Jonathan Haidt's Moral Foundations Theory identifies two distinct intuitions that both operate under the heading of "fairness": equality (equal treatment, anti-domination) and proportionality (reward commensurate with contribution, merit, and effort). Your article focuses almost entirely on the equality dimension, more equal bargaining power produces more egalitarian norms, but proportionality is largely absent from the analysis. This isn't a minor gap, because proportionality turns out to be doing enormous amounts of moral work both historically and in modern liberal democracies.
Consider the surgeon and the burger flipper. Modern western societies, your own example of relatively equal bargaining power, accept very large income and status differentials between them, and crucially, burger flippers themselves typically endorse this as fair. This can't be explained purely by the surgeon's superior bargaining leverage over minimum wage workers.
What's actually happening is an intersubjective judgment of proportional desert: the surgeon's work is more valuable, more difficult, and accessible to far fewer people for reasons that are themselves recognizable as genuine rather than arbitrary. The scarcity of good surgeons isn't socially constructed; it's grounded in real cognitive and technical demands that most people cannot meet regardless of opportunity. The proportionality intuition fires even in anonymous one-shot experimental conditions where no power differential exists, which is difficult to square with a purely bargaining-power account.
But proportionality as fairness isn't a feature of modern liberal democracy specifically, or a byproduct of relatively equal bargaining power. It appears persistently across highly unequal historical arrangements and your own historical evidence, read carefully, supports this.
The clearest example may be Imperial China's keju examination system, which selected government officials through competitive written examinations for more than a millennium. This was among the most hierarchical, power-concentrated societies in human history, yet it voluntarily institutionalized a meritocratic selection mechanism that explicitly overrode hereditary privilege for its most consequential administrative positions. A peasant's son who passed could become a senior official; an aristocrat's son who failed could not. Under a pure bargaining-power account, this is hard to explain. Why would power-holders institutionalize a system that could displace their own children? It certainly wasn't by mass demand of the peasantry using their collective leverage to bargain for it.
The answer is that proportional competence-based selection was recognized as both genuinely fair and functionally necessary. Leadership and large-scale administration of a complex empire is genuinely difficult work, valuable to everyone it governs, and executable well only by a relatively small number of capable people. Concentrating resources, education, and authority in those people isn't arbitrary domination. It's a rational solution to the problem of distributing scarce, high-stakes roles. The Confucian framework underpinning the system made this explicit: legitimate authority was earned through demonstrated virtue and competence, and the Emperor's own legitimacy rested partly on maintaining a well-ordered meritocratic bureaucracy. This is Haidt's Authority foundation operating as a complement to proportional fairness rather than in tension with it.
The same logic, more clumsily instantiated, ran through European feudalism. The ideology of noble blood was a poor mechanism (hereditary transmission is a crude proxy for inheritance of an ancestor's demonstrated talent) the system removed many of the selection pressures it needed to maintain, and it calcified badly. But these are failures of system design and the practical limits of pre-modern understanding of heritability, not purely moral failures.
Noblesse oblige encoded genuinely reciprocal obligations, and the animating aspiration was proportional and practical: concentrate the scarce resources required for effective leadership in those most capable of using them. When serfs described good lords as fair, they weren't only registering that the lord had chosen not to fully exploit his power advantage. They were also recognizing, as your own citations of Thompson and Moore suggest with their language of reciprocal obligation and rough balancing out, that the lord was performing a genuinely difficult and valuable function they could not easily replace (not merely "could not replace" as in lacking the political power to do so, but in already having the best of the available candidates for the position). Running a medieval estate was demanding work; lords who did it poorly brought their families to ruin, much as a bad CEO eventually bankrupts a company.
The variation you're tracking across societies, more versus less egalitarian norms, is real, and the bargaining-power mechanism is a genuine part of the explanation. But it captures movement along the equality axis of fairness while the proportionality axis operates throughout. A framework built on Binmore alone doesn't seem to account for proportionality intuition of Fairness that is cross-cultural, empirically basic, and present even in the most unequal societies in the historical record.
The difference between a serf accepting aristocratic privilege because defiance means death and a burger flipper accepting a surgeon's higher income because they genuinely think it's warranted isn't a minor detail; it's the moral core of what fairness is actually doing in society, and it requires proportionality to explain.
I fully agree that proportionality is central to fairness. In fact, it is central to Binmore’s framework. I simply did not go into the formal details of his model in this post.
When bargaining power is unequal, the solution in Binmore’s framework is a proportional bargaining solution. Fairness norms assign people social indices, and the fair solution is the one in which people’s gains over the status quo are proportional to these indices. Binmore explicitly connects this to Aristotle’s idea that fairness is proportional: fairness means equality among equals and inequality among unequals.
So I do not think there are two different explanations here, one based on power and one based on proportionality. There is a unified explanation. Equality is the special case in which people’s claims are given equal weight. When bargaining power is unequal, the solution remains proportional, but the relevant social indices give unequal weight to different people’s claims. These indices reflect the long-run balance of bargaining power, but they also shape moral perception: what people come to see as a legitimate claim, a legitimate contribution, or a legitimate entitlement.
The possible misunderstanding comes from the fact that I focused in the post on raw power. But talent, contribution, effort, scarcity, responsibility and need can also enter the relevant social indices because they affect what people can credibly claim. Take work. In a society where workers are free to work here or there, and can credibly withhold their labour, they have bargaining power. Work will then be rewarded with a higher social index: when splitting a pie, the person who worked more can claim more. But in a society where some people are compelled to work and have few exit options, as under serfdom, labour has lower bargaining power. The fact that one’s contribution took the form of labour will then receive lower weight relative to other claims, such as the lord’s control of land.
The post did not go into the weeds of Binmore’s proportional bargaining solution. We might still discuss whether it perfectly captures all our intuitions about proportionality. But I think it does capture something very general: fairness is proportional. What changes across societies is not whether fairness is proportional, but which claims count, how much weight they receive, and how these weights reflect the long-run balance of bargaining power.
Thank you for the generous and thoughtful response. This is exactly the kind of rabbit hole worth going down and I'm glad to hear that Binmore indeed goes deeper on it.
