Apparently there is a way, but it's complicated and probably doesn't translate from cake to maps (you don't end up with neat slices, but rather a collection of different sized pieces):

https://www.quantamagazine.org/new-algorithm-solves-cake-cut...

And it's not clear if one of the cake cutters could sacrifice their own slice to benefit one of the others (in return for a bribe).

One could almost be certain there would be some underhanded quid pro quo with this situation.

> Is there a way to cut a cake between 3 people with this sort of approach?

Cake? Maybe. Equal-population single-winner firdt-past-the-post political districts, no. But that's okay, because single-winner districts don't practically support more than two competitive parties, especially when you have separately elected statewide and national executives rather than a parliamentary system.

Of course, get rid of single-winner FPTP districts, and you not only can support more parties, you make gerrymandering mostly pointless, even if you do still have districting.

I'm starting to think FPTP is at the root of all of our problems.

It's pretty bad if you consider the repeated action of electing candidates who do not represent nearly 50% of the electorate

You could do it the Settlers of Catan way.

(Suppose four players, P1 to P4. They each get to place two settlements, and there's an advantage to getting first pick. You place settlements in this order: P1, P2, P3, P4, P4, P3, P2, P1)

Now, there is a cake (map) to cut, and 4 parties. P1 draws one line, then P2, then P3. Then, each party picks one of the 4 slices, starting with P4.

Yes, “envy-free” cake cutting.

https://en.m.wikipedia.org/wiki/Envy-free_cake-cutting

Ha, the "Robertson–Webb rotating-knife procedure" sounds like a move from Kill Bill.

The two parties run the organization which works to keep any other parties out of televised debates. They don't care what anyone thinks as long as both parties agree to cooperate on screwing everyone else over. They're willing to have an uneasy truce with each other at the expense of all others.

IIRC the three slice solution is: I cut a piece. You decide if I get the piece or half of what’s left. The third guy cuts and whoever else doesn’t have a piece now, choses.

There is a general solution. Im not sure how you could apply it to creating districts for voting though.

https://www.youtube.com/watch?v=kaMKInkV7Vs