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How do you evenly split a quantity of something (e.g. drugs) when you have no scales? One person does the splitting, then presents both halves to the other pers

by Jedi72 8y ago

How do you evenly split a quantity of something (e.g. drugs) when you have no scales? One person does the splitting, then presents both halves to the other person, who can choose either one as the half they keep. Everyone is incentivized to transact as fairly as possible.

bryanrasmussen 8y ago
The problem is that cake cutting means that the solution that is most preferred by both parties is chosen, and who are the parties doing the choosing. The incumbent member of a party doing the cutting and the incumbent member of another party doing the choosing. whatever solution comes out of that will be most liable to help incumbency.
- taejo 8y ago
  Exactly! Gerrymandering is often seen as one party stealing votes from the other, but really the more important problem is that elected officials are stealing power from the electorate. In some cases officials of the two parties are even happy to collaborate to achieve this.
  - zerebubuth 8y ago
    I think you're absolutely correct! In each round, I reckon the optimal strategy for the "cut" will likely be the same as partisan cuts are now; densely pack the opposition's supporters into a small number of districts, while slicing the rest up to have a small but stable majority for one's own party. This gives the opposition the chance to choose/freeze either a district they know they'll win, or a district they're pretty sure they won't win. I would choose the one I know my party would win, and redraw to pack all my opposition's voters into as few districts as possible. If this is repeated a few times, the map ends up with many safe districts for each party and a small number of "left-overs" which will be contested. This means parties will have an incentive to concentrate on the small number of voters in the few contestable districts, at the expense of probably the majority of voters. It doesn't seem like a recipe for every vote counting and voters' voices being listened to. If we break up monopoly businesses when the lack of choice increases the cost to consumers, should we also break up monopoly parties when the lack of choice increases the "cost" in time and effort that voters must "spend" to get their issues dealt with?
  - barking 8y ago
    Same thing can happen in countries where the state funds political parties and outlaws large private/corporate donors. The funding is given according to how many seats each party already has and so favours the status quo.
  - bryanrasmussen 8y ago
    I believe that cake cutting would improve on the current situation, when it is the incumbents of one party cutting and choosing, but it is not a full solutions to all the problems in the space.
  - Eridrus 8y ago
    Beyond just incumbents - this would favor whatever the party favors, since it still let's you pack and crack anti-establishment forces in your primaries. Though I think primaries are a real cause of our polarisation.
pryce 8y ago
My older brother's "solution" to being told he must cut the cake and let me choose which half to take was: a sloped cut similar to the one in this picture [1] but which slightly exaggerated the uppermost surface area of the smaller volume. An analogous tactic against this "I-cut-you-freeze" task might be to provide especially appealing district boundary for your opponent to freeze, while harbouring some knowledge about that district that that your opponent is unaware of (eg suppose that you know the trajectory of demographic changes much better than your opponent) [1] https://imgur.com/a/Doy6lPg https://imgur.com/a/Doy6lPg
- JulianMorrison 8y ago
  Informational asymmetry seems unlikely though. It would require one or other party to be asleep on the job.
- empath75 8y ago
  The competence of the participants to judge the slices is outside the scope of this. If one of the parties doesn’t know what they’re doing, that’s their problem.
- sorokod 8y ago
  I think that the underlying assumption is that cutter and freezer have utility functions they believe in.
learnstats2 8y ago
In the politics example: 1. The party with more knowledge about how people vote can game the system. This is not a desirable feature of an electoral system. 2. This proposed method depends on a two-party system. There are cake cutting methods for more parties, but they take arbitrarily long to solve.
- wool_gather 8y ago
  What do you mean by "arbitrarily long"? There's this related procedure for N cake eaters, which is straightforward: 1. Arbitrarily choose an order 2. Repeat while not everyone has a slice: a. First person without a slice cuts a slice b. Each other person, in order, who's without a slice may either take the slice or pass it c. If everyone else has passed, the cutter must take that slice It's quadratic time -- worst case you go fully around the (remaining) circle for every slice -- but that's still not a very big number even for four or five political parties. How many parties are there actually going to be? (I'm not exactly sure how this maps to the article's scheme, either; the point is that I'm not sure it's all that complex.)
  - learnstats2 8y ago
    From the relevant wikipedia page: "envy-free divisions of connected intervals to 3 or more people cannot be found by any finite protocol." - I can agree that your algorithm is quadratic, and therefore, that your algorithm is not envy-free. Your suggested algorithm seems to be unfair because the first party to choose has a clear advantage over the parties who choose later and did not cut: depending on the order of the parties there is also likely to be collusion. The immediately easiest (and politically realistic) way to game your system is to split yourself into multiple parties and then cut your allies/sock puppets a massive slice.