I take the point that Binmore's proportional bargaining solution already attempts to incorporate proportionality through the social indices mechanism, and that equality is just the special case where indices are weighted equally. That's a more unified framework than I gave it credit for, which is a pleasant surprise, and I'll want to dig more into that as opportunity permits. .
I think the social indices concept is where the real question lives then, and your serfdom example actually sharpens it for me. You note that serf labor received lower weight in the indices because workers couldn't credibly withhold it, their bargaining power was too low. That's one clean explanation for why THAT outcome was what it was. Your historical example again well supports your claim. Other historical examples though, like the keju examination system, sits awkwardly here. Peasant scholars had essentially no bargaining leverage over the imperial court, yet the system assigned very high social index weight to demonstrated administrative competence, enough to override hereditary claims from people who actually did have power. The index in that case doesn't appear to me to be tracking what people could credibly claim through leverage. It was tracking something the powerful recognized as genuinely valuable independent of the scholar's ability to withhold his services.
This suggests to me that the social indices are doing two distinct kinds of work that the framework may be collapsing together: one is genuinely bargaining-derived (what can you credibly threaten or withhold), and the other is something closer to an independent moral perception of legitimate contribution that shapes the bargaining structure from outside rather than emerging from within it. If that's right, then Binmore's framework describes how fair outcomes get negotiated given a set of social indices, but leaves the question of where those indices get their content, and why some weightings feel legitimate and others feel like mere coercion, only partially answered.
Haidt's proportionality foundation might be better understood as part of the explanation for 'why' certain contributions attract high index weight across very different power environments, rather than as a competing explanation to Binmore's conception of proportionality (I'm not familiar with how his indices are constructed to say). The two frameworks may be operating at different levels rather than genuinely contradicting each other. That would still mean that bargaining power isn't the whole story of Fairness though, a meaningful distinction for the broader thesis. If you're open to editing the article, it might be worth integrating Binmore's take on proportionality into it, possibly with a link to background reading for those interested in a more nuts and bolts view of the inputs and outputs for the indices.
Again, thanks for the article and reply, some fascinating stuff to ponder here.
Your mention of the keju examination system is very interesting. I think there are several things to say to explain this system.
First, the perspective from Binmore is not that fairness norms track bargaining power here and now, but that they reflect the long-run structure of bargaining power. In the short run, some people with low bargaining power can benefit from fairness norms. Fairness norms are equilibria of the game. They work because people share expectations that others will respect them, and that others expect them to be respected. An equilibrium is sticky: one does not change shared expectations from one day to the next. So it is often people with low bargaining power now who can benefit from the protection of norms.
In the case of the keju examination system, it was not expected that peasant scholars would be the main beneficiaries of the system. If one or two managed to pass through it successfully, they could benefit from the protection of the norm even though they themselves had low bargaining power. This answer, however, does not explain why a system would be created by the elite that allowed even a few peasants to succeed.
A second point is that an explanation in terms of bargaining power does not exclude the possibility that agents without much bargaining power can benefit from the social contract. For that to happen, enough people with bargaining power need to care about them, or to have reasons to support norms protecting them. Consider children, they have little direct bargaining power, but societies can grant them rights because adults care about them. This does not yet provide a decisive answer in the case of the keju, because one can still ask why the elite would care about a few peasants who might succeed in the examination system.
The answer, I think, is that there is also an efficiency element. Societies benefit from allocating talent to the right places. Plato’s highly hierarchical project in the Republic already recognised this point. In the myth of the metals, people are divided into three broad classes: rulers, whose souls contain gold; auxiliaries or soldiers, whose souls contain silver; and producers, whose souls contain bronze or iron. But Plato also allowed for movement between classes: if a child born from bronze or iron parents had gold or silver in his soul, he should be promoted; if a ruler’s child had bronze or iron in his soul, he should be demoted. Even in a hierarchical system, some promotion of talent is efficient.
Many societies used versions of this logic. Slaves could be freed in Rome if their masters were satisfied with their work. Non-citizens could become citizens through military service. In Islamic empires, slaves could rise to become soldiers, administrators, or even rulers. Why would an elite allow this? One answer is that accepting a few capable people from lower classes can benefit the elite itself. Society works better; lower classes may accept the social contract more easily if, in theory, some can rise; and rulers can use promoted outsiders to counterbalance entrenched hereditary elites.
A further answer lies in cultural evolution driven by intergroup competition. When there is no competition, elites can shape institutions almost entirely to their own advantage. But when there is intergroup competition, more efficient groups are better at organising, producing, administering, and fighting. They are more likely to survive and replace less efficient groups. In China, the emergence of the empire followed an extraordinary selection process among polities: from 148 recorded states engaged in recurring conflict during the Spring and Autumn period, to Qin’s unification of China in 221 BCE. Qin was characterised by higher quality institutions for large-scale administration, mobilisation, taxation, and war. Qin’s success helped shape the long-run political culture of imperial China. The keju system emerged much later (7th century AD), but it came within a political tradition that had valued bureaucratic competence very highly.
My overall take is that Binmore’s framework provides the right underlying foundations to explain fairness and morality. Many psychological accounts, even insightful ones, give us categories that fit our observations of moral intuitions. Binmore’s framework goes deeper: it starts from the fundamental problem of human interaction, namely how agents with partly conflicting interests can sustain cooperation over time. His results are generated in a simplified setting, especially with only two social groups, but they are rigorous. They do not merely organise what we already think about morality; they explain why fairness norms take the form they do, and often force us to accept conclusions we would not have reached intuitively but that seems actually right when thinking about it.
This exchange has genuinely piqued my interest in Binmore's framework beyond what I'd previously encountered, so I did some initial reading into the intersection of his work with cultural and evolutionary theory. The intergroup competition mechanism you describe does seem to be present in his account, the idea that societies landing on more efficient fairness equilibria are more likely to survive and propagate their norms through cultural selection, with the social indices as the ever-shifting product of that process. That's a more complete picture than I had coming in, and it does address the keju case more than I thought it could.
