The short answer is that peoples behaviours with respect to money do not meet the requirements of the definition of 'utility' in a formal sense.

I've often seen the somewhat arbitrary number 95% used as a standard for confidence levels and statistical significance. Does this suggest that a willingness to be wrong once in twenty is efficient and reasonable -- beyond reasonable doubt? If so, then the likelihood of an actor risking a gamble should be near zero until p(success) nears 0.95 or above.

The weight of the prize is only temptation. It could be used to rank potential prizes of equal risk, but not differing risk. Of course the concept of equality in a continuous number is subject to granularity. Perhaps +/- 2.5% giving a 5% band would be appropriate in this example.

In other news, according to this wiki on parachutes, the US fatality rate those risk takers willingly perform is 1:80,000.

[Edited by - AngleWyrm on April 18, 2008 3:50:00 AM]

Quote: Original post by Timkin
The short answer is that peoples behaviours with respect to money do not meet the requirements of the definition of 'utility' in a formal sense.

That's fine, because I'm purely working on an abstract level. I just need to curve that graph slightly.

Not sure how useful this'll be (and you may already be familiar with it and have considered it...) but it struck me this bears some similarities to The Knapsack Problem. Though I suspect much of your effort is devoted to ensuring it isn't the same (NP-Hard) problem.

Yeah, this occurred to me when posting on someone else's thread about assigning people to teams. But as you hint at, since I don't have any exact variable I need to optimise, I don't necessarily need to worry about finding a solution to doing exactly that.

My current prototype is interesting because it shows how poor the initial estimations of a task are. A task that looks like it would require about 8 average people might be feasible with only 1 or 2 experienced people, so I tend to get a lot of small groups of experts. I guess a lot of this is domain specific though; if I introduce more tasks that only the experts can do, and ensure there is a reward commensurate with the increase in difficulty, that should give the little guys more opportunity to take on the smaller jobs.

Quote: Original post by Timkin
Start with a random seed of agents to tasks (including DEFER) and then allow each agent assigned and not assigned to make a choice about which task to go to. All agents make their decision at once given the current assignments. Agents should choose the task to move to that would maximise their expected reward given the current assignment of agents to tasks.

In this simple approach you are not guaranteed to converge on an stable assignment of agents to tasks... but you should be able to get something that looks reasonable within a few iterations. You can damp the assignment dynamics by adding a cost to change groups, or limiting the number of times an agent can change (staying doesn't count as a change).

I finally got around to trying this. Unfortunately the behaviour is always as follows:

- Then, at the first opportunity to move from the random assignments, the more skilled people move to the best looking group. The less skilled move to the DEFER group.
- On the second iteration, the skilled stay where they are, and the unskilled all join their group.
- On subsequent iterations, nothing changes. Nobody can unilaterally leave this group and get a better deal elsewhere without others coming with them.

Quote: Original post by Kylotan
I finally got around to trying this. Unfortunately the behaviour is always as follows:

- Then, at the first opportunity to move from the random assignments, the more skilled people move to the best looking group. The less skilled move to the DEFER group.
- On the second iteration, the skilled stay where they are, and the unskilled all join their group.
- On subsequent iterations, nothing changes. Nobody can unilaterally leave this group and get a better deal elsewhere without others coming with them.

Well, at least we know there IS an equilibrium solution... it just shows that your problem design doesn't admit a useful solution!

The problem you're having is that a task with many participants still has a finite value to a skilled participant, whereas a currently empty task has an effectively zero value for anyone.

Basically your assessment of task value isn't workable (useful for making decisions within this problem). If the unskilled join a group with skilled participants, you would expect that the value of the task has dropped for the few skilled members. The most highly skilled of these should be looking for an empty task/group or one with only a few members. You don't want them to leave as a cohort for a single other task, because then the unskilled will simply follow on the next iteration (which is what is happening in your first and second iterations above).

I would think the solution is one that has been suggested before... make skilled participants greedy (in that they don't want hangers on) and make unskilled participants sly (they don't want others to get in on their free ride).

Yeah, the approach where actors pick groups in competence order, but are only added to the group if the value doesn't drop for any of the existing members, works ok. The groups look a bit predictable so I may randomise them a bit after the fact, but at least they are workable.