Learnings from Oxford, part 1: academics

I previously wrote about how I found the content of my PPE course disappointing, but I think this was overly harsh. Looking back on my three years here, there’s actually a lot that I am glad to have learned. Some of these things are particular arguments I find compelling, or economic models with neat properties – but a lot of them are more general frames for thinking about the world. Economics especially, I think, is good for building these sorts of intuitions.

One difficulty I had when putting this post together was that the most valuable conceptual tools are often the ones you use without even noticing. So, writing this has partly been for me, to better-notice how my mental models for understanding the world have been made richer while at Oxford.

I might write another post in future about my non-academic learnings from Oxford, but that one will take longer, since it’s easy to fall into platitudes.

There’s lots beyond this list that I learned at Oxford, and there are concepts that I used at Oxford which would fit onto this list (thinking on the margin; Berkson’s and Simpson’s paradoxes; comparative advantage; etc). But here, I’ve tried to restrict myself to ideas or frames which (i) are of general value, or if not are just so elegant that they’re worth knowing anyway, and (ii) I learned studying PPE, rather than from e.g. pop-econ books / LessWrong / the SEP.

Optimisation and incentives

• Maybe the most important of everything: agents respond to incentives. When incentives change, you should expect agents’ behaviour to, too.
• Lagrange multipliers tell you how costly a constraint is for the objective you’re optimising.
  • If you’re not being bound by a constraint, then relaxing it can’t make you any better off. (This is known as complementary slackness.)
  • When one feature of a situation changes, the optimum behaviour might change a lot, and the constraints which bind might be very different to before.
    • e.g., in a hidden action principal-agent problem, if you impose a limited liability constraint (where the agent cannot receive a negative wage), you might move from second-best to third-best outcome, where the participation constraint no longer binds, and instead non-negativity does.
• Incentives apply to political actors just as much as anybody else, and there are neat explanations of behaviour using this (although sometimes they verge on just-so stories):
  • How do states form? Maybe it’s when rent-extracting elites decide to fix themselves in a particular region, turning from “roving bandits” to “stationary bandits” – meaning that it’s now in their interests to invest in that area.
  • Why do democracies tend to have more public goods provision? Maybe it’s because the minimum winning coalition is very large (compared to the small groups of elites needed in autocracies), and it’s not sustainable for leaders to simply buy them off with private transfers.
  • Why do dictators often create absurd cults of personality? Maybe it’s so that citizens (and other elites) have a way to credibly show they are supportive, beyond simply mouthing vague enthusiasm.
• If someone is acting optimally, then only the direct effect of small changes to the parameters of their optimisation matters for the outcome – even though the agent will re-optimise under these new conditions, the effects of that re-optimisation on the maximised value vanish.
  • (This is the Envelope Theorem.)
• An optimum almost always involves marginal indifference on the part of the agent.
  • When you’re doing dynamic optimisation (i.e. choosing actions over time), you should be indifferent between consumption now and the present value of consumption in the next period (this is the Euler equation).
    • One practical implication of this, when combined with diminishing marginal utility, is that you should engage in consumption smoothing – i.e., in a sense live (and invest) beyond your means when young, since your lifetime wealth is much greater than your current income naively multiplied out.
    • Learning this was one of the things that contributed to me becoming somewhat less frugal than I had been previously, and I endorse that!
• You can simplify the value of a state recursively, by decomposing it into the utility you obtain moving from that state to the next, plus the discounted value of the next state (the “continuation value”). Intuitively, all that matters is how good what’s next is, and how much you benefit from getting there.
  • (This is the Bellman equation. I had seen it before Oxford in a CS course, but it was completely forgotten by the time it reappeared in third year.)