I did happen to run across some of the academic critiques of Natural Justice in the process, and one in particular seems topical to where this conversation has been going. Seabright raises the concern that if bargaining power and self-regarding preferences do the heavy lifting throughout, it becomes difficult to explain why genuinely moral intuitions about fairness would have evolved at all — why couldn't naked bargaining simply coordinate on equilibria without any accompanying sense of justice? The implication being that the existence of what feel like hardwired moral intuitions suggests something beyond pure power-tracking is doing work in shaping which index weightings propagate and why. https://www.joelvelasco.net/teaching/5330/seabright06_essayonBinmore.pdf
I'm not raising that as a gotcha. I don't know Binmore's response, if there was one, to Seabright, and you might. But it seems to sit right at the intersection of everything we've been discussing, arguing that the moral sense of Fairness is truly more than merely bargaining power over time with weighted indices, that there is an other-regarding element demonstrated to be involved, to be significant, to be not adequately explained and even seemingly rejected in Binmore's account, so I'm curious whether you think that critique lands or whether Binmore has a satisfying answer to it somewhere other than in Natural Justice.
I know Paul very well but I actually did not know about this paper. Nice find! As you say it is not a fundamental critique, rather something about the details. Paul asks a good question about why we need moral intuition. My take is that one way to think about them is that they embody the shadow of the future. In repeated interactions, the cost of violating a norm is not only immediate punishment; it is the future loss of trust, cooperation, reputation, and membership in a social equilibrium. Moral emotions make these future costs and benefits motivationally present. Guilt, shame, resentment, gratitude and indignation help agents enact equilibrium behaviour without having to calculate the repeated game each time.
This is one of the main explanations of social emotions: they reflect values to guide decision (I discuss this role of social emotions in my book). Now we can discuss why emotion would take exactly the features they have but I think it is a discussion which can take place within Binmore’s framework.
This is an excellent description of what I too am uncomfortable with on the essay series. Power differentials are a relevant factor, but in my opinion an even more important factor is proportional fairness.
It seems to me that people have different notions on fairness which can differ based on the circumstances.
1. Equal rewards regardless of contribution
2. Rewards proportionate to contribution
3. Rewards proportionate to position or title (which may be a shortcut to #2)
4. Rewards proportionate to need
To this LP adds one which I haven’t previously thought about…
5. Rewards proportionate to power
I certainly understand that there is no intrinsic way to decide which of these is best for any particular situation, (though I think the veil exercise can get us a long way there).
You've omitted the modern case of the credentialing class hoarding opportunity in the name of fairness and merit, while it couches this in language that leaves no recourse for the people for whom it did not work fairly at all. The contemporary credentialing class needed a justification for continuing to hoard opportunities for itself through elite education. That subverts the stated goal of our supposedly egalitarian society by failing to apportion opportunity based on ability, because we know educational pedigree basically determines whether a talented but poor kid's potential will ever be met. You've concluded that we have fairly equal distribution of bargaining power, but the above would seem to contradict that conclusion.
I think it is a matter of degree. I do not claim that modern societies are perfectly egalitarian, only that bargaining power is much more widely distributed than in feudal, slave-holding or patriarchal societies.
You are right that education and credentialing remain major sources of inequality, and that these inequalities come with their own justifications. This is close to one of Bourdieu’s central critiques: the credentialed class can function as a new nobility, with its own mechanisms of reproduction and its own legitimising language.
This fits the framework I have presented. Modern societies are more egalitarian than past hierarchical societies, but they still contain some concentrations of power, and these are also justified through the fairness language of the time.
Excellent quotes. I checked the Sallust line and it actually says "iustos dominos", which translates more precisely as “just masters” or “fair masters”. So it is exactly a case in point.
A great example is the 1515 Slovene peasant revolt, where rebels demanded the reintroduction of the original feudal obligations and trade rights, "old rights" or "stara pravda" in Slovenian.
Great post, one question. Would you argue that the same principle applies to failed "democratic" interventions into Libya, Iraq, Afghanistan, etc.?
Thanks Jaros. On Libya, Iraq, Afghanistan, and similar cases, yes, I think the same principle partly applies. My post was already too long, so I shelved a section on failed institutional change. Democratic institutions do not take hold simply because they are formally introduced. They require expectations, habits, organisations and norms that make people believe the new rules are the real rules of the game.
There are earlier examples in Europe. In France’s first democratic presidential election in 1848, voters chose Louis-Napoléon Bonaparte, a Bonapartist strongman who later staged a coup d’état in 1851. In 1871, after the fall of the Second Empire, French voters elected a monarchist majority. Democracy had arrived institutionally before democratic norms had fully taken root.
So I would say that failed democratic interventions are often cases where the formal rules changed faster than the underlying social contract. If large parts of the population still trust older sources of order, such as tribe, sect, religion, patronage, monarchy, military authority or local strongmen, then elections alone will not create a liberal-democratic equilibrium. Gordon Brown put the point well: “In establishing the rule of law, the first five centuries are always the hardest.”
I'm likely anticipating what you plan to address in your next post, but two things struck me here and when I read Binmore. They concern what happens when an "external" shock changes the size of the pie. Those shocks tend to lead to renegotiation, not just proportional changes in the slices the bargainers get.
1. If I understood correctly, Binmore argued (Natural Justice, p. 175) that bargaining after a shock tends to lead to more egalitarian solutions (at least when there is no external enforcer).
2. Shocks may be strictly "external," but they may also be the result of choices made by people or groups. Technological innovation is one such shock; or entrepreneurship more broadly.
Because a shock could be pursued intentionally (2), it could itself be a strategic move to bring about a more egalitarian equilibrium (1).
Couldn't I reasonably ask whether provoking renegotiation (with a bias towards egalitarianism) by bringing about a shock is something I "ought to do?" And would I be able to answer that from within Binmore's framework or would I not have to resort to some other justification for aiming for egalitarianism?
Hi Nathan, that’s a very interesting question, and it does indeed anticipate the next post.
I think the key point in the passage you mention is the short-run role of fairness norms as coordination devices. When circumstances change, for instance because the feasible set expands through a new technology, innovation, or institutional opportunity, people need to coordinate on a new social contract. The existing fairness norm helps them do so without having to haggle from scratch, which could easily produce conflict.
Binmore’s use of the word “egalitarian” here can be a bit confusing. In this context, it means the egalitarian bargaining solution given the relevant social indices. These indices reflect the accepted social weights of the different parties. So the solution is “egalitarian” in the technical sense that weighted gains are equalised. It is not necessarily egalitarian in the everyday sense of giving people equal shares.
