March 08, 2014

The reputation 1%

Yesterday over dinner, while discussing alternative monetary systems, reputation economy came up. While most discussions centre on using on-line reputations to stabilize virtual social structures or reduce transaction friction (often as a enabler of sharing systems), others wonder if one could not go all the way to Doctorow's Whuffie. In a post-scarcity economy, why not make social capital your real capital? The idea is used to good effect in the Eclipse Phase (see Reputation and Social Networks for more game details). There is something intuitively appealing in the idea that your social merit determines what resources you get and how big projects you can undertake: people who do good things for others ought to be rewarded.

Still, appealing-sounding economic ideas have frequently had serious flaws. One issue is distribution: many proponents of reputation economies are egalitarians who think very unequal distributions of wealth are inherently bad (even if everybody came to their wealth through honest means). Would a reputation economy be more equal?

The nature of a reputation

A reputation in general can be seen as 'the beliefs or opinions that are generally held about someone or something'. It is a social evaluation not done by just one person, but by the network of people interacting or opining about the target. It is generally not a mere number, but have evaluative elements (some of us are infamous, and you can be known as unreliable yet entertaining). In short, real reputations are 'thick' concepts that are more like micro-biographies or association clouds linked to the person: they are not at all like a single number or rating.

It is not obvious how to replace money (scalar, fungible, well defined value) with something as rich as reputations. It would be like replacing coins with individual artworks.

However, simple scalar reputation ratings are easy to handle, so most digital systems compress reputations into shorthand numbers. Research Gate gives me a RG score of 20.65 for the moment, based mainly on the papers I have uploaded but also on how much I interact usefully with other researchers (of course implicitly rewarding people who do much within RG over people who do stuff elsewhere). Some academics spend far too much time worrying about their citation indices, which again are widely recognized as misleading and too limited - but if important decisions like tenure decisions are based on them, even a pointless number matters. So it is not too hard to imagine some kind of scalar reputation measure being developed, perhaps calculated from richer social data.

In practice, the data seems to split into attention and evaluations. The more people know about you, the bigger your reputation. The more people like you, the more positive evaluations. However, while very critical people are likely to voice disagreements and negative evaluations, most people who don't care for you will stay silent or not not interact, and friends and admirers are likely to leave positive signals. In fact, most current sites (with the exception of Reddit) only have upvotes. Hence the total amount of positive evaluation is likely proportional to attention: he who is known by most will also have the highest reputation. It might be a mixed reputation, but unknown people are unlikely to get very high or low evaluation scores.

The distribution of fame

So, to a first approximation, we should expect reputations to be distributed like how well-known somebody is. Basically, reputation equals fame.

The distribution of fame has been investigated a fair bit.

Blogs can be studied in terms of how many links they get, which is a plausible measure of how many read and react to them. Henry Farrell and Daniel W. Drezner 2008 found that the links were lognormally distributed. In general it is taken as a stylized fact that the link distribution is power-law distributed (e.g. Weblogs and power laws), perhaps with a stricter power law distribution in domains with stronger competition.

Eric Schulman has written a series of papers for the Annals of Improbable Research about estimating fame using web hits: 1999, 2001, 2006, 2009. While intended slightly tounge-in-cheek the findings are consistent with other studies. Most importantly, the number of references to a person can range over many orders of magnitude: the distribution of attention to people is clearly very skew.

Looking at references to scientists in books, a similarly skew distribution emerges: Science Hall of Fame. The distribution appears to be slightly lighter than a power-law (see diagram at the bottom), but the general heavy tail property remains.

M.V. Simkin and V.P. Roychowdhury examine the amount of writing and google hits about pilot aces, finding that fame grows exponentially with achievement (here measured in number of kills). They build a mathematical theory of fame, where they argue that 'the number of people with a particular level of achievement decreases exponentially with the level, leading to a power-law distribution of fame'.

Bagrow et al. argued for a linear relationship between fame and merit, based on number of papers published. But Simkin and Roychowdhury pointed out that the number of publications is not really a measure of merit, just productivity (which might be naturally lognormal). Number of citations are likely a better measure.

However, Bagrow et al. note that scientists may also be more known within small fields rather than across the whole public: reputations may not carry that far. In a more recent study Bagrow et al. find that scientists, fighter aces, actors, fictional villains, runners, programmers, and students have google mentions distributed with skew enough distributions that a power law cannot be excluded. This paper is interesting because it includes non-famous people (the students): the heavy tail of attention seems to be universal.

See also table 2 of Kunegis & Preusse 2012 for a long list of empirical skewness distributions.