by Jedi72 8y ago

bryanrasmussen 8y ago

The problem is that cake cutting means that the solution that is most preferred by both parties is chosen, and who are the parties doing the choosing. The incumbent member of a party doing the cutting and the incumbent member of another party doing the choosing. whatever solution comes out of that will be most liable to help incumbency.

taejo 8y ago
Exactly! Gerrymandering is often seen as one party stealing votes from the other, but really the more important problem is that elected officials are stealing power from the electorate. In some cases officials of the two parties are even happy to collaborate to achieve this.
- zerebubuth 8y ago
  I think you're absolutely correct! In each round, I reckon the optimal strategy for the "cut" will likely be the same as partisan cuts are now; densely pack the opposition's supporters into a small number of districts, while slicing the rest up to have a small but stable majority for one's own party. This gives the opposition the chance to choose/freeze either a district they know they'll win, or a district they're pretty sure they won't win. I would choose the one I know my party would win, and redraw to pack all my opposition's voters into as few districts as possible. If this is repeated a few times, the map ends up with many safe districts for each party and a small number of "left-overs" which will be contested. This means parties will have an incentive to concentrate on the small number of voters in the few contestable districts, at the expense of probably the majority of voters. It doesn't seem like a recipe for every vote counting and voters' voices being listened to. If we break up monopoly businesses when the lack of choice increases the cost to consumers, should we also break up monopoly parties when the lack of choice increases the "cost" in time and effort that voters must "spend" to get their issues dealt with?
- barking 8y ago
  Same thing can happen in countries where the state funds political parties and outlaws large private/corporate donors. The funding is given according to how many seats each party already has and so favours the status quo.
- bryanrasmussen 8y ago
  I believe that cake cutting would improve on the current situation, when it is the incumbents of one party cutting and choosing, but it is not a full solutions to all the problems in the space.
- Eridrus 8y ago
  Beyond just incumbents - this would favor whatever the party favors, since it still let's you pack and crack anti-establishment forces in your primaries. Though I think primaries are a real cause of our polarisation.

pryce 8y ago

My older brother's "solution" to being told he must cut the cake and let me choose which half to take was: a sloped cut similar to the one in this picture [1] but which slightly exaggerated the uppermost surface area of the smaller volume. An analogous tactic against this "I-cut-you-freeze" task might be to provide especially appealing district boundary for your opponent to freeze, while harbouring some knowledge about that district that that your opponent is unaware of (eg suppose that you know the trajectory of demographic changes much better than your opponent) [1] https://imgur.com/a/Doy6lPg https://imgur.com/a/Doy6lPg

JulianMorrison 8y ago
Informational asymmetry seems unlikely though. It would require one or other party to be asleep on the job.
empath75 8y ago
The competence of the participants to judge the slices is outside the scope of this. If one of the parties doesn’t know what they’re doing, that’s their problem.
sorokod 8y ago
I think that the underlying assumption is that cutter and freezer have utility functions they believe in.

learnstats2 8y ago

In the politics example: 1. The party with more knowledge about how people vote can game the system. This is not a desirable feature of an electoral system. 2. This proposed method depends on a two-party system. There are cake cutting methods for more parties, but they take arbitrarily long to solve.

wool_gather 8y ago
What do you mean by "arbitrarily long"? There's this related procedure for N cake eaters, which is straightforward: 1. Arbitrarily choose an order 2. Repeat while not everyone has a slice: a. First person without a slice cuts a slice b. Each other person, in order, who's without a slice may either take the slice or pass it c. If everyone else has passed, the cutter must take that slice It's quadratic time -- worst case you go fully around the (remaining) circle for every slice -- but that's still not a very big number even for four or five political parties. How many parties are there actually going to be? (I'm not exactly sure how this maps to the article's scheme, either; the point is that I'm not sure it's all that complex.)
- learnstats2 8y ago
  From the relevant wikipedia page: "envy-free divisions of connected intervals to 3 or more people cannot be found by any finite protocol." - I can agree that your algorithm is quadratic, and therefore, that your algorithm is not envy-free. Your suggested algorithm seems to be unfair because the first party to choose has a clear advantage over the parties who choose later and did not cut: depending on the order of the parties there is also likely to be collusion. The immediately easiest (and politically realistic) way to game your system is to split yourself into multiple parties and then cut your allies/sock puppets a massive slice.