If you are aiming for fairness, I would recommend the approach recommended by Barry Nalebuff in his book “Split the Pie”. The idea is that you are creating a “pie” of value by coming together as opposed to going separately. Whatever that pie is, you should split equally.

To figure out the size of the pie you would need to figure out what the cost would be to each party alone vs what the cost would be going together. You then take the difference and split it equally. In your case it would be split 3 ways because there are 3 parties. In a simple case if each of the 3 parties could get there separately for $100 each ($300 total) or get there together for $125 (perhaps it would cost more for gas with everyone), the savings ($300 - $125 = $175) would be split 3 ways and each party would save $58.33 and pay $41.67. So in this simple case the right way is to split the cost in thirds.

This makes it simple and it’s usually close enough.

For fun, here is a more complex example of splitting the pie.
Let’s say one couple has a Tahoe and can get there for $100. Couple 2 has a Camry and can get there for $80 The solo friend has no car and would need to Uber for $150. If you can take the Tahoe all together for $125, the total pie you are saving is ($100 + $80+ $150) - $125 = $205. You split this pie equally so each party saves $68.33

This means party 1 pays $100 - 68.33= $31.67

Party 2 pays $80- 68.33 = $11.67

The solo fried pays $150 - $68.33 = $81.67

I get it, this method is too pedantic for a situation like this. It does provide a framework for an absolutely fair way to split cost between parties. Fairness often goes beyond splitting it proportionally or splitting it evenly among parties. This isn’t the simplest method but it is absolutely fair.