Topic: Nontransitive Bits (Read 149 times)

There's an idea that I still like. I call it nontransitive bits. A bit is 0 or 1, an nontransitive bit would be 0,1 or 2 (up to n) and there goes a definition with it that 0 wins against 1, 1 wