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March 25, 2014

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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.

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