Binmore’s point is about the time scales of fairness. In the short run, the fairness norm uses social indices inherited from the old situation. It can therefore guide people toward a new settlement when a shock expands the set of possibilities. But over time, if the new situation persists, the social indices themselves adjust to the new balance of bargaining power.
Regarding your second point, Binmore only considers external shocks in that passage because he wants to explain how fairness norms work as coordination devices in new situations. To think of a game where people can deliberately create shocks, one would need to model the whole game. That can get tricky. If I know you might make a move that increases your bargaining power later, I may act differently now to prevent you from making it. This is a very interesting dynamic, but it adds layers of complexity to Binmore’s framework.
Now to answer your question: you ask whether we “ought” to create these shocks. I interpret this as: given that shocks may lead to an egalitarian solution, should we create them? I think the answer is that shocks do not generally lead to “egalitarian” solutions in the everyday sense. That was my point above. And even if a shock could lead to a more egalitarian solution in the everyday sense, there is nothing in Binmore’s framework that says we categorically “ought” to create it.
The injunctions in Binmore’s framework are not categorical imperatives but hypothetical ones. If we want society to work well, we should look for social contracts that are: 1) stable, in the sense that they are equilibria of the social game; 2) efficient, in the sense that they do not leave gains from cooperation on the table; and 3) fair, in the sense that they coordinate people around a solution using social indices that, in the long run, reflect the balance of bargaining power.
In our modern liberal democracies, this tends to support fairly egalitarian social contracts. But from this perspective, if we “ought” to aim for egalitarian solutions, it is because they fit our preferences and because they are better suited to our modern societies, not because Binmore’s framework gives us an absolute moral command to seek equality.
I look forward to your next installment then! I'm still trying to wrap my head around exactly how the social indexing works, what it means for interpreting "egalitarianism," and how it evolves. Regardless of how it works, though, the fact that shocks can be strategically deployed (or strategically prevented, as you rightly point out) means that its "games all the way down."
That's why, after reading Binmore, I felt like the questions "What do we owe others?" and "What is the good life?" transformed into "What kind of player do you want to be?"
Binmore's description of social indices is, I think, harder than it needed to be because he does not want to describe them as reflecting the social worth of individuals. I think it is easier to think about them as reflecting the conventionally recognised social worth of individuals, not absolute worth. In the egalitarian case, people with higher indices receive larger gains over the status quo, so we can think of these indices as reflecting the social consideration given to their needs and desires relative to others. In the medium term, these indices change to reflect the balance of power, so people with greater bargaining power may end up benefiting from higher indices, giving them more.
Great work and an important reorientation of morals/norms to the realities of bargaining/power.
One thing I'm pondering is the possible feedback loop here. New power relations, coalitions, etc. mean that groups have more bargaining power and hence new fairness norms represent stable solutions to the new power arrangement (I hope I've got that right so far). But in the case of democracy, at least, the new arrangement can be parlayed into further increasing the bargaining power of a particular group. E.g. once people have secured the vote, they can vote for candidates who promise to further increase their bargaining power (through wealth redistribution, new rights, greater enfranchisement, etc.). I don't know if this generally happens, but it seems like it can happen, such that "the people" use their bargaining power strategically to increase their future bargaining power.
This is seems like it's importantly distinct from the usual trend whereby bargaining power is increased because of some endogenous factor: population growth, urbanisation, a new weapon or technology, etc.
Binmore’s formal framework is deliberately static and does not really model coalitional dynamics, because doing so would make the problem vastly more complex. I see it more as a foundation on which this kind of dynamic analysis can be built.
The feedback loop you describe is relevant. New bargaining power can generate new institutions and fairness norms, but those institutions can then be used to increase bargaining power further. Democracy is the obvious case: once a group secures the vote, it can support candidates and policies that increase its future bargaining power through redistribution, labour rights, education, welfare protections, or further enfranchisement.
This is the logic behind the “slippery slope” fear that played such a large role in debates over franchise extension. Opponents understood that granting political rights to new groups would not merely recognise an existing shift in power. It could also give those groups the institutional means to reshape the future balance of power.
Right. And then I guess this leads into a separate question of whether people do generally vote to increase their own bargaining power… although that’s usually framed in terms of whether this or that group vote for their own self interest.
This is a great essay! But I don't buy that our moral intuitions are completely flexible and depend only on the power distribution. You show that to some extent they do depend - but in so complex phenomenon it would be kind of absurd to assume that it is completely determined by one factor.
In other words, fairness is what seems fair to the powers that be? We see this in Plato's dialogs on the definition of justice. Also in the property qualification for the right to vote in the early American republic. We do not see it in the Old Testament however, where God is depicted as being no respecter of persons. Nor in the modern idea that justice should be blind. Equality under the law is a democratic ideal with roots in Judeo-Christian tradition. All premodern societies by contrast rested in the final analysis on military conquest. Full disclosure: I have not yet read the article.
Hi Luke, I think the view that fairness is simply what is convenient to the powerful is not Socrates’ view, but Thrasymachus’. Plato has Socrates argue against it.
Binmore’s position is subtler. Over time, fairness norms tend to adjust to the underlying balance of power. In that sense, Thrasymachus has a point. But this does not mean that, day to day, the powerful can simply redefine fairness at will. Once a fairness norm is established, it is a rule of the social contract. It binds expectations and constrains even the powerful, at least in the short run.
Binmore explicitly discusses Plato's text about justice:
“In Plato’s Republic, Socrates disputes the nature of justice with Glaucon and Thrasymachus. Glaucon gets short shrift for putting a view close to the social contract ideas defended in this book. Thrasymachus proposes that justice is simply what the powerful are able to impose. One might categorize the result obtained in Section 4.6.4 by saying that Thrasymachus turns out to be right in the medium run. However, decisions are not made in the medium run—they are made in the short run.”
This is a genuinely interesting application of Binmore's framework, and the core descriptive thesis (that fairness norms reflect the long-run balance of bargaining power) is well-supported by the specific historical evidence you marshal. But I think that account is incomplete in a way that matters, because it only addresses one of the two recognized components of fairness as a moral foundation.
