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The Tree of Authority


So, suppose everyone has described their views. What then? The basic idea is that each description would be a vote, and that the majority of votes on each issue would directly determine law or policy for that issue.

We wouldn't want to use a simple majority, though, because it would be awkward to have policy shift back and forth if an issue got balanced right on the line. So, instead, we'd use some other threshold—declare that we don't have consensus until, say, 60% of the votes agree. And, until we had consensus, we'd maintain the status quo. That would create a nice hysteresis effect.

We'd probably also want to add some delay into the system. If an issue was polling at 59%, and there weren't any delays, then a small concerted effort, or even just a random fluctuation, might push the issue over the line and change the policy. Then, even if people wanted to react against the change, it would be too late—the issue would need to go all the way down to 40% to restore the old situation. In other words, change wouldn't require a solid consensus, only a temporary one. To prevent such things, we ought to declare that policy doesn't change unless an issue remains over the threshold for, say, a week.

I'm tempted to say that the changes should also be synchronized, so that, much as in the first solution, each Tuesday you could pick up the political news and read about both proposed changes that had just crossed the threshold temporarily and actual changes that had remained above the threshold for the past week. I think that would be convenient, for reasons similar to the ones in New Content.

On the other hand, I may just be old-fashioned—you could equally well have a continuous news feed carry the same information. The fact that it's a little awkward to keep track of which items you've read is really just a limitation of present-day browsers.

Now that you've got the basic idea, let's make things more complicated. We want our authority to be narrow, so let's organize voters into cells to form a tree of authority, as I described in The Problem. Specifically, let's organize voters into cells geographically, with some maximum width, and attach authority to the resulting tree at the city, county, state, and national levels.

For example, suppose we have a county that contains two cities, one with 100,000 voters, the other with 10,000, along with another 10,000 voters in unincorporated areas; and suppose we set the maximum width to 100. The smaller city could be organized into a “standard” tree of depth 2 and width 100; the larger, into a tree of depth 3 containing ten standard trees. The county, then, would contain the two cities, and would also act as the root of another standard tree representing the unincorporated areas. (That gives it width 102, I know, but you get the idea.)

Then, at each cell, or node, of the tree, the votes would be aggregated according to the rules above. Each cell would have its own status quo, requiring solid consensus to change, that would serve as the vote of the cell to its parent.

Now, there are several points I'd like to make about this arrangement.

  • Authority is only attached to a few cells. For the other, non-authoritative cells, a change in the status quo doesn't cause any immediate change in policy, but it is nonetheless a tangible political event.
  • It may seem strange to aggregate the votes at each cell, but if you don't, then the authority isn't narrow, and in fact there's almost no reason to have a tree of authority, because the non-authoritative cells don't do anything.
  • One of the strange things about aggregation is that you can get consensus without having a true majority. In fact, all it takes is a small fraction of the population, the fraction being roughly one factor of the threshold per level of the tree. So, for the larger city in the example above, the fraction would be 0.63 = 0.216, so that consensus could be obtained with only 21,600 people (if they were distributed correctly).
  • One thing I haven't mentioned is the problem of weighting. As I was writing down the example above, it first seemed clear to me that the vote of each cell should be weighted by the number of voters it represents. Unfortunately, that wouldn't work very well—the larger city has more voters than the smaller city and unincorporated areas combined, so its vote would always win. The other extreme, giving each cell equal weight, wouldn't work very well either, because it would give the larger city no more authority than the smaller.

    I'm not sure what the right answer is, if any. It might be possible to use a weighting function, some function f of the number of voters n that lies between the extremes fA(n) = n and fB(n) = 1 … maybe the square root of n, or the logarithm. In any case, it's certainly interesting that the same problem was solved at the national level by having the House use fA and the Senate use fB.

  • Another thing I haven't mentioned is the problem of gerrymandering. Because of the vast number of cells, and the small consensus fraction, gerrymandering could be a huge problem, if we let it. Probably we'd want to define standard algorithms for determining cell boundaries.

I'd also like to say a bit more about the idea of attaching authority to the tree at different levels.

  • I guess I didn't say so, above, but I'm thinking that the different levels would have authority over different things, just as they do today. I think that's good. Some policies need to be defined at the highest level, so that they're uniform; but many don't, and allowing variation, while somewhat inefficient, also makes it possible for evolution to occur. (See, for example, the last paragraph of Different Kinds of Sameness.)
  • I don't know if this is true everywhere, but in Colorado, the state defines a default set of city-level policies that apply to unincorporated areas. That seems exactly right to me—every level of authority should define default policies for the lower levels. Then, when a city (or whatever) incorporates, the default policies would be used as the status quo.
  • The attachment of authority could be extended further downward. Condominiums, neighborhood associations, gated communities, and so on often have policies of their own; authority over those policies could be attached to the tree below the city level.
  • Wouldn't it be funny if it turned out that the brain makes decisions by obtaining consensus among subsystems? That would extend the attachment of authority even further downward.
  • The attachment of authority could also be extended upward, to a world government, if we ever wanted to create one.



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@ May (2002)