Reputation is Powerful

Vampire bats cannot survive more than about 2 days without blood, yet they will frequently fail to find a meal in a given day. To solve this problem, they invented insurance… well a primitive version of it anyway. An unlucky Vampire bat will often be able to borrow food from another bat (via regurgitation) today and pay back the debt later when their fortunes are reversed. This kind of transaction is known as direct reciprocity and it is the principle behind some really fascinating interactions in the animal kingdom. It is also an important idea in a famous problem of game theory called the prisoner’s dilemma. I encourage you to read up on the prisoner’s dilemma if you aren’t familiar with it. For now, what’s important to know is that a single game of prisoner’s involves 2 players who may each either cooperate or defect. They both have an incentive to defect but will mutually benefit if they both cooperate.

There is a particular very simple strategy that performs exceptionally well in the iterated prisoner’s dilemma. It is called Tit for Tat. You may know the principle as “you scratch my back; I’ll scratch yours” or “an eye for an eye”. Yeah. That strategy. Tit for Tat embodies direct reciprocity. It punishes defection and rewards cooperation and thus increases the total amount of cooperation that occurs in a population which is a good thing because more cooperation means more total wealth generated.

We humans are capable of a more advanced kind of reciprocity than direct reciprocity called indirect reciprocity. Indirect reciprocity makes defection more costly and cooperation even more lucrative with respect to direct reciprocity. If you are a defector who is unfortunate enough to find oneself surrounded by indirect reciprocators, then you will quickly discover that after your first lucrative defection, your neighbours have all stopped trusting you and defect against you every game. If you are a cooperator, on the other hand, then not only do you get to bask in the wealth of large-scale mutual cooperation that permeates your environment, but you get told who the defectors are and can avoid them or punish them with mutual defection at your whim. Indirect Reciprocity magnifies the cost of defection and the rewards of cooperation through the power of reputation.

So it turns out that cooperation is a good thing. This is first and foremost because there are lots of situations in real life that resemble the prisoner’s dilemma in nature. There is an incentive for individuals to defect in a given round in order to reap disproportionate rewards for themselves at the expense of others (think Steve in The Italian Job[1]), but the wealth-maximising outcome is mutual cooperation. There is another interesting reason why cooperation is a good thing that I want to explore, though, and that is the power it brings to problem solving.

To begin with, I’m going to make a case for the following claim: diversity is more powerful than ability for problem solving.

Imagine you have 100 people with expertise in a field of knowledge X. You select 2 groups of 10 from among the 100. Group 1, Ability, consists of the 10 most competent experts in field X. Group 2, Diversity, consists of 10 randomly selected members of the original 100. Now I ask you, which group will, on average, be better at solving a problem in the field of X?

Oh, by the way, assume both groups cooperate excellently🙂

Let’s play a game. It’s called Sum to Fifteen. The rules are pretty simple. Two players take turns to take 1 card from among cards labelled 1 to 9. The first player to collect 3 cards that sum to 15 wins. Ok, I pick 6. You pick 2. Guess what – I’ve won! See if you can figure out which number I will take next.
Let’s try a more complicated game. This one’s called The Unpacking Game. Two players take turns to take a picnic basket from a set of nine baskets each containing a different combination of food items. The baskets are:

1. Apples, Juice
2. Sausage Rolls, Eggs, Sultanas
3. Pies, Cookies
4. Pies, Eggs, Brownies
5. Apples, Cookies, Brownies, Sultanas
6. Sausage Rolls, Juice, Brownies
7. Sausage Rolls, Cookies
8. Pies, Juice, Sultanas
9. Apples, Eggs

The first player to collect all 3 copies of one of the food items wins. I pick basket 5. Which do you pick?
How about an old favourite: Tic Tac Toe! This one’s easy right? I take the middle square. Where do you play? Corner or side?

Which of these 3 games would you feel most confident at performing well in? Tic Tac Toe right? Well guess what? They’re ALL Tic Tac Toe – from different perspectives! The key to seeing this is to overlay the Tic Tac Toe grid with a magic square like so:

I’ll let you figure out how this magic square ties the 3 games together [2]. It’s pretty cool. But what’s the point of all this, I hear you ask? Well…

Every problem is a Tic Tac Toe game… er, metaphorically… You see, every problem you can imagine can be looked at from different perspectives, just like Tic Tac Toe can be viewed from the Sum to Fifteen perspective, the Unpacking Game perspective or the traditional Tic Tac Tac toe grid perspective. And some perspectives are more useful than others for solving a given problem. So being good at problem solving is just a matter of using the best perspective right? Well, no, not exactly… the trouble is that there is no general purpose way of knowing exactly which perspective is the best one for solving a given problem without trying every one. You can find perspectives that are typically good ones for problems in a particular category, but for every specific problem, the best perspective may be some obscure one that no one has ever tried before [3]. And here lies the key to understanding why Diversity will defeat Ability in our little academic rivalry.