Jonathan Haidt's Moral Foundations Theory identifies two distinct intuitions that both operate under the heading of "fairness": equality (equal treatment, anti-domination) and proportionality (reward commensurate with contribution, merit, and effort). Your article focuses almost entirely on the equality dimension, more equal bargaining power produces more egalitarian norms, but proportionality is largely absent from the analysis. This isn't a minor gap, because proportionality turns out to be doing enormous amounts of moral work both historically and in modern liberal democracies.
Consider the surgeon and the burger flipper. Modern western societies, your own example of relatively equal bargaining power, accept very large income and status differentials between them, and crucially, burger flippers themselves typically endorse this as fair. This can't be explained purely by the surgeon's superior bargaining leverage over minimum wage workers.
What's actually happening is an intersubjective judgment of proportional desert: the surgeon's work is more valuable, more difficult, and accessible to far fewer people for reasons that are themselves recognizable as genuine rather than arbitrary. The scarcity of good surgeons isn't socially constructed; it's grounded in real cognitive and technical demands that most people cannot meet regardless of opportunity. The proportionality intuition fires even in anonymous one-shot experimental conditions where no power differential exists, which is difficult to square with a purely bargaining-power account.
But proportionality as fairness isn't a feature of modern liberal democracy specifically, or a byproduct of relatively equal bargaining power. It appears persistently across highly unequal historical arrangements and your own historical evidence, read carefully, supports this.
The clearest example may be Imperial China's keju examination system, which selected government officials through competitive written examinations for more than a millennium. This was among the most hierarchical, power-concentrated societies in human history, yet it voluntarily institutionalized a meritocratic selection mechanism that explicitly overrode hereditary privilege for its most consequential administrative positions. A peasant's son who passed could become a senior official; an aristocrat's son who failed could not. Under a pure bargaining-power account, this is hard to explain. Why would power-holders institutionalize a system that could displace their own children? It certainly wasn't by mass demand of the peasantry using their collective leverage to bargain for it.
The answer is that proportional competence-based selection was recognized as both genuinely fair and functionally necessary. Leadership and large-scale administration of a complex empire is genuinely difficult work, valuable to everyone it governs, and executable well only by a relatively small number of capable people. Concentrating resources, education, and authority in those people isn't arbitrary domination. It's a rational solution to the problem of distributing scarce, high-stakes roles. The Confucian framework underpinning the system made this explicit: legitimate authority was earned through demonstrated virtue and competence, and the Emperor's own legitimacy rested partly on maintaining a well-ordered meritocratic bureaucracy. This is Haidt's Authority foundation operating as a complement to proportional fairness rather than in tension with it.
The same logic, more clumsily instantiated, ran through European feudalism. The ideology of noble blood was a poor mechanism (hereditary transmission is a crude proxy for inheritance of an ancestor's demonstrated talent) the system removed many of the selection pressures it needed to maintain, and it calcified badly. But these are failures of system design and the practical limits of pre-modern understanding of heritability, not purely moral failures.
Noblesse oblige encoded genuinely reciprocal obligations, and the animating aspiration was proportional and practical: concentrate the scarce resources required for effective leadership in those most capable of using them. When serfs described good lords as fair, they weren't only registering that the lord had chosen not to fully exploit his power advantage. They were also recognizing, as your own citations of Thompson and Moore suggest with their language of reciprocal obligation and rough balancing out, that the lord was performing a genuinely difficult and valuable function they could not easily replace (not merely "could not replace" as in lacking the political power to do so, but in already having the best of the available candidates for the position). Running a medieval estate was demanding work; lords who did it poorly brought their families to ruin, much as a bad CEO eventually bankrupts a company.
The variation you're tracking across societies, more versus less egalitarian norms, is real, and the bargaining-power mechanism is a genuine part of the explanation. But it captures movement along the equality axis of fairness while the proportionality axis operates throughout. A framework built on Binmore alone doesn't seem to account for proportionality intuition of Fairness that is cross-cultural, empirically basic, and present even in the most unequal societies in the historical record.
The difference between a serf accepting aristocratic privilege because defiance means death and a burger flipper accepting a surgeon's higher income because they genuinely think it's warranted isn't a minor detail; it's the moral core of what fairness is actually doing in society, and it requires proportionality to explain.
Thanks Steven for this very thoughtful criticism.
I fully agree that proportionality is central to fairness. In fact, it is central to Binmore’s framework. I simply did not go into the formal details of his model in this post.
When bargaining power is unequal, the solution in Binmore’s framework is a proportional bargaining solution. Fairness norms assign people social indices, and the fair solution is the one in which people’s gains over the status quo are proportional to these indices. Binmore explicitly connects this to Aristotle’s idea that fairness is proportional: fairness means equality among equals and inequality among unequals.
So I do not think there are two different explanations here, one based on power and one based on proportionality. There is a unified explanation. Equality is the special case in which people’s claims are given equal weight. When bargaining power is unequal, the solution remains proportional, but the relevant social indices give unequal weight to different people’s claims. These indices reflect the long-run balance of bargaining power, but they also shape moral perception: what people come to see as a legitimate claim, a legitimate contribution, or a legitimate entitlement.
The possible misunderstanding comes from the fact that I focused in the post on raw power. But talent, contribution, effort, scarcity, responsibility and need can also enter the relevant social indices because they affect what people can credibly claim. Take work. In a society where workers are free to work here or there, and can credibly withhold their labour, they have bargaining power. Work will then be rewarded with a higher social index: when splitting a pie, the person who worked more can claim more. But in a society where some people are compelled to work and have few exit options, as under serfdom, labour has lower bargaining power. The fact that one’s contribution took the form of labour will then receive lower weight relative to other claims, such as the lord’s control of land.
The post did not go into the weeds of Binmore’s proportional bargaining solution. We might still discuss whether it perfectly captures all our intuitions about proportionality. But I think it does capture something very general: fairness is proportional. What changes across societies is not whether fairness is proportional, but which claims count, how much weight they receive, and how these weights reflect the long-run balance of bargaining power.
Thank you for the generous and thoughtful response. This is exactly the kind of rabbit hole worth going down and I'm glad to hear that Binmore indeed goes deeper on it.
