Sunday, 25 September 2016

Love, the Efficient Market Hypothesis and Berkson's Fallacy

Waking up the day after a late-night out always makes me slightly melancholic... which obviously means we're discussing the Efficient Market Hypothesis (EMH). The EMH is this decades old idea about the perfect efficiency of asset markets, arguing that all (publicly) available information is already priced into any asset. In other words, it's impossible to "beat the market" since the market at any given moment is correctly priced.

The one area I believe the EMH is fairly accurate is in the market for love. Or relations. Or hook-ups – whatever you want to call it, the part of our lives we devote to (semi-)romantic affairs, for longer or shorter time periods. This conviction is something that has gradually grown stronger ever since Adam Smith Economics Society brought Will Nicolson to Uni and I traded a good night’s sleep for giggling my way through his book The Romantic Economist: A Story of Love and Market Forces (and occasionally crying out “this is so neeeerdyyy!”, much to the despair of my flatmates).

In his book, Nicolson describes incidents in his search for love through the lens of common economic concepts; finding undervalued assets, or restricting supply in order to increase one’s price are some of the strategies he attempts. His explanation of the EMH comes through dating a girl he was completely infatuated with. She was brilliant, funny, gorgeous and for some strange reason she seemed to like him. One night out, he rather quickly realized that this amazing girl transformed into a monster from the slightest touch of alcohol, causing a massive scene, throwing up on the dancefloor and eventually passing out in the bathroom; Nicolson’s dream girl was indeed too good to be true. The take-away story here was the EMH, that Nicolson hadn't seen one important part of her price (=what you'd have to put up with to be with her). Clearly, it seemed like Nicolson had stumbled upon a fabulous girl he really fancied, and it was only revealed later on that he indeed had mistaking the price for something much less valuable. 

Or, to state it more bluntly: there’s a reason people are single. If there were no such reason, somebody else would have found and charmed this girl by now, in a sense "taking her off the market".

Yesterday, I found another concept in Ellenberg’s wonderful story (How Not To Be Wrong: The Hidden Maths of Everyday Life) that, combined with the EMH applied to love, gives an astonishingly interesting picture. He explains why handsome guys normally aren't nice - and why nice guys aren't very handsome. Ellenberg calls the graph below The Great Square of Men, and assumes that men are equally scattered across the entire square. 

He is trying to illustrate Berkson's fallacy (also known as Berkson's bias or paradox) by showing how the conclusion ("Handsome men aren't nice") isn't drawn from a random sample, as it should have been, but from the area above the line, to the north-east, labelled ACCEPTABLE. Since we never even consider men below that line, we falsely believe that there's an inverse relationship between nice and handsome, even though the distribution is equally scattered around the Square. 

Now, if we combine this insight with the EMH above, we can actually create the trade-off between handsome and nice that Ellenberg tried to disprove. Since most guys in the area above the line will, at any given moment, be taken and charmed by someone already (EMH...), an observer is unlikely to see them – or even consider them. And since the large area below the line won't be considered either, that leaves a narrow corridor of acceptable yet available guys for anyone on the hunt. Hence, the trade-off still holds, emerging only because you discard guys either side of it. 

Melancholy, perhaps, and maybe even hopelessly mistaken. But I seem to find a certain element of truth in it.

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