Binary Tree Legislature

This is an idea that grew out of an Election Methods [EM] list discussion on ways to prevent gerrymandered political districts and later posted on www.halfbakery.com. Gerrymandering (for those who don't already know) is the process of drawing political districts so that politicians can choose the voters rather than having the voters choose the politicians. By drawing districts around voters they want and leaving enough of a margin to cover any defections from one party to another, politicians can not only make their seats safe, they can completely skew the representation of the district.

As an example, let's assume that a state's electorate is evenly divided between Democrats and Republicans. For simplicity, let's make the state square and give it four representatives, with Democrats clustered on the West ("left") side of the state and Republicans on the East ("right") side of the state. Here are some possibilities in creative redistricting:

What I wanted was a simple way of drawing districts that could not be corrupted by political machinations. After looking at the problem for a while, I remembered seeing how certain wavelet algorithms broke up images using a simple "divide and conquer" strategy before compressing it -- the main image was divided up into sub-images, and the sub-images were then broken up even smaller, until the desired resolution was achieved. Not only could you define a standard rule for cutting up the image, it could easily be automated.

Using this as a starting point, I came up with the following algorithm:

1. Have voters order candidates on a ranked ballot.

2. The Kemeny winner for the entire region is placed at the top of a binary tree.

3. The winner's name is removed from the ballots.

4. The longitudinal median line dividing the electorate precisely in half is drawn.

5. The winners on each side of the median are chosen, and placed at the appropriate point on the binary tree.

6. If the same person wins more than one area, he or she is placed according to the greatest margin of victory.

7. The names of the winners are removed from the ballot.

8. A single great circle segment running through the median of the previous two districts is drawn.

9. Go to step 5.

Here is a graphical example:

Once we have generated a binary tree, we need some rules for the passage of laws. The first rule is that two sub-representatives can overrule the single representative immediately above them. This means that each triad is effectively majority rule - two "leaves" can overrule the "branch" they both attach to, but if the two "leaves" vote differently the branch makes the deciding vote. Through the magic of iteration, this means that four sub sub-representatives can overrule the two sub-representatives which can overrule the representative. This process continues to the very base of the binary tree - only the representatives closest to the voters cannot be overruled.

The rationale behind this is thus: candidates elected with a Kemeny/Condorcet method tend to be the ones closest to the median voter in the district they are elected to. If you split that district in half, the winning candidates for each subdistrict will tend to lie on each side of the median for the whole district. In other words, a centrist representing a district would tend to have someone more conservative and someone more liberal underneath him, rather than two conservatives or two liberals. If a liberal and a conservative agree on a course of action, then it is more likely to benefit the entire electorate than the decision of a single centrist - after all, the centrist might be wrong. If a liberal and a conservative disagree, the centrist should get the deciding vote. This is an important check on power.

The result of this rule is there must be an unbroken string of "yes" votes from the bottom to the top of the binary tree in order for a bill to pass - if at any level all of the representatives voted against a bill, it will not become law. On the other hand, while this is a necessary condition, it is not a sufficient one. To prevent a minority cabal from taking over simply because of a fortuitous placement of representatives, we have one further condition.

Once a binary tree is created, a Borda count is carried out using the national vote for each representative compared to other representatives. If there are 256 districts, there will be 511 total representatives, with 510 points given for each first place vote, 509 points for each second place vote, and so on down to 0 points for each last (or 511^th place) vote. This gives a "power" score for each representative. A bill must have at least half of the total power of all representatives put together to pass.

The reasoning behind this is that a person could very well become a representative by preying on the fears of a group or by pitting one group against another. If a majority of the electorate considered this representative a hatemonger or otherwise undesirable, his or her power to enact laws would be lessened by a lower ranking of the electorate as a whole. Their minority views would still be protected - they could vote against bills they didn't like - but they couldn't push bills onto the legislature that a majority didn't approve of. It takes a combination of power and placement to pass legislation.

Unfortunately, we are already presented with constitutionally pre-made political divisions called "states." A unicameral binary-tree legislature at the national level would take a major rewrite of the U.S. Constitution, which makes this an idea suitable for www.halfbakery.com. On the other hand, one state - Nebraska - went from a bicameral to a unicameral legislature early in the 20^th century (though still with a governor). On the state level, this idea is merely improbable rather than practically impossible.

Let's use my state - Oregon - for example. We have 60 House districts and 30 Senate districts. That is a total of 90 seats plus the Governor. If we were to replace it with 32 districts, we would have a total of 63 legislators. The top one we'd call "Governor" for convenience. Underneath him, we'd a coastal vice-governor and an eastern interior vice-governor. Below them we'd have a north coast, south coast, northeast interior, and southeast interior senior senators. There would be 6 ranks of legislators - Governor, Vice-Governor, Senior Senator, Senator, Senior Representative, and Representative. Power and seniority would be based on what the voters wanted rather than simple longevity.

There are some arguments against a binary tree legislature. One is that it would be too easy to pass laws. If that is true, simply add a few more limitations for legislation. For example, by requiring agreement in at least half of each binary tree level, we would theoretically make it much harder than it is at present to pass laws -- not necessarily a bad thing. Another argument is that the unicameral nature removes necessary checks and balances in government; in actuality, there are checks at every level of the binary tree, more so than with our present government, and other countries (and Nebraska) do just fine with a unicameral legislature. Yet another argument is that it doesn't follow natural or political boundaries - which may be a bit of a problem, though present representative districts often follow such boundaries only if it also makes a district safe for a particular representative or party.

Of course, there are some real problems as well. Political boundaries would be fluid, changing from election to election, which means that political candidates would advertise in a much wider area just to cover all bases. Voters would have several times as many candidates asking for their vote, which gives a greater choice but also has the potential of being a lot more irritating. Since representative districts are based on voter turnout rather than population, certain groups will probably be under-represented in some elections - though this presents more of an opportunity to the smart legislator who can successfully mobilize the vote rather than the one who cashes in on voter apathy. Centrist philosophy will rule the legislature, and while this will prevent lurches between liberal to conservative philosophy after each election, it will also make change a more gradual process (Lincoln may never have become President under such a system, though it's also possible that we would never have fought the Civil War either).

Despite the problems, there are some advantages to such a system. The complete hierarchy and order of succession is determined by the voters rather than by longevity and esoteric party formulae, and vertical mobility (both up *and* down the power pyramid) is much easier. Voters do not lose a representative when he seeks higher public office, and representatives do not have to weigh running for higher office against losing a "safe" seat. Representatives - even representatives of the same party - will be judged against each other as well as against those in opposing parties, so there is less reason to cover-up another's wrongdoing. On the other hand, annoying voters in other parties will reduce your own power, curbing the more egregious mudslinging. Lawmakers will not be able to hide legislation changes as easily in conference committee. The makeup of government will be more fluid without requiring term limits, yet experienced and effective legislators won't be arbitrarily kicked out after a specified period of time.

Finally, it would bring more excitement, interest, and accountability back into elections. Voters would have more power - not only does their first choice count, so does their last choice, and every choice in between. Representatives of the smallest possible district clear across the country would have a reason to help a cause they believed in, because favorable votes from the entire country count toward their power to pass legislation. This makes representatives more accountable as well - push a pork-barrel project that benefits only a small number in your district, and you can see your power diminish in the next election. Elected officials would have to find a balance between serving their direct constituents and alienating those that aren't.