= 27d567bc2d48d9f40e9ccc20ea370b15)
fiddlemath comments on Game for organizational structure testing - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (28)
Er, why would you want to do this? Do you have a specific management domain in mind, where these things actually don't matter?
If not, perhaps you can just watch what happens in carefully-selected, massively-multiplayer games? Eve, maybe?
Most people don't know the reputations or the personalities of the local councillors or board members they elect. It is these types of political situations I want to improve.
Is this a game about getting elected; about testing social structure within an existing framework?
Pretty much. You want to find a social incentive structure such that it is at least an evolutionarily stable strategy for the participants to try and maximise their teams score while being selfish agents. And is compatible with human psychology and mental limits.
Your summary does not appear to agree with mine; it seems like you want to create a game where the strategy which is personally selfish is also ideal for a group, which is wildly different from a game where getting elected scores points regardless of one's competence.
One solution would be an incentive system that managed to reward each individual proportionately to their contribution to the group; that roughly reduces to free-market capitalism, which appears to be bad at the intended goal (based on previous results). Does that issue boil down to difficulty determining the value of each person's contribution to total welfare?
I didn't quite get your message, so I think I interpretted it incorrectly.
My goal is a game where different organizational structures can be compared for effectiveness.
One of organizational structure would be voting. In this structure getting elected would be a win of some sorts. In another structure there would be a different win condition. Seeing which type of win conditions and rules motivated people the best, is the reason I want to make the game.
I agree there is problems with free market capitilism as it is currently practised. However there are lots of knobs we could twiddled about how they work. E.g. fractional reserve banking or long term land ownership and other monopoly issues. If we could try out these changes on a smaller scale and they are successful compared to our current systems, then we might be able to convince people to make real changes later on.
My point was that a system where people want to maximize their chances of getting elected is wildly different from a system in which people want to elect the person which maximizes group utility.
The bonus for getting elected in a democracy would have to come either out of a higher-sum total or at the cost of someone else in the group, not be free. Assuming all candidates are equally qualified and every voter has full knowledge, the person who believably promised the best kickbacks would end up elected, right? Any leader who took kickbacks for himself could be outbid by one that took smaller kickbacks- but at some point it would be better to be on the receiving side of the pork.
To find the winner in a democracy (with perfect knowledge, identical values, and fungible utility), determine how much total utility each person will generate if elected; the winner is the person who can maximize the total score; he distributes to half of the voters, excluding himself, as much as the second-place leader could have, plus epsilon, and takes the remainder for himself. The second-place leader and half the voters earn epsilon more than he would have if he were elected, and just under half the voters get nothing.
If we define the total score to be equal to the sum of the square roots of each individual's effort put forth, and the effort put forth by an individual to be equal to the log of their final expected score, (forcing a lower bound of 1 effort), that makes the total wealth generated by a democracy dependent on how it is distributed; can the leader of a democracy outperform the electorate under those rules?
Formal proposal: Teams consist of n characters, each of which understands the rules. The total score of the team is equal to the sum of the square roots of the 'effort' produced by each team member, and the effort produced by each team member is proportional to the expected log10 of the score assigned to that member by the leader. (Production is exponentially more expensive, and rewards are logarithmically less rewarding) (Method of determining score need not be deterministic) (individuals need not have the same proportionality constant relating score received and effort, but each team has an identical set of members) A) What form of distribution results in the highest maximum score for the team? Is it possible to have a team of n score higher than n times what a team of one scores? B) What method of selecting a dictator/distribution method results in the form of distribution that maximizes the team score, given that every individual is selfish and wishes only to maximize their own score?
Not sure if this is fruitful path (we would need to justify the logarithm and square root empirically). But it is an interesting problem. Assuming each person is equally productive for now. In pseudo code
S = score
P = vector of proportions
sum ( sqrt (log (p*S)) ) = S
This can be simplified (if my rarely used math muscles are correct) to
sum ( sqrt( log pi + log S) /S) = 1
I can't see anything to solve it analytically easily. So let us assume that we have 3 people and they are equally distributed to for now. As I expect this is the maxima?
sqrt(log(1/3) + log(S) ) / S - 1/3 = 0
Newton's method isn't being very helpful at the moment. I'll try some other numerical methods tomorrow.
Hmm. Wolfram Alpha suggests it doesn't have any positive solutions. Have I made an error in the maths?
Generalizing a bit more: Each player has an effort function E(s) which determines how much effort they exert based on their expected score; they also have a production function P(e) which determines how much they add to the team production based on their effort. (These two functions can probably be combined for all intents and purposes) Further, the team has a score function S(p), describing the total score of the team based on the total of the team member's production.
With a few constraints on those functions, I think I can guarantee at least one solution: All three functions are continuous, strictly increasing, and their first derivatives approach zero as the independent variable tends towards infinity. The form of group leadership divides the group score S among the individuals according to the methodology of leadership: a dictator chooses the distribution which maximizes his own score; each type of democracy selects the distribution which maximizes the score of enough of the team to win the election; a pure socialism divides the team score evenly between the members; a different system divides the score proportionately to each member's production; and the ideal system divides the score in such a manner as to maximize the team score.
Another possible formulation is if E is a function of expected proportion of score. People seem to be interested in relative status and also this would also stop the crazy feedback loop and possible unintuitive things like working harder when someone else is working with you than you do on your own (if they are a lot better at getting score than you and so increase your expected score, even taking a share).
I still favour empirical testing to see how people actually behave.
taking the log of something less than one gives a negative result. I'm too tired to do the math right now, but I'll give it a shot when I can.