In designing such systems, you need to be very careful about assymetry. Profit-sharing generally has a lower-bound, so it can never turn into loss-sharing, which means that averaging across time variant time periods gives very unequal results.
Very often, you can get MOST of the incentive value, and a good part of the feel-good-for-mutual-aid value, with bonus levels, rather than continuous or linear sharing or attendance pay. For instance "$x base, +$y if attendance over z, +$w if attendance over v". And stop there (perhaps negotiate separately for established superstars). This is simple, pretty safe, and gets the incentives aligned just as well as a more formulaic pay structure.
I know nothing about dance-performance pay structures, but the "per performer" difference is odd to me - how much fixed-expense difference is there really (I presume in time to set up)? I assume, for most acts, there's no incentive effect of differential pay - you're not trying to break a quartet into two duos to get more music per player or something. So. the main payment structure should be agnostic - you pay the same amount to a duo as to a foursome, for the same size crowd at the same ticket price.
There is basically no fixed expense difference in the larger bands, at least at our scale. We rent the hall for the same amount of time for setup, have the same amount of sound equipment, etc.
Our dance, and most dances, pay per person instead of per band. I don't entirely know where that is, though I do have some guesses? Mostly I think it's that it feels like you're paying someone to do work, and there's an amount that feels fair to pay them regardless of how many other people are working alongside them?
If you switched from paying per person to paying per band, I think you would have a problem where musicians would form smaller bands even in cases where that meant the music was not as much fun to dance to. Because there is currently no negotiation on price (almost everywhere pays some fixed rate plus maybe a bonus as discussed in this post) it's pretty hard for the organizers to encourage larger groups when that makes sense.
The main push towards smaller bands today is that organizers are more likely to book them, especially in cases where the smaller band is just as fun to dance to as a larger one. I do think passing through the economic pressures that make organizers want to book smaller bands is reasonable, but given the rest of how musicians are compensated it's hard to do this in a way that doesn't exaggerate the incentive.
It's an interesting equilibrium for this - once everyone expects to be paid individually, it'll be tough to switch to the "pay for entertainment sum" model that I understand is more common for small music venues (though the rates vary pretty widely, so it may have similar effects for larger groups).
At a very basic level, your revenue per attendee doesn't change, so your ability to pay doesn't scale with number of musicians. Since you probably shouldn't buck the expectations of base pay per person, you likely need to set different bonus/incentive levels for different sizes of group, to take into account the assumption that bigger groups have more attendance (justifying their higher expense) as a baseline.
With most endeavors that have a financial component there's a spectrum of approaches that differ on how they assign risk. At the "low risk" end you have agreements to pay a specific amount ("we pay $100/person"), while at the "high risk" end it depends on how things go go ("everyone gets a share of the take"). Contra dance events generally go towards the low risk end: most of the time I'm playing for a fixed fee.
I've been thinking about this, though, because the dance I help run does profit sharing. The idea is, we guarantee $125/performer and then if there's profit left over after fixed expenses half of it goes to the performers. I wasn't around for the initial implementation, but I think there were probably two reasons:
When a band or caller draws a big crowd that's something we'd like to encourage, and we're happy to share some of the rewards with them.
How much money we have available to pay performers depends on attendance. Profit sharing means that we pay performers more, to the extent that it doesn't risk our financial health.
You don't want to go too far in the direction of sharing risk, though, because the event has most of the responsibility for attendance and is also in a better position than many of the performers to take the loss from a low-turnout dance.
While I like this system overall, a major downside is that it requires you to determine how profitable this event was before paying the performers. I mean, it's possible to just pay everyone the guarantees and sort it out later, but that means following up with people to send additional payments, which might be relatively small. So you're filling out a pretty complicated form by hand at the dance after counting the money when you'd rather be dancing.
Could we get similar effects without needing to compute profit in the moment? What if we use attendance instead? Here's how payments would look with a bonus of $1 for every attendee over 120:
The main places where these two systems differ is in their handling of large and small bands. With the current system a duo is much more likely to get additional money than a quartet, because fixed expenses are two performers lower. While I do play in a duo and would be tempted to say otherwise, I don't see a general reason to pay smaller bands more.
Another nice thing about this structure is that it's easy to tweak to keep the dance financially healthy. The threshold or per-person amount could change in either direction, and it's much less of a big deal than changing guarantees.
I don't know if our dance will switch to this, but if we do I'll plan to post back in a year or so with how it's gone for us.