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Scott Aaronson has written an interesting post (HT: mathbabe) proposing borrowing concepts from ‘eigenmorality’ and Google page-ranking to improve democracy. I thought I’d go into it a little if you don’t mind.
The core of the idea is this:
A trustworthy source of information is one that’s considered trustworthy by many sources who are themselves trustworthy (on the same topic or on closely related topics). The current scientific consensus, on any given issue, is what the trustworthy sources consider to be the consensus. A good decision-maker is someone who’s considered to be a good decision-maker by many other good decision-makers.
…once people’s individual decisions did give rise to a giant connected trust component, the recommendations of that component could acquire the force of law.
Essentially, some Google PageRank-like algorithm would be set up (by Smart People) to rank how ‘trustworthy’ people are (according to definitions and metrics presumably defined by Smart People). Starting from how much people ‘trust’ each other, the ‘largest connected trust component’ would be extracted via some basic linear algebra, and that component would be deemed to be Trustworthy, hence would rule. (And then we’d have a carbon tax1.)
In a sense, this is just a description of a hagiocracy – rule by priests, by people who are sufficiently holy. He just defines his ‘priesthood’ implicitly, in a certain way that (he is confident) would include himself and other Smart People who agree with him about stuff (like, a carbon tax). So in particular, the overall idea constitutes a decent outline of a formal, workable mechanism for setting up an Yglesiocracy:
Smart People favor the rule of Smart People.
Oh, but don’t worry, he doesn’t seek dictatorship and he doesn’t like numbers-based amorality that allows one gang to tyrannize another. Just ask him. He says so and everything. He just wants the views of the ‘largest connected trust component’, whatever they are, to ‘acquire the force of law’. Apples and oranges!
Let me start by dialing back his concept a bit and then seeing where it goes off the rails. Because he is right that our current system, (nominally) democracy, does a similar sort of thing: it is The Majority that rules. He just wants to replace The Majority with something else, The Smart People. But there would be advanced math™ behind it, so it’s all good.
In fact, we can cast winner-take-all democracy into his framework quite easily. To simplify matters imagine a country with five people (A,B,C,D and E) who are sharply divided into two Parties: A,B, and C implicitly trust each other about everything and distrust D & E, and vice versa. (This is an admittedly extreme but for our purposes reasonable approximation to how our society already works for certain issues.)
It’s easy to write down the equivalent of the trust-matrix for this setup:
(I hope this is pretty self-explanatory. Row A has 1s for columns A, B, and C since that’s who he trusts. It has 0s for columns D and E since that’s who he distrusts. Etc.)
The ‘eigenmorality’/Google approach suggests that we convert this trust matrix, which encodes how much people (rightly or wrongly) trust each other, into something we interpret as an absolute, external, objective measure of trustworthiness, using the circular/implicit reasoning I excerpted above:
A trustworthy source of information is one that’s considered trustworthy by many sources who are themselves trustworthy
Or, as I put it in my groundbreaking, award-winning^H^H^H^H^H^H^H -eligible, seminal post on Smart People,
The odd thing about Smart People is that they all seem to know who they are. They recognize each other, instinctively.
It appears the Google/eigenmorality idea is that (due to some hand-waving) the most-likely-to-be-the trustworthy bloc would be represented by whoever’s in the primary eigenvector of the trust matrix, since if we ran this game a bunch of times, [a. give people some Trust Points, b. let them distribute them to those they Trust], that would characterize the long-term equilibrium.
In our above ABCDE case that primary-eigenvector happens to be (a multiple of) this vector:
What those 1s mean is that the people in party ABC are part of the largest eigenvector; the 0s mean that those in party DE are not. Which is just to say, for our simplified all-or-nothing party-system trust model, the largest eigenvector = largest connected component = the party with the most votes. So winner-take-all majority-rule democracy is the same thing as Aaronson’s ‘eigenmorality’ if ‘trust’/’morality’ is assumed to be binary and to correspond to simple-agreement on the issue in question.
And we even already have a mechanism for discovering this largest-connected-component too. It uses no advanced linear algebra. It’s called ‘voting’.
Aaronson is clearly unhappy with this mechanism though, since it doesn’t produce the outcomes he wants (e.g. a carbon tax). The policy he wants hasn’t gotten enough of this ‘voting’ thing and so there must be something wrong with that process, says he. What other process might his idea lead to, exactly?
Let’s modify our model a little. After all, it was admittedly an oversimplification. Let’s look for areas to improve and generalize. The first one is pairwise trust. I can buy that A trusts himself 1 trust-unit, but all other people? Just because they’re in his party? People aren’t so groupthink-minded right? So make things slightly more realistic: let’s say that instead of trusting each other 1, party members trust each other p<1:
But it doesn’t matter what p is (as long as it’s not 0): this still has the same leading eigenvector, the majority party ABC, as before. So this is still just a model of majority-rule democracy.
What to change next? One more thing oughta do it: Maybe the members of party DE trust each other a different amount, say q, than do the members of party ABC:
Does this change things? It turns out that it could: if q>2p then Party DE, not ABC, actually becomes the first-eigenvector.
Despite being a minority, the PageRank Democracy Machine would do its linear algebra and declare – ultimately, simply because they ‘trust’ each other more, or whatever q is measuring exactly – that Party DE is the Most-Trustworthy-Connected-Component and therefore that their preference – not that of the majority, ABC – should carry force of law.
Another way to get the same exact outcome, clearly, is just to give the votes of Party DE, the Smart People, extra weight.
So don’t be fooled; that is what he is saying he wants. If Smart People can convince Linear Algebra that they’ve arranged themselves into an impressive-enough Mutual-Trust-Admiration-Society (and is that not, if nothing else, exactly what Smart People are good at doing?), then they get to rule, regardless of such parochial concepts as actual voter preferences.
Thus we see that this ‘eigenmorality’/PageRank-based reform of democracy is really just a roundabout way of overweighting the votes of Smart People (more generally, of whoever can figure out how best to game the math and control the spigots of who is given ‘trust’ – but we’re all pretty convinced that would be Smart People, right?), in the guise of Google-like hi tech and advanced math™.
Now sure. A straightforward, overt appeal to give Smart People double-votes, to count non-Smart People as 3/5 of a vote, or whatever it takes, probably wouldn’t have been so appealing or palatable. But perhaps this idea of ‘using linear algebra to discover the Most-Trustworthy-Connected-Component’ could sneak through?
I’m just here to tell you that, despite the hifalutin language and math, for all intents and purposes they’re the same exact thing. Do not be fooled; Aaronson wants the votes of himself and people-who-agree-with-him-about-stuff to count more than they currently do. That is what he is saying. That is all he is saying.
In fairness, it’s a pretty common wish.
1It’s pretty amusing just how important something like a carbon tax is to Smart People, even those who don’t know the first thing about either climate modelling or economics and thus have no idea whatsoever what if anything a carbon tax would accomplish.
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