3 ms·

I've been thinking about the cake cutting problem recently, with a bit more "physical world" and dexterity in mind. Even in the two-player version, one can add

I've been thinking about the cake cutting problem recently, with a bit more "physical world" and dexterity in mind. Even in the two-player version, one can add few more criterion. * Cutting a cake is a skill; it takes an effort (thus associated cost) and you may not be accurate at cutting it. There may be some error bound epsilon. * If so, in the traditional "I cut you choose" model, as there are risks associated with cutting (what if you intend fairness, but you ended up with lopsided 49:51 cake due to an error?), one may not volunteer to cut the cake; if so, how can we encourage / compensate one to cut the cake? * The "skill" can go both ways; it takes an effort to figure out which cake is bigger - even more then the cut itself. both parties may volunteer to cut the cake. if so, how can we encourage / compensate one to be the chooser?

deleted 3y ago
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videogreg93 3y ago
Assuming a homogeneous cake, I think you can get around this by cutting the cake in half, and then cutting a line perpendicular to that one. Each person takes 2 pieces that touch each other diagonally, which should in theory give each person half of the cake.
- lupire 3y ago
  That requires "cutting the cake in half", which is begging the question, and also makes the second cut irrelevant. If the first cut is not a true half, then the method doesn't work. It gives you equal perimeter cuts, nt equal area cuts. That method is slightly better than making only one cut, though.
MichaelZuo 3y ago
> If so, in the traditional "I cut you choose" model, as there are risks associated with cutting (what if you intend fairness, but you ended up with lopsided 49:51 cake due to an error?), one may not volunteer to cut the cake; if so, how can we encourage / compensate one to cut the cake? Why is that important? There's always someone willing to step up to the plate, if person A doesn't want to, then person B, or C, etc...

deleted 3y ago

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videogreg93 3y ago

Assuming a homogeneous cake, I think you can get around this by cutting the cake in half, and then cutting a line perpendicular to that one. Each person takes 2 pieces that touch each other diagonally, which should in theory give each person half of the cake.

lupire 3y ago
That requires "cutting the cake in half", which is begging the question, and also makes the second cut irrelevant. If the first cut is not a true half, then the method doesn't work. It gives you equal perimeter cuts, nt equal area cuts. That method is slightly better than making only one cut, though.

MichaelZuo 3y ago

> If so, in the traditional "I cut you choose" model, as there are risks associated with cutting (what if you intend fairness, but you ended up with lopsided 49:51 cake due to an error?), one may not volunteer to cut the cake; if so, how can we encourage / compensate one to cut the cake? Why is that important? There's always someone willing to step up to the plate, if person A doesn't want to, then person B, or C, etc...