Equilibrium and efficiency

• A state of affairs can be an equilibrium even if it looks very silly for everybody involved. It’s interesting to think about what the right solution concept is – equilibrium is a static one, so it doesn’t say anything about how you’d arrive at it!
  • It’s fairly well-known that equilibria can be socially bad – e.g. Prisoner’s Dilemma. But they can also be simply implausible as a prediction of outcomes.
    • Consider e.g., the Nash demand game, which has a Nash equilibrium at the inefficient point where both demand the whole prize, knowing that they will receive nothing. It’s very hard to motivate why the players would do this!
    • (Conversely, as a dominant strategy equilibrium, Prisoner’s Dilemma is actually a pretty good prediction of how a one-shot game would turn out, absent altruistic preferences.)
• There are very elegant connections between static equilibrium selection methods and evolutionary game theory, capturing the idea of equilibrium robustness.
  • Every evolutionary stable strategy (one resistant to invasion by mutant strategies) is a locally stable rest point of the replicator dynamic (where strategies grow in proportion to their fitness).
  • The Foster-Young stochastic best-reply process, where a subset of agents at each timestep change their strategy to the current best-reply with some probability of making a mistake, converges on the risk dominant equilibrium – that is, the one which the players jointly have least incentive to deviate from.
    • In the language of ML, we’d say that this equilibrium has the largest basin of attraction. Equivalently, it’s the best response to maximal uncertainty about what your opponent will do (a Laplacian prior).
• Utility representations of preferences really are just that, representations.
  • Debreu’s theorem and similar tell us that – provided an agent’s actions are rationalizable (which mostly means transitive preferences) and meet certain other technical conditions – we can model the agent as maximising a utility function. Nobody thinks she actually has a utility function coded into her brain!
  • (There’s a loose analogy here to multilevel theories in ethics: the actual decision procedure used by agents need not be the same as the theory’s criterion of rightness.)
• With repeated strategic interactions, selfish rational agents can often reach the socially-optimal outcome even if they couldn’t in a one-shot game – but almost anything can be an outcome in this setting, and it’s hard to conclude which.
  • This is the trouble with the folk theorem, or rather theorems – we get an embarrassment of equilibria. You could end up at the socially-pessimal outcome!
• In a bargaining context, where two agents are negotiating over how to allocate resources, increasing the value of your outside option (or your “BATNA”) is a generally reliable way to improve your equilibrium payoff.
  • Being more patient and less risk-averse also helps, at least in the Rubinstein model.
• Under (strong) assumptions, competitive equilibrium is Pareto efficient – or more informally, the invisible hand works. More interestingly, shuffling around initial endowments can sustain any Pareto efficient outcome as a competitive equilibrium.
  • (These are the Fundamental Welfare Theorems.)

Information and risk

• Imperfect information is an incredibly widely-valuable concept, and including it makes economic models much richer (and more realistic).
  • It can be corrosive to trades, especially when parties are asymmetrically informed (see e.g. Akerlof).
  • But sometimes it also makes everyone better off, e.g. by keeping agents disciplined when they would otherwise fail to coordinate.
    • Overlooking this was a mistake a lot of rationalist-adjacent people made in the Midjourney scanner discourse.
    • As another example, a correlated equilibrium with noisy private signals can achieve expected payoffs beyond simple combinations of the convex hull of Nash equilibrium payoffs, whereas public signals cannot.
  • Risk aversion makes dealing with asymmetric information especially difficult.
    • Otherwise, at least in principal-agent problems, you might be able to achieve the first-best outcome just by transferring all the risk to the agent.
  • Because agents lack information, they have to go search for it before they can make trades. Modelling the costs of search can help explain why, for example, homogeneous goods like flour can vary in price significantly between retailers.
• (In)ability to commit can be a big deal. Tools that allow people to make enforceable agreements often allow for Pareto improvements.
  • Variants of hold-up problems appear a lot around us.
• Risk is very valuable for showing where ethical theories like contractualism might go wrong (see Frick and Ashford, and also Bentham’s Bulldog on deontology).
  • (That said, contractualism is a very interesting theory. Emma Curran has some great readings on this whole area of ethics.)
• Impossibility results are a useful way of making intellectual progress in an otherwise intractable space.
  • For microeconomic theory, there are famously many in voting (Arrow, Condorcet, Gibbard-Satterthwaite), but also in e.g. matching and school choice (Kesten), bargaining (Myerson-Satterthwaite), and public goods provision (Green-Laffont)
  • In ethics, but especially axiology-flavoured work, they’re also fruitful. You can show that a set of attractive axioms is mutually inconsistent, or that regardless of which position you adopt, you have to accept an unintuitive result.
    • (See, for example, Hilary Greaves on population ethics, or this decision theory paper from my tutor Hayden Wilkinson.)