I take the point that Binmore's proportional bargaining solution already attempts to incorporate proportionality through the social indices mechanism, and that equality is just the special case where indices are weighted equally. That's a more unified framework than I gave it credit for, which is a pleasant surprise, and I'll want to dig more into that as opportunity permits. .
I think the social indices concept is where the real question lives then, and your serfdom example actually sharpens it for me. You note that serf labor received lower weight in the indices because workers couldn't credibly withhold it, their bargaining power was too low. That's one clean explanation for why THAT outcome was what it was. Your historical example again well supports your claim. Other historical examples though, like the keju examination system, sits awkwardly here. Peasant scholars had essentially no bargaining leverage over the imperial court, yet the system assigned very high social index weight to demonstrated administrative competence, enough to override hereditary claims from people who actually did have power. The index in that case doesn't appear to me to be tracking what people could credibly claim through leverage. It was tracking something the powerful recognized as genuinely valuable independent of the scholar's ability to withhold his services.
This suggests to me that the social indices are doing two distinct kinds of work that the framework may be collapsing together: one is genuinely bargaining-derived (what can you credibly threaten or withhold), and the other is something closer to an independent moral perception of legitimate contribution that shapes the bargaining structure from outside rather than emerging from within it. If that's right, then Binmore's framework describes how fair outcomes get negotiated given a set of social indices, but leaves the question of where those indices get their content, and why some weightings feel legitimate and others feel like mere coercion, only partially answered.
Haidt's proportionality foundation might be better understood as part of the explanation for 'why' certain contributions attract high index weight across very different power environments, rather than as a competing explanation to Binmore's conception of proportionality (I'm not familiar with how his indices are constructed to say). The two frameworks may be operating at different levels rather than genuinely contradicting each other. That would still mean that bargaining power isn't the whole story of Fairness though, a meaningful distinction for the broader thesis. If you're open to editing the article, it might be worth integrating Binmore's take on proportionality into it, possibly with a link to background reading for those interested in a more nuts and bolts view of the inputs and outputs for the indices.
Again, thanks for the article and reply, some fascinating stuff to ponder here.
Your mention of the keju examination system is very interesting. I think there are several things to say to explain this system.
First, the perspective from Binmore is not that fairness norms track bargaining power here and now, but that they reflect the long-run structure of bargaining power. In the short run, some people with low bargaining power can benefit from fairness norms. Fairness norms are equilibria of the game. They work because people share expectations that others will respect them, and that others expect them to be respected. An equilibrium is sticky: one does not change shared expectations from one day to the next. So it is often people with low bargaining power now who can benefit from the protection of norms.
In the case of the keju examination system, it was not expected that peasant scholars would be the main beneficiaries of the system. If one or two managed to pass through it successfully, they could benefit from the protection of the norm even though they themselves had low bargaining power. This answer, however, does not explain why a system would be created by the elite that allowed even a few peasants to succeed.
A second point is that an explanation in terms of bargaining power does not exclude the possibility that agents without much bargaining power can benefit from the social contract. For that to happen, enough people with bargaining power need to care about them, or to have reasons to support norms protecting them. Consider children, they have little direct bargaining power, but societies can grant them rights because adults care about them. This does not yet provide a decisive answer in the case of the keju, because one can still ask why the elite would care about a few peasants who might succeed in the examination system.
The answer, I think, is that there is also an efficiency element. Societies benefit from allocating talent to the right places. Plato’s highly hierarchical project in the Republic already recognised this point. In the myth of the metals, people are divided into three broad classes: rulers, whose souls contain gold; auxiliaries or soldiers, whose souls contain silver; and producers, whose souls contain bronze or iron. But Plato also allowed for movement between classes: if a child born from bronze or iron parents had gold or silver in his soul, he should be promoted; if a ruler’s child had bronze or iron in his soul, he should be demoted. Even in a hierarchical system, some promotion of talent is efficient.
Many societies used versions of this logic. Slaves could be freed in Rome if their masters were satisfied with their work. Non-citizens could become citizens through military service. In Islamic empires, slaves could rise to become soldiers, administrators, or even rulers. Why would an elite allow this? One answer is that accepting a few capable people from lower classes can benefit the elite itself. Society works better; lower classes may accept the social contract more easily if, in theory, some can rise; and rulers can use promoted outsiders to counterbalance entrenched hereditary elites.
A further answer lies in cultural evolution driven by intergroup competition. When there is no competition, elites can shape institutions almost entirely to their own advantage. But when there is intergroup competition, more efficient groups are better at organising, producing, administering, and fighting. They are more likely to survive and replace less efficient groups. In China, the emergence of the empire followed an extraordinary selection process among polities: from 148 recorded states engaged in recurring conflict during the Spring and Autumn period, to Qin’s unification of China in 221 BCE. Qin was characterised by higher quality institutions for large-scale administration, mobilisation, taxation, and war. Qin’s success helped shape the long-run political culture of imperial China. The keju system emerged much later (7th century AD), but it came within a political tradition that had valued bureaucratic competence very highly.
My overall take is that Binmore’s framework provides the right underlying foundations to explain fairness and morality. Many psychological accounts, even insightful ones, give us categories that fit our observations of moral intuitions. Binmore’s framework goes deeper: it starts from the fundamental problem of human interaction, namely how agents with partly conflicting interests can sustain cooperation over time. His results are generated in a simplified setting, especially with only two social groups, but they are rigorous. They do not merely organise what we already think about morality; they explain why fairness norms take the form they do, and often force us to accept conclusions we would not have reached intuitively but that seems actually right when thinking about it.
This exchange has genuinely piqued my interest in Binmore's framework beyond what I'd previously encountered, so I did some initial reading into the intersection of his work with cultural and evolutionary theory. The intergroup competition mechanism you describe does seem to be present in his account, the idea that societies landing on more efficient fairness equilibria are more likely to survive and propagate their norms through cultural selection, with the social indices as the ever-shifting product of that process. That's a more complete picture than I had coming in, and it does address the keju case more than I thought it could.