So, to sum up: the amount of references to people, presumably a good measure of the attention and fame they receive, has a tail distribution that is at least as heavy as a lognormal distribution. There is some linear or nonlinear relation to merit, at least in the cases where merit is defineable, but it is likely very domain dependent.

The inequality of fame

If we for simplicity assume fame is distributed as a power law P(F) = F-a (a>0, F>=1), how unequally distributed is it?

We can calculate the Gini coefficient G=1/(2a-1). Power-law distributions with high a are more equal, as measured by the Gini coefficient.

The median fame grows as 21/(a-1) (Newman 2004). It descends from a singularity at a=1 to a median fame of 2 for a=2 and 1.41 for a=3: 50% of people have less fame than this. But the fraction of total fame (wealth in a reputation economy) in the more famous half is 2-(a-2)/(a-1) (if a>2). For a just above 2 the fraction is huge: a=2.1 gives 94% to the top half of the population. For a=3, 70% belongs there, and one needs to go up to a=4.8 to get it down to 60%. Indeed, the most famous 1% have 10% of all the fame in the a=3 case... and 65% in the a=2.1 case. For a less than or equal to 2 the single most famous individual will have a significant fraction of the entire fame of the society.

What is the fame distribution exponent? The power-law fits of Bagrow and ben-Avraham give a in the range 1.77 to 2.69 for scientists, 2.74-3.62 for aces, 1.88-2.10 for actors, 1.57-2.03 for villains, 1.88-2.43 for programmers, 1.71-1.92 for runners, and 1.74-2.57 for students.

The American income distribution is roughly a=2.1. So fame is just as unequally distributed as income. In some populations it might even be way more unequal!


Maybe this not a problem for a reputation economy. If we think fame is a honest indicator of merit (leaving aside infamy) then a very unequal distribution of fame might just mean an unequal distribution of merit. Some people just are nicer, more constructive or more ingenious than others. Maybe they should be given a large chunk of the total economy to play with.

If we think fame is at most a crude measure of merit, then these results become more problematic. It is not hard to build models of fame based on preferential attachment (you are more likely to hear about famous people than unknown people) or even limited memory capacity. Here fame does not track merit, and who ends up getting most of the attention cake may have very little to do with how good they are.

An idealist may argue that this is the fault of current reputation systems: first, they are one-dimensional and leave out important qualities, and second, a future reputation system may tie reputation to actual social merit rather than extraneous factors. Then a reputation currency would make sense and would be properly egalitarian (or at least merit based). I am somewhat pessimistic about this.

Non-scalar reputations are hard to compare, and people will likely want easy methods of allocation. Since deciding whether to do a trade or give something is binary, there is going to be some kind of personal decision boundary based on the reputation information. Insofar people have similar views of what makes a good reputation - remember that this is a social evaluation - their decisions boundaries are going to be correlated. So while I may care more about your reputation for rationality than my neighbour does, our decision to give you a gigabit of bandwidth are likely to be similar since we also weigh in your overall reputation for honesty, good computer security, reciprocity, being a god-fearing Dawkinite or what else is valued in our community. (The community-subjective aspects of reputations are of course another can of worms - reputation currencies might serve to enforce bad social ideals). In the end, reputations are going to be fairly one-dimensional since most parts of a good reputation are correlated or at least compensate for each other.

The second issue is probably even harder. Tying reputation to actual merit requires an objective evaluation that is hard to do, especially since social merit is something evaluated subjectively by people. But the subjective aspect means we get the usual very unequal fame dynamics again. The preferential attachment model suggests that someone doing something noticeably good (or bad) is likely to attract a nonlinear amount of attention: the total change in reputation is not going to be proportional to the good or bad done. A system that gives you an exponential reward for being nice sounds good at first, but since your reputation is always compared to the total reputation of the society that nonlinearity just leads to a winner-take all dynamics - especially if you get more attention for having more reputation. And conversely, somehow dampening the reputation reward for a good deed (improving equality) makes extremely good deeds requiring some work less appealing than doing smaller easy good deeds: the total amount of social utility produced would go down.

Maybe these problems can be solved. But we should recognize that money, for all its faults, doesn't discriminate about who you are. Reputations are always tied to who and what you are, who you associate with, and what others think about it. People who are bad at navigating the social space around them will be at a disadvantage in a reputation economy, while the charming butterflies will be rewarded. Maybe that is something we would enjoy, but from an ethical standpoint it doesn't seem that different.

(Bill Gates has merely 90 times as many Google hits (229 on Bing) on his name as I have on mine, but is at least 2.3 million times richer. So in reputation-world we would be more equal... but he would still be way richer.)

Posted by Anders3 at March 8, 2014 04:13 PM