Prediction and causality

• Like with much else linear algebra-flavoured, the geometric interpretation of linear regression makes things so much more intuitive. OLS projects your response variable $Y$ into the column space of the regressors $X$, so you mechanically obtain a residual $\hat U$ orthogonal to $X$.
  • From this, the familiar interpretation of $\hat Y$ as the best linear predictor of $Y$ using only $X$ falls out directly.
  • This also helps with understanding what it really means to “control for” a covariate $W$: you take the component of $X_1$ orthogonal to $W$, and project $Y$ onto that. So each of your coefficients can be recovered one at a time, and this is why the coefficient $\hat \beta_1$ tells you the effect of $X_1$ holding $W$ constant.
• Even if you don’t think you’ve managed to control for everything that matters, you can still reason about the sign of the omitted variable bias to figure out whether your estimated coefficients are likely to be under- or over-estimates of the true parameters.
  • For example, suppose you’re looking at economic returns to education, and you think the dominant omitted variable is something about students’ work ethic. Presumably students with a better work ethic would have higher incomes without education, and work ethic also contributes to their enrolling in education. So the coefficient on education is an upper bound on how much it matters for earnings.
• Perhaps surprisingly, omitted variable bias isn’t always a bad thing! If you’re just trying to make predictions, then it’s actively helpful, because it gives you some of the explanatory power of the unobserved variables for free.
• Recovering causal effects is really hard – questions of economic interest are rife with unobservable variables that bias your coefficients – and you can’t do that much better than making theoretical arguments to justify whether you’ve successfully identified causal effects.
  • Instrumental variables are a very neat way around the identification problem: if you can find something that affects the outcome only through the variable of interest, then you can extract an exogenous component and recover the causal effect.
    • But again, the difficulty is in establishing that the instrument actually is exogenous – and that comes back to telling convincing-enough stories about the causal mechanisms in play.
    • The Acemoglu et al. settler mortality paper, and subsequent criticism, is a very nice illustration of this. (It was also just an exceptionally cool paper to read, as an introduction to the concept of IVs and their value.)
• Even when you do recover a causal effect, you need to be careful with its interpretation. Since treatment effects vary between individuals (and this plausibly affects their decision about whether to take up treatment), the effect you measure in a study very often won’t be the same as what happens in the real world.
• Regression to the mean is a mechanical property of imperfectly correlated variables. When one has an extreme realisation, the conditional expectation for the other is always less extreme, being pulled back towards the mean.
  • In the context of stationary time series variables, this means that the best prediction of future values is simply a weighted average of the current value and the long-term mean.

Methodology in ethics

• Although you can just bite every bullet, that’s not a very clever way to do philosophy. Other theories really do have some appeal, sometimes.
• It’s rare that you’ll find a self-defeating theory in ethics, so victories over opposing theories will never be totally complete. What you actually need to do is marshal evidence (in the form of intuitions, usually) that your opponents have to stomach some unappealing consequences if they’re to remain internally consistent.
  • This means ideally you want to construct arguments in neutral-ish territory, rather than preaching to the converted. Richard Chappell explains this well.
  • David Sobel on the impotence of the demandingness objection as levelled against consequentialism is an excellent example of this done successfully, and it’s one of the papers I most enjoyed reading.
  • Sometimes the strategy will be to show that an opposing theory faces a dilemma between two costs: perhaps it is either trivial or false (like Aristotle’s Doctrine of the Mean); either redundant or incoherent (like rule consequentialism); either self-effacing or egoistic (like eudaimonistic virtue ethics).
• It’s not much use complaining that an ethical theory doesn’t justify why it thinks that such-and-such (say, pleasure) is a good-making / right-making property – every theory has to bottom out somewhere. A better line of attack is to object that a theory makes the wrong thing fundamental, or that it’s redundant.
  • For an ethical theory to be worth engaging with, we usually want it to say something distinctive that other theories do not. This doesn’t mean it needs to disagree with them extensionally (i.e., about what is right) – it could offer different justifications for why certain actions are right, and that would be interesting. But if you start patching a theory so that it departs from our intuitions less often, then you’ll often lose what made it worth caring about in the first place.
    • E.g., many of the difficulties contractualism faces in explaining the moral importance of numbers can be addressed by relaxing its restrictions on aggregating claims between individuals – but this undermines the attractive person-to-person justifiability that it supplies.
• You can often have multiple versions of an ethical theory, which agree substantively about what matters, but are just better suited to different kinds of applications.
  • For example, ex ante and ex post consequentialism aren’t really in conflict with each other – the former is how you ought to make decisions (and thus is sensible for deciding whether to praise or blame), while the latter lets you retrospectively assess how well actions turned out (and perhaps learn for the future). And indeed, the decision procedure can differ from the criterion of rightness.
  • As Richard Chappell argues, the apparent conflicts between satisficing, maximising, and scalar consequentialism can be dissolved in this way too.
• “Spectrum arguments” are a particularly effective kind of reductio – you start off with one innocuous premiss, take another innocuous-looking premiss like “if n is F then n + 1 is F”, and then apply transitivity to arrive at a conclusion you’d otherwise have dismissed as absurd.
  • Parfit uses these extensively in his discussion of personal identity, but others like Huemer also deploy them in ethics.
• It’s nice when you can show that an argument proves too much, rather than too little.
  • (I may have learned this from ACX, not sure.)
• You can distinguish between an action being (i) deserving of blame and (ii) productive to blame; similarly so for praise.
• Aristotle writes movingly in Books VIII and IX of Nicomachean Ethics about the special value of virtue-friendship, between two individuals who love each other as another self, and whose relationship is centred around the cultivation of excellence.

Logic and metaphysics

• The question of whether or not another (potentially future) person is identical with you probably doesn’t matter very much for how much you should prudentially care about them. Instead, you should ask how psychologically connected they are with you – and this relation also holds, in varying degrees, with individuals totally discontinuous with you (e.g., friends, family-members).
  • Parfit writes about this at length.
• Logicians actually have pretty good ways of handling vagueness about the truth-value of propositions, and these often involve something like going through each case of how the vagueness could be resolved, to see if they all agree on the final truth-value.
  • (In particular, I’m thinking about supervaluations, but also to a lesser extent Kleene and Łukasiewicz logic.)
  • This feels a bit like doing a sensitivity analysis, and the technique is generally useful for bracketing off uncertainty (or at least understanding how important it is for the conclusions you’re trying to draw).
• The machinery of possible worlds (and their closeness to the actual world) turns out to be broadly useful, because often we need to reason about what might have been – i.e., counterfactuals. Sometimes you even want to quantify over possible worlds, though that gets more difficult.

An assortment of other ideas

• First-order and second-order stochastic dominance are useful ways of thinking about how to compare distributions.
  • They also connect nicely to Gini inequality measures.
• Practically all philosophers agree that moral facts supervene on natural facts: you can’t have a change in moral facts without some natural facts having changed. The disagreements are about why, and whether the co-extension is necessary (which Frank Jackson has a good argument in favour of).
• Rae Langton’s paper on speech acts was a good read, and her argument that certain harmful speech can not only undermine others’ dignity, but also their ability to exercise speech, is clever.
• I had thought about these before starting at Oxford, but having Frankfurt’s precise terminology of higher-order desires to describe, for example, “wanting to want to exercise” is quite helpful.
  • This also connects to Aristotle’s (obviously much earlier) discussion of enkrateia, or self-controlledness in Book VII of his Nicomachean Ethics. His treatment of akrasia (weakness of will) is far better-known, but the enkrates is an almost perfect example of someone whose second-order desires are in conflict with their first-order (unvirtuous, appetitive) ones.