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I think it would be simplest to use an existing game. Players would send you their moves and you'd make the changes to the game by hand (at least at first). For possible games you could look for suitable turn-based games in this list of multiplayer browser games. Would poker or chess be a possibility?
In response to
Game for organizational structure testing
A rules light game such as poker or chess would give you a lot of leeway in designing a scoring system and implementing the social systems, but probably has an insufficiently complex game state to allow for a large team size while still minimizing redundancy. If you want to develop for large teams (which is almost required to create a difference between true democracy and a representative system), I would suggest a highly customizable, complex game such as Civilization 5, perhaps by allowing each player to control and receive data from an initial unit with socially selected ability to control cities and subsequently produced units within the team.
In response to
I need help: Device of imaginary results by I J Good
I have the same reservation regarding the probability regarding propositions 1) and 2) as army1987. In particular, I find that the probability that all writings regarding the aforementioned people are true is exceedingly low for both, but the probability that some person existed bearing that name, who performed at least one action or bore one trait that was subsequently recorded is rather high. Considering that this is meant to be an exercise on evaluating one's priors (or at least that is how it appears to me), I would consider choosing one interpretation or the other and work from that. If you feel the need, simply try both interpretations or find a middle ground that you feel comfortable with. If this is not your issue with the propositions, then I would require more information on your attempts to solve the exercise in order to provide meaningful feedback.
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(As promised, I post description of my attempts here)
Case 1: Julius Caesar. The existence of Caesar seems very likely for me. Therefore, I will think about evidence that would convince me that Caesar is a myth.
I decided that the following three pieces of evidence will be enough for me to start doubting existence of Julius Caesar:
1) I don't know anything about the process of burial of the Roman emperors. Hence it wouldn't be inconsistent to assume that there is an official "emperor's tomb", a luxurious necropolis where the crypts of every emperor are located. Having assumed that this true, I imagine a discovery saying that the crypt of Julius Caesar is missing, or his tomb is empty, or the body inside couldn't belong to Julius, or something along those lines.
2) Similarly, the existence of a reliable independent Arabian historian similar to Herodotus wouldn't contradict my worldview. So I can assume that there indeed was such a historian. If his book about Roman Empire had failed to mention Julius Caesar at all, that would have been an evidence pointing to Julius being a myth.
3) Why can't I imagine the second Arabian history book failing to mention Caesar?
Having imagined all that, I decided that it would be enough for me to start doubting Julius Caesar's existence.
Let's turn to the probabilities.
1) P(no crypt|no Julius Caesar) ~ 1. P(no crypt|Julius Caesar) = ?
It doesn't look like there's some way to easily estimate that quality. I notice that I'm confused, but let's try anyway. It's possible to convert this probability into the relative frequency: there were cases of some monarch's bodies having been removed from their graves. I know two such cases: False Dmitriy I of Russian Tsars and Akhenaten of the Eighteenth dynasty of Egypt. Counting the other people of their lineage gives the approximate figure around 2/350 which I consider kind of satisfying, though it appears to be somewhat higher than desired. However, I had to consult Wikipedia to get this estimate, and that kind of violates the "no gathering other relevant real-world data" rule.
2) and 3) P(no mention of Caesar in the Arabic book|no Julius Caesar) ~ 1 P(no mention of Caesar in the Arabic book|Julius Caesar) = ?
I have trouble estimating that at all. I have no slightest idea how to estimate this without a lot of imaginary betting, and imaginary betting kind of defeats the whole point. Why shouldn't I estimate P(Julius Caesar existed) via betting?
Well, betting makes sense only when my utility function is linear in money, and that holds only when the probabilities are sufficiently close to 0.5. Maybe I should break my prior into several parts via Good's device and then estimate the parts via betting.
It seems plausible. However, I think that if Jaynes had meant his exercise to be done in that way, he would have explicitly told so.
I notice that I'm confused. Let's try to find my mistake:
1) The alternative hypothesis "Julius Caesar existed" is too vague, and hence it is difficult to come up with the conditional probabilities. It seems likely, but I can't come up with something better.
2) The experiment is bad. I should think about something else: for example, I draw a random portrait of Roman emperor from the urn containing portraits of every Roman emperor, how many non-Caesar's portraits are enough? Coming up with something like that seems very difficult for me. I'm very bad at selling non-apples.
This is a reason I wanted to find a new perspective and don't wanted to spoil anyone by anchoring him/her to my vision.
3) The evidence is bad. I should come up with some new evidence such that I can calculate the probability P(E|Julius Caesar)
4) There is a good way to estimate conditional probabilities, I just missed it.
I haven't worked much with the other cases, but it seems that it would be difficult to calculate their relevant probabilities as well (how can I calculate anything about geology in (3), for example?). So I think that I've misunderstood something, and maybe someone there can describe the correct way of doing this exercise to me.
It seems to me that it would be more effective to work from evidence that you have encountered personally or in the case of hypothetical evidence, could have hypothetically encountered. In the case of historical figures, unless you happen to be an archaeologist yourself, the majority of the evidence you have is through secondary and tertiary sources. For example, if a publication alleged that Julius was a title, not a name, and was used by many Caesars, and thus many acts attributed to the person Julius Caesar were in fact performed by separate individuals, you would probably have little reason to believe this. If a great number of publications, especially from respected organizations and individuals within the archaeological field posited the same thing, it might be sufficient to give you pause (it would for me in any case).
It seems to me that the intent here is to evaluate a prior based on a great quantity of weak evidence. Both weak evidence directly to the contrary in sufficient quantity, or evidence that discredits the sources used to generate your prior should sufficiently alter the probability to create doubt.