All the experts in the Ability group will tend to have developed a similar set of optimal perspectives for solving problems in field X. There will, after all, be a small number of best overall perspectives across the whole field and the best performing experts in that field are likely to have found them [4]. When Ability collaborate to solve a problem, they will attack each sub-problem with the same set of best overall perspectives, largely duplicating effort because they are each likely to be running similar algorithms in their brains. The group of 10 thus has limited advantage over the single best expert.

When Diversity attack a problem, every member will bring a different set of perspectives to the table. For each sub-problem the group encounters, one member of the 10 is likely to have a perspective that is uniquely suited to that problem. The discovery of that uniquely good perspective is done in parallel across 10 brains and then all 10 brains get to use the insights of that uniquely good perspective as a starting point for the next sub-problem, for which a different member of the group may have an ideally suited perspective. So where Ability were using globally excellent perspectives that are moderately good for each sub-problem, Diversity is using globally poor perspectives that are individually excellently suited to each sub-problem.

This is all well and good, but, you may well complain, it all sounds very anecdotal. How do I know how much effect this principle has in practice? Well, in his book, The Difference, Scott Page demonstrated mathematically that, given some reasonable assumptions, “a randomly selected collection of problem solvers outperforms a collection of the best individual problem solvers”. If you want to know more details of how the Diversity Trumps Ability Theorem works, I suggest reading his book.

Alight, let’s take stock. So reputation facilitates cooperation via indirect reciprocity and cooperation facilitates diverse groups of people working together to solve problems, and diversity is more powerful than ability for problem solving. Oh, and problem solving is useful for making the world better.

So one might wonder, if one were to strengthen the force of reputation in society, would the effect flow all the way through this chain and make the world better? Well I wonder that anyway. Our reputation tracking faculties evolved in social groups of less than about 150 people. Keeping track of reputation signals in modern society requires modern communication technologies, but centralized reputation databases like Yelp, LinkedIn and Reddit require trust of the database controller for the reputation signals to be trustworthy. The usefulness of the entire database of reputation signals is subservient to the reputation of the database owner. So you have to take into account your assessment of the likelihood that any given database owner will decide it is in their interests to distort the reputation signals it reports. Plus, even if you trust, say, Reddit to report the reputation signals it collects with integrity, you shouldn’t trust everyone who uses their platform to refrain from gaming the reputation system to unfairly boost their own reputation or as a means of blackmail.

So how might we obtain, on a global scale, the kind of quality reputation information that would have been ubiquitous in the ancestral environment? Well there is a technology called cryptography that allows trusted systems to be built on top of untrusted systems. There is also a technology called a Prediction Market that is particularly effective at extracting accurate information from people, even when they have a motive to keep knowledge secret or manipulate the information available to others. These seem like a promising start for solving our little dilemma. Maybe I’ll write more about this some time…😛

Endnotes

1. You might describe this as an example of meta-defection (if you were a little biased in favour of using the word Meta wherever it is remotely applicable) because Steve is defecting against a group of social defectors (thieves). Actually this is just ordinary defection, though, because the concept of defection applies with reference to a particular cooperative group. John’s team were defecting against society at large, while Steve was defecting against John’s team.
2. I borrowed this perspectives illustration from the first chapter of Scott Page’s The Difference, where you can find a more detailed explanation of it.
3. By the way, as well as having varying perspectives, different people may also use different heuristics for problem solving. For the sake of this argument, heuristics and perspectives have similar properties so I’m going to just use the term perspectives and you can imagine that it refers to both perspectives and heuristics.
4. Important to note is that a human is only capable of holding a limited number of perspectives in his/her brain and can only use one at a time.

Sources of Insight
SuperCooperators – Martin Nowack
The Wisdom of Crowds – James Surowiecki
The Difference – Scott Page
Diversity and Complexity – Scott Page