I did happen to run across some of the academic critiques of Natural Justice in the process, and one in particular seems topical to where this conversation has been going. Seabright raises the concern that if bargaining power and self-regarding preferences do the heavy lifting throughout, it becomes difficult to explain why genuinely moral intuitions about fairness would have evolved at all — why couldn't naked bargaining simply coordinate on equilibria without any accompanying sense of justice? The implication being that the existence of what feel like hardwired moral intuitions suggests something beyond pure power-tracking is doing work in shaping which index weightings propagate and why. https://www.joelvelasco.net/teaching/5330/seabright06_essayonBinmore.pdf
I'm not raising that as a gotcha. I don't know Binmore's response, if there was one, to Seabright, and you might. But it seems to sit right at the intersection of everything we've been discussing, arguing that the moral sense of Fairness is truly more than merely bargaining power over time with weighted indices, that there is an other-regarding element demonstrated to be involved, to be significant, to be not adequately explained and even seemingly rejected in Binmore's account, so I'm curious whether you think that critique lands or whether Binmore has a satisfying answer to it somewhere other than in Natural Justice.
Hi Steven,
I know Paul very well but I actually did not know about this paper. Nice find! As you say it is not a fundamental critique, rather something about the details. Paul asks a good question about why we need moral intuition. My take is that one way to think about them is that they embody the shadow of the future. In repeated interactions, the cost of violating a norm is not only immediate punishment; it is the future loss of trust, cooperation, reputation, and membership in a social equilibrium. Moral emotions make these future costs and benefits motivationally present. Guilt, shame, resentment, gratitude and indignation help agents enact equilibrium behaviour without having to calculate the repeated game each time.
This is one of the main explanations of social emotions: they reflect values to guide decision (I discuss this role of social emotions in my book). Now we can discuss why emotion would take exactly the features they have but I think it is a discussion which can take place within Binmore’s framework.
This is an excellent description of what I too am uncomfortable with on the essay series. Power differentials are a relevant factor, but in my opinion an even more important factor is proportional fairness.
It seems to me that people have different notions on fairness which can differ based on the circumstances.
1. Equal rewards regardless of contribution
2. Rewards proportionate to contribution
3. Rewards proportionate to position or title (which may be a shortcut to #2)
4. Rewards proportionate to need
To this LP adds one which I haven’t previously thought about…
5. Rewards proportionate to power
I certainly understand that there is no intrinsic way to decide which of these is best for any particular situation, (though I think the veil exercise can get us a long way there).
Hi Swami, you might find my answer to Steven about proportionality relevant to your concerns.
Great discussion. Thank you so much for conducting it!
You've omitted the modern case of the credentialing class hoarding opportunity in the name of fairness and merit, while it couches this in language that leaves no recourse for the people for whom it did not work fairly at all. The contemporary credentialing class needed a justification for continuing to hoard opportunities for itself through elite education. That subverts the stated goal of our supposedly egalitarian society by failing to apportion opportunity based on ability, because we know educational pedigree basically determines whether a talented but poor kid's potential will ever be met. You've concluded that we have fairly equal distribution of bargaining power, but the above would seem to contradict that conclusion.
I think it is a matter of degree. I do not claim that modern societies are perfectly egalitarian, only that bargaining power is much more widely distributed than in feudal, slave-holding or patriarchal societies.
You are right that education and credentialing remain major sources of inequality, and that these inequalities come with their own justifications. This is close to one of Bourdieu’s central critiques: the credentialed class can function as a new nobility, with its own mechanisms of reproduction and its own legitimising language.
This fits the framework I have presented. Modern societies are more egalitarian than past hierarchical societies, but they still contain some concentrations of power, and these are also justified through the fairness language of the time.
Sallust famously said that, what most humans say they want liberty, what they mean is that they want kinder masters.
Cicero said that the slaves dreams, not of liberty, but of having his own slaves.
Excellent quotes. I checked the Sallust line and it actually says "iustos dominos", which translates more precisely as “just masters” or “fair masters”. So it is exactly a case in point.
A great example is the 1515 Slovene peasant revolt, where rebels demanded the reintroduction of the original feudal obligations and trade rights, "old rights" or "stara pravda" in Slovenian.
Great post, one question. Would you argue that the same principle applies to failed "democratic" interventions into Libya, Iraq, Afghanistan, etc.?
Thanks Jaros. On Libya, Iraq, Afghanistan, and similar cases, yes, I think the same principle partly applies. My post was already too long, so I shelved a section on failed institutional change. Democratic institutions do not take hold simply because they are formally introduced. They require expectations, habits, organisations and norms that make people believe the new rules are the real rules of the game.
There are earlier examples in Europe. In France’s first democratic presidential election in 1848, voters chose Louis-Napoléon Bonaparte, a Bonapartist strongman who later staged a coup d’état in 1851. In 1871, after the fall of the Second Empire, French voters elected a monarchist majority. Democracy had arrived institutionally before democratic norms had fully taken root.
So I would say that failed democratic interventions are often cases where the formal rules changed faster than the underlying social contract. If large parts of the population still trust older sources of order, such as tribe, sect, religion, patronage, monarchy, military authority or local strongmen, then elections alone will not create a liberal-democratic equilibrium. Gordon Brown put the point well: “In establishing the rule of law, the first five centuries are always the hardest.”
I'm likely anticipating what you plan to address in your next post, but two things struck me here and when I read Binmore. They concern what happens when an "external" shock changes the size of the pie. Those shocks tend to lead to renegotiation, not just proportional changes in the slices the bargainers get.
1. If I understood correctly, Binmore argued (Natural Justice, p. 175) that bargaining after a shock tends to lead to more egalitarian solutions (at least when there is no external enforcer).
2. Shocks may be strictly "external," but they may also be the result of choices made by people or groups. Technological innovation is one such shock; or entrepreneurship more broadly.
Because a shock could be pursued intentionally (2), it could itself be a strategic move to bring about a more egalitarian equilibrium (1).
Couldn't I reasonably ask whether provoking renegotiation (with a bias towards egalitarianism) by bringing about a shock is something I "ought to do?" And would I be able to answer that from within Binmore's framework or would I not have to resort to some other justification for aiming for egalitarianism?
Hi Nathan, that’s a very interesting question, and it does indeed anticipate the next post.
I think the key point in the passage you mention is the short-run role of fairness norms as coordination devices. When circumstances change, for instance because the feasible set expands through a new technology, innovation, or institutional opportunity, people need to coordinate on a new social contract. The existing fairness norm helps them do so without having to haggle from scratch, which could easily produce conflict.
