Randomness in decision-making

Nobody will thank me for saying so, but I have a bit of a mancrush on Ed Smith. Yet again, he has raised a profound point in the social sciences:

Nakedly ambitious people rarely achieve their ambitions...Simplistic self-interest is not just bad PR, it is often bad strategy. It suffers from a fatal flaw: it is predictable.

This draws our attention to the fact that, in some domains, randomness is the best policy.

This is most clear - and has been formalized by game theorists - in the case of games such as rock-paper-scissors where predictability leads to defeat. In such circumstances, the optimal strategy is to randomize.

To what extent do such games exist in the real world? They're common in sport. The penalty-taker who always aims low and left will find goalkeepers quickly wising up. The batsman whose best shots are all on the legside will soon get most balls pitching outside off.

I suspect they exist in other fields. If you're negotiating with a nutter who might randomly choose violence, you might well make concessions that a more rational counterpart couldn't extract; Colonel Gadaffi stayed in power for so long in part because of this, and it seems to have worked for North Korean dictators. One reason why interviewers at Oxbridge or Google have traditionally asked candidates unpredictable questions is to test their powers of thinking on their feet. And one sign of genuine entrepreneurship is the ability to do - or blunder upon! - the unexpected, to wrongfoot rival companies.

However, randomness doesn't just work when the other player is trying to anticipate our actions. It can also work where there's environmental uncertainty.

Take a simple example. Strategy A has a 60% chance of a payoff of 3 and a 40% chance of a payoff of zero. Strategy B has a 40% chance of a payoff of 3 and a 60% chance of a payoff of zero. A is obviously the strategy with the highest expected payoff.

But it doesn't follow that it is the optimum strategy. If the payoffs are the number of descendants the members of a species has, then when that 40% chance comes up, followers of strategy A go extinct.

To maximize the chances of survival, a mixed strategy is needed. The species that randomizes will therefore survive. The one that "optimizes" does not*. This was the failure of the banking system in 2008. In trying to "optimize" banks ran the risk of extinction.

As John Kay showed, very often our goals are reached not through direct optimization, but obliquely.

And as Bruno Frey argues in a new paper, there's much to be said for using random selection in numerous contexts.

This poses the question: why, then, is randomness not used more often? And why do almost no decision-makers admit to using it, preferring instead to emphasize their "careful judgment"?

I suspect it's because we have fallen into a practice of cargo cult optimization and management. In business, politics and even in parts of our personal lives, we use the gestures and language of direct control in the hope that these suffice to achieve our aims. But sometimes, they don't.

* The scare quotes are because I want to duck the question of whether randomization is a form of rational maximization or an alternative to it. In biology, for example, mixed strategies are not consciously chosed by species but rather emerge by selection if they do so at all.

Comments

[Luis Enrique]

um, should there be a non-zero pay-off with 60% prob for strategy B?

[Luke]

Luis, don't think so. Think of two crops. A fails less often than B, but both produce the same if successful. Still might be worth planting a bit of B on the basis it might succeed in a year that A fails. (I'm ignoring storage, available land.)

[Luke]

Luis, not necessarily. Say two crops, A and B, produce the same amount of edible stuff. But A fails 40% of the time, B 60% of the time. It could still be worth planting some B, in the hope that it will succeed in a year that A fails.

[Luis Enrique]

Luke, thanks. Remaining confusion: you seem to be interpreting a "mixed strategy" to mean "plant some A and plant some B". I interpret mixed strategy as "plant only A with some probability and plant only B with some probability" (I think that's the game theory sense of randomising over strategies). In that case I think picking A beats randomising over A and B?

hope I am not embarrassing myself.

[breviosity]

Naked ambition is a bad strategy. The best strategy of all is to be ambitious but not naked about. One way is by disguising it from others. But the best way is by disguising it from oneself by self-deception.

Self-deception is a problem among Left-wing leaders. The Left is opposed to ambition (for evidence see the above post), is as good as anyone at recognizing decievers, so the best way to get ahead as a Leftist is to self-decieve, by truly thinking one is just doing it all for the cause.

[Luke]

Luis, I could be embarrassing myself. How about at a species level? For a species to survive, it might be best for some of them to choose a suboptimal strategy like planting B. Evolution might favour a species in which every third member (or whatever - I can't do the maths) chose to plant B, provided that was random, not hereditary.

[Luis Enrique]

Luke, yes that makes perfect sense to me but again it is interpreting "mixed strategy" to mean some do this others to that. Whereas I'd interpreted Chris to be using the words in this sense:
http://en.wikipedia.org/wiki/Strategy_(game_theory)#Mixed_strategy

[Luis Enrique]

ah no I get you, if you have many individuals each playing mixed strategies in that sense you will end up with some doing A others B. Duh me.

[Luis Enrique]

this paper on relevant topic might interest some:

http://elsa.berkeley.edu/users/cshannon/wp/what.pdf

I *think* it says that in strategic situations if you do not maximize, you actually do better because of the effect "not maximizing" has on your opponents behaviour.

[Jacques René Giguère]

No one with a time horizon longer than one will bet on a strategy where the Markov chain will inevitably produce a 0 result at some point.
That's why there is no lottery with a $10K ticket for an extremely large payoff.
No one, except Mitt Romey would propose such a bet. And he was ridiculed.
And Putin has not won on Ukraine. He merely showed that, after supply lines had been established, everybody will be againsy him. For such small hills we sometimes chose to die.

[Wpaul63]

Love this.
You may want to have a nice chat with that brilliant guy, Brian Eno, who many many many tens of moons ago invented an inspirational deck of cards aptly called... "Oblique Strategies".
:-)

[Luke]

Luis, you have overestimated my knowledge of game theory. As a concrete example, think of salmon. For any river, there must be some optimal trade-off between (a) staying at sea several years to fatten up and produce more eggs/milt and (b) returning ASAP to start breeding. Might vary between males and females. But salmon from most rivers follow a mixed strategy, with some staying one year at sea, others several years (and not a consistent number). Not all "choices" (we're talking fish) can be optimal. But the variation provides insurance against years when spawning conditions are bad (or years when a river is too low for big fish to ascend etc).

My point is that random variations might be beneficial *without* opponents trying to guess your next move as in game theory.

[Luis Enrique]

Hi Luke, yes you're quite right, no need to invoke game theory. I made a simple error, effectively thinking of an entire species acting as one, rather than a multitude, each playing mixed strategies.

[A. Nony. Mouse.]

To remain anonymous for obvious reasons.

I suspect the reason is far less to do with cargo cult adherence and more to do with the remarkable difficulty in explaining to those affected by a policy that incorporates randomness exactly how such randomness is congruent with fairness. Sometimes, fair outcomes are suboptimal, but are what is acceptable.

[Blissex]

«No one with a time horizon longer than one will bet on a strategy where the Markov chain will inevitably produce a 0 result at some point.»

You have just solved (replacing "inevitably" with "likely" the equity premium puzzle... :-)

[Blissex]

«remarkable difficulty in explaining to those affected by a policy that incorporates randomness exactly how such randomness is congruent with fairness.»

This is a good insight, but plausibly leads immediately to one of the best themes of our blogger, cognitive biases.

First of all "randomness" above usually does not mean all-or-nothing lottery, but variability in the outcome, that is risk.

One of the most important cognitive bias is that most people instinctively fear a lot the risks that they don't control and they don't have to pay directly for minimizing, versus being unduly relaxed about the risks they can control and they have to pay directly for minimizing.

The classic example is air travel vs. car travel, where car travel is far riskier, but most people are far less worried about it.

As to policies which imply variability, I suspect that the main worry is not fairness, because a lottery with somewhat limited spread of winnings is "fair", but the lack of control over the odds and costs in the policy.

[Blissex]

«thinking of an entire species acting as one, rather than a multitude, each playing mixed strategies.»

That's a good comparison, but it does not go far enough.

The better comparison is between the notional interests of the group, and the material interests of the individual, which can be conflicting.

The notional interests of the group may be for it members to have a wide variation of strategies, so as to minimize the chances that a sudden change in the environment will wipe all individuals out and thus the whole group; the material interests of the individual might be to adopt the best strategy for the current environment in order to win the competition with other individuals in that current environment.

This is related to the usual choice between minimax/maximin and maximax strategies, where usually maximin ones are best for changing environments, and maximax ones for unchanging ones.

In a competitive environment an individual who adopts a maximin (low beta?) strategy will have lower average winnings than some of the players who adopt the maximax (high beta?) strategy, and the latter having more resources may well be able to leverage that into domination over the former.

Suppose that there are four companies A B C D, and A B adopts a maximin strategy, and C D adopts a maximax one, and the earnings end up being 8 and 12 for A B (narrow spread around average of 10) and 0 and 20 for C D (wide spread around average of 10).
C disappears, but potentially A and B too, as D will often be able to take over A and B. This is BTW the advantage of a classic maximax financial strategy, the one usually called "capital decimation partners", or more in general the maximax strategy going "aggressively" for tail risk.

Markov chains ;-).

[weareastrangemonkey]

"Nakedly ambitious people rarely achieve their ambitions"

This is true, largely because it is also ture that

"people rarely achieve their ambitions"

[A. Nony. Mouse]

@blissex: You have a good point in that randomness inherently implies a lack of control, which is, as you point out, instinctively distasteful not only to the affected, but also the implementer.

But policymakers' considerations in choosing a policy often include more concerns than those intended to be addressed by any one policy.

I reiterate my suspicion that the main reason that policies which incorporate randomness are not often implemented is that no explanation of how a policy is random is likely to be easily accepted by those affected by the policy.

"Stop and frisk" comes to mind - even if it is in fact random (which is by no means clear), can you satisfactorily address the Ali-G question: "Is it because I is black?" (Chosen specifically because Ali-G is a white comedian asking a question which may have little obvious relation to the interviewee's intentions but which forces an instant "Erm".)

[Socialism In One Bedroom]

When I look at the stats, that the top 100 families or so are worth more than the bottom 18 million people etc etc, I think we can say that naked ambition is working pretty well for some and not well for a whole lot of others.

The ruling elites lack of randomness doesn't seem to be hindering them at present!

[Redwood Rhiadra]

"And why do almost no decision-makers admit to using it, preferring instead to emphasize their "careful judgment"?"

It's quite simple - if your job requires "careful judgement", you have a skill for which you can get paid. If you admit to using randomness to make decisions, you will be immediately fired and replaced by a trivial computer program.

[theOnlySanePersonOnPlanetEarth]

Is careful judgement a skill as such or simply a requirement that everyone, and I mean almost every single human being, has to make from time to time?

[Blissex]

«You have a good point in that randomness inherently implies a lack of control,»

That's not what I meant, which is the cognitive bias is about randomness *imposed by others* as in «affected by a policy that incorporates randomness».

It is not the randomness in itself that gives a feeling of not being in control of how to react to the (partially) random path as it develops: it is not being in control of reactions that make people fear randomness, and the cognitive bias is that high randomness/risk when people feel in control is rated preferable to low randomness/risk when people feel they don't have control.

The example I made of randomness of outcome, that is risk, in car vs. air travel: in both case travel incorporates randomness, but for car travel most people think they are in control of the *car*, and thus underestimate the risk unrelated to the car, while for air travel most people fear not being in control of the *airplane*, and thus overestimate the risks unrelated to the airplane.

It is the "if risk materializes I can look after myself", the "I can stop doing this anytime" that presumably causes the cognitive bias.

If it has a basis, it is the idea that other people when in control don't react to events in your interests as well as yourself, that not being in control of reactions to random events is therefore a risk *on top* of the risks of randomness.

[Bialik]

I've had a crush on him ever since he joined TMS and I read his book about luck. So I understand.