Half a croissant, on a plate, with a sign in front of it saying '50c'
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American presidential race-inspired legislative system

Could also go in [public: election: game show], [public: election: random], [public: politics], [public: voting: weight]…
 
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Looks like you want to make some laws for your country. Here's how:

Start by soliciting bills (i.e., proposals for laws) from your citizens. Anyone may submit one, as long as they can prove that their income is in the top 50%. Also, each citizen may only submit one bill every ten years or so.

This will result in a lot of bills—up to 1/20 of your population with those settings. Thin it out by randomly selecting a thousand or so. Then eliminate any that aren't sufficiently well-written to become laws. This should leave you with somewhere between ten and twenty. If there are too many, throw out the boring ones.

Next, randomly divide the remaining bills into two groups. Set up a tournament of your country's most popular sport or competitive TV show. (Tip: This is a good place to get creative with this process! The more types of competition you include, the more of your population will be interested.) Have the two groups compete, either one-on-one matches with a bill from each group, or all together. One team in the sport or one contestant on the TV show represents each group or individual bill. Each competitive event should be held in a different random city in your country.

After each competitive event, the whole audience—only 50% of whom you told which team/contestant represented which group/bill—votes on which side they think performed better. However, only votes from people within a radius of 1/20 of your country's width from the city where the event took place are actually counted. (Also, if some of that radius covers the ocean, take the vote weight of the area covering the ocean and give it to the area covering land, so that those voters near the coast get stronger votes.) Those bills that win more of these audience votes get ranked higher, and people will follow the rankings as the season goes on.

If, during the sport/TV show portion of the legislative season, the writer of any of the bills drops below the 50th income percentile, or their bill goes below 3% audience popularity, the bill gets withdrawn and the writer loses their job.

At the end of the sport/TV show portion, ignore the results of the audience votes. Randomly choose one bill from each group. These two become the official candidates. From now on, you can ignore the groups you assigned the bills to earlier. Randomly choose 10% of the remaining non-candidate bills; put these aside and re-enter them next season.

Now you have your two candidate bills. One of these is going to become law and the other isn't. For the rest of the legislative season, have these two bills (which are likely about completely different subjects) compete against each other directly, with debates and such. Obviously everyone will know which debater is on which bill's side, but that's okay, because there's no other option to vote for now.

Also, the two candidate bills should be gradually randomly mutated (using Markov chains, neural nets, or whatever you want) throughout the debate portion of the legislative season, so that by the end of the season, they're only 50% coherent and 50% recognizable as their originally written versions.

At the end of the season, ask every single citizen which of these bills they would rather have as a law. Toss out half of the votes from the poorer half of the population. Then count the votes. The winning bill becomes law.

At least, that's what you tell everyone. The real laws are made by the small neighboring country. They really do want your country to prosper—it will benefit them too—but they're often clueless about how to achieve that. They're willing to take suggestions (if only anyone would give them any)… as long as they don't conflict with the interests of the more powerful neighbors.

notexactly, Sep 22 2016

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