Binmore’s use of the word “egalitarian” here can be a bit confusing. In this context, it means the egalitarian bargaining solution given the relevant social indices. These indices reflect the accepted social weights of the different parties. So the solution is “egalitarian” in the technical sense that weighted gains are equalised. It is not necessarily egalitarian in the everyday sense of giving people equal shares.
Binmore’s point is about the time scales of fairness. In the short run, the fairness norm uses social indices inherited from the old situation. It can therefore guide people toward a new settlement when a shock expands the set of possibilities. But over time, if the new situation persists, the social indices themselves adjust to the new balance of bargaining power.
Regarding your second point, Binmore only considers external shocks in that passage because he wants to explain how fairness norms work as coordination devices in new situations. To think of a game where people can deliberately create shocks, one would need to model the whole game. That can get tricky. If I know you might make a move that increases your bargaining power later, I may act differently now to prevent you from making it. This is a very interesting dynamic, but it adds layers of complexity to Binmore’s framework.
Now to answer your question: you ask whether we “ought” to create these shocks. I interpret this as: given that shocks may lead to an egalitarian solution, should we create them? I think the answer is that shocks do not generally lead to “egalitarian” solutions in the everyday sense. That was my point above. And even if a shock could lead to a more egalitarian solution in the everyday sense, there is nothing in Binmore’s framework that says we categorically “ought” to create it.
The injunctions in Binmore’s framework are not categorical imperatives but hypothetical ones. If we want society to work well, we should look for social contracts that are: 1) stable, in the sense that they are equilibria of the social game; 2) efficient, in the sense that they do not leave gains from cooperation on the table; and 3) fair, in the sense that they coordinate people around a solution using social indices that, in the long run, reflect the balance of bargaining power.
In our modern liberal democracies, this tends to support fairly egalitarian social contracts. But from this perspective, if we “ought” to aim for egalitarian solutions, it is because they fit our preferences and because they are better suited to our modern societies, not because Binmore’s framework gives us an absolute moral command to seek equality.
I look forward to your next installment then! I'm still trying to wrap my head around exactly how the social indexing works, what it means for interpreting "egalitarianism," and how it evolves. Regardless of how it works, though, the fact that shocks can be strategically deployed (or strategically prevented, as you rightly point out) means that its "games all the way down."
That's why, after reading Binmore, I felt like the questions "What do we owe others?" and "What is the good life?" transformed into "What kind of player do you want to be?"
Binmore's description of social indices is, I think, harder than it needed to be because he does not want to describe them as reflecting the social worth of individuals. I think it is easier to think about them as reflecting the conventionally recognised social worth of individuals, not absolute worth. In the egalitarian case, people with higher indices receive larger gains over the status quo, so we can think of these indices as reflecting the social consideration given to their needs and desires relative to others. In the medium term, these indices change to reflect the balance of power, so people with greater bargaining power may end up benefiting from higher indices, giving them more.
Great work and an important reorientation of morals/norms to the realities of bargaining/power.
One thing I'm pondering is the possible feedback loop here. New power relations, coalitions, etc. mean that groups have more bargaining power and hence new fairness norms represent stable solutions to the new power arrangement (I hope I've got that right so far). But in the case of democracy, at least, the new arrangement can be parlayed into further increasing the bargaining power of a particular group. E.g. once people have secured the vote, they can vote for candidates who promise to further increase their bargaining power (through wealth redistribution, new rights, greater enfranchisement, etc.). I don't know if this generally happens, but it seems like it can happen, such that "the people" use their bargaining power strategically to increase their future bargaining power.
This is seems like it's importantly distinct from the usual trend whereby bargaining power is increased because of some endogenous factor: population growth, urbanisation, a new weapon or technology, etc.
Binmore’s formal framework is deliberately static and does not really model coalitional dynamics, because doing so would make the problem vastly more complex. I see it more as a foundation on which this kind of dynamic analysis can be built.
The feedback loop you describe is relevant. New bargaining power can generate new institutions and fairness norms, but those institutions can then be used to increase bargaining power further. Democracy is the obvious case: once a group secures the vote, it can support candidates and policies that increase its future bargaining power through redistribution, labour rights, education, welfare protections, or further enfranchisement.
This is the logic behind the “slippery slope” fear that played such a large role in debates over franchise extension. Opponents understood that granting political rights to new groups would not merely recognise an existing shift in power. It could also give those groups the institutional means to reshape the future balance of power.
Right. And then I guess this leads into a separate question of whether people do generally vote to increase their own bargaining power… although that’s usually framed in terms of whether this or that group vote for their own self interest.
This is a great essay! But I don't buy that our moral intuitions are completely flexible and depend only on the power distribution. You show that to some extent they do depend - but in so complex phenomenon it would be kind of absurd to assume that it is completely determined by one factor.
In other words, fairness is what seems fair to the powers that be? We see this in Plato's dialogs on the definition of justice. Also in the property qualification for the right to vote in the early American republic. We do not see it in the Old Testament however, where God is depicted as being no respecter of persons. Nor in the modern idea that justice should be blind. Equality under the law is a democratic ideal with roots in Judeo-Christian tradition. All premodern societies by contrast rested in the final analysis on military conquest. Full disclosure: I have not yet read the article.
Hi Luke, I think the view that fairness is simply what is convenient to the powerful is not Socrates’ view, but Thrasymachus’. Plato has Socrates argue against it.
Binmore’s position is subtler. Over time, fairness norms tend to adjust to the underlying balance of power. In that sense, Thrasymachus has a point. But this does not mean that, day to day, the powerful can simply redefine fairness at will. Once a fairness norm is established, it is a rule of the social contract. It binds expectations and constrains even the powerful, at least in the short run.
Binmore explicitly discusses Plato's text about justice:
“In Plato’s Republic, Socrates disputes the nature of justice with Glaucon and Thrasymachus. Glaucon gets short shrift for putting a view close to the social contract ideas defended in this book. Thrasymachus proposes that justice is simply what the powerful are able to impose. One might categorize the result obtained in Section 4.6.4 by saying that Thrasymachus turns out to be right in the medium run. However, decisions are not made in the medium run—they are made in the short run.”
The problem with the way you're treating the attitude of slaves, is that people only complain if they expect their complaints to be listened to.