Markovian Humans Make Markovian Markets

Summary: A Markov model is a system whose next move depends only on where it is now, with the past mattering only through whatever it has left behind in the present. I would argue that people work in much the same way, acting on a compressed state of mood, money, memory and whatever happened to them most recently. Real estate, meanwhile, is a slow auction run by these compressed humans, and treating it as a chain of states goes a long way to explaining why prices anchor, why valuations lag, and why the most useful thing you can know about a deal is its present state, $P(X_t)$, if you want any chance of understanding $P(X_{t+1})$.

What Is a Markov Model

In 1913 Andrey Markov took the first 20,000 letters of Pushkin’s Eugene Onegin and counted the vowels and consonants by hand. His interest was in probability, and he wanted to show that a sequence of dependent events could still obey the law of large numbers; in the process he found that the chance of the next letter being a vowel depended heavily on whether the current letter was one.

That is a simplified, but equally comprehensive, compression of the core idea. A process $X_0,X_1,X_2,\dots$ is Markovian when the future, given the present, is independent of the past:

$$P(X_{t+1}=j\mid X_t=i,X_{t-1},\dots ,X_0)=P(X_{t+1}=j\mid X_t=i)=p_{ij}$$

Every rule of the system then fits inside a transition matrix $P$, where $p_{ij}$ is the probability of moving from state $i$ to state $j$, and if you run such a chain for long enough many of them settle into a stationary distribution $\pi$, the share of time spent in each state, which another step leaves unchanged:

$$\pi P=\pi$$

The obvious objection is that almost nothing in the world forgets its past. A loan’s default risk depends on its payment history, and a building’s value depends on decades of maintenance (or the lack of it). The answer is, at face value, very simple. Take whatever part of the past matters and put it into the state, so that a chain which remembers its last three moves becomes a Markov chain over triples. Seen this way, the Markov property is really a claim about how well you have defined the present, and a good model is one in which the current state is a sufficient summary of everything that came before it.

Why People Are Markov Models

Take your past as the universe of everything that has happened to you, every attributable occurrence across your life, so that together they form the set $H_t$ that is your life up to now. Any opinion, position or belief you hold is formed by drawing some subset out of that set, and the number of possible subsets is incomprehensibly large. If we took an exhaustive, time-insensitive approach, any combination would be as valid as any other: when I was two I liked sausages, and I bought a coffee this morning, therefore I will have steak for dinner.

Obviously this is not how decisions get made. Our present state is an aggregate of previous states, and while liking sausages at two may have had some butterfly effect on my decision to have steak for dinner, we can infer that it has been heavily compressed within the experiences that shaped the present state that made the choice. Formally, the decision runs on some compression of that set, $s_t=f(H_t)$.

To put it more concisely, and without making you hungry, consider what you actually know about your own past. Your experience of the present is the culmination of a handful of vivid episodes, a general sense of how things went, a set of habits and a bank balance, with almost everything else compressed away somewhere along the line. When you decide what to do next, that compressed bundle is all you have to work with, which in the language above makes it your state.

The psychology literature reads like a catalogue of this compression.

We Remember the Peak and the End: In a 1993 experiment, Daniel Kahneman and colleagues asked people to hold a hand in painfully cold water for 60 seconds, and separately for 90 seconds in which the final 30 were slightly less cold. Asked which trial they would rather repeat, most chose the longer one, accepting more total pain in exchange for a better ending; the full trajectory had been discarded, a summary had survived, and it was the summary that drove the choice.

We Anchor on the Last Number We Saw: Tversky and Kahneman showed in 1974 that an arbitrary number from a spun wheel was enough to shift people’s estimates of quantities that had nothing to do with it. Whatever number sits most recently in the state tends to leak into the next decision, irrespective of relevance or intent.

Markovian Habits: Most of what any of us does in a given day is whatever we did yesterday in the same context, and a habit is really just a transition probability that has hardened through repetition, where state $i$ is “7am, kitchen” and the next state is coffee with a probability very close to one.

There is a more flattering version of the argument too, because a perfectly rational agent updating its beliefs with Bayes’ rule turns out to be Markovian as well. If $b_t$ is your belief after seeing the evidence up to time $t$, then the next belief needs nothing beyond the current belief and the newest observation:

$$b_{t+1}(s)\propto P(o_{t+1}\mid s)b_t(s)$$

The posterior is a sufficient statistic for the entire history, which means the ideal reasoner and the forgetful human are both Markov; where they differ is in what their state contains. The Bayesian compresses losslessly with respect to everything that matters, while the rest of us compress lossily, holding on to the vivid parts and quietly losing the base rates.

So the question worth asking about a person, a team or a market is what their state contains, since history only matters through it. If you want to predict what someone will do next, their life story is far less useful than their current position, their most recent experience and the last number they anchored on.

Real Estate as a Slow Auction

Real estate is an auction that happens to run in slow motion. A property comes to market, buyers arrive at irregular intervals, offers are made and withdrawn, and eventually a price is discovered by whichever bidder is left standing. Formal auctions compress the whole process into an afternoon, and electronic markets traded by high-frequency firms clear in microseconds, while private treaty sales can stretch it over months. In every case each participant is a compressed human (or a model built by one) acting on a current state, and the market inherits their Markov behaviour.

Asking Prices Anchor Buyers and Professionals Alike: In 1987 Gregory Northcraft and Margaret Neale gave estate agents identical information packs on a real house, varying only the listed price. The agents’ own valuations moved with the list price, and most of them insisted afterwards that the list price had played no part in their thinking, which is about as clean a demonstration as you could hope for of the last number in the state doing the work.

Valuations Remember Too Much of the Last Valuation: Appraisal-based property indices are smoother than transaction prices and lag behind them, a pattern that David Geltner and others documented from the late 1980s onwards. A valuer’s new figure tends to be a weighted blend of the previous figure and whatever new evidence has arrived since:

$$V_t=\alpha P_t+(1-\alpha )V_{t-1}$$

That is a Markov update with a heavy weight on the old state. For any individual valuer it is perfectly sensible behaviour, since a single comparable is a noisy thing to hang a number on, but across a whole market it means that reported values trail reality, which is exactly how portfolios end up marked at last year’s prices in a falling market.

Deals Move Through Markovian States (The Important Bit): A sale or a letting progresses from listed, to viewed, to offer, to under offer, to exchanged and finally to completed, and it can fall back at almost every step along the way. Some of those transitions are far more likely than others, and the probabilities shift with the time a deal has already spent in its current state. A property that has been on the market for six months is in a genuinely different state from the same building in its first week, because buyers read time on market as information and bid accordingly; stale stock is a state in its own right.

Seen this way, a pipeline is a transition matrix. If you estimate the probability of each move from your own history, you can say for any deal how likely it is to complete and roughly when, and most firms already hold the raw material for this in their CRM as a record of stage changes with timestamps, even if almost none of them use it in this way.

The practical lesson is the same one Markov found in Pushkin, which is that if you define the present carefully, the past largely takes care of itself. For a deal, that means recording its stage, how long it has sat there, the last price anchor and who is still bidding; for a market, it means current listings, recent comparables and the age of the valuations that everyone is relying on. Good analysis in property currently comes down to a guesstimate of the state, with mistakes coming from forgetting that every person in the room carries a compressed past into the next decision. The question I would leave you with, then, is why so many real estate firms are failing to make meaningful progress in building the models that would give them an objective, compressed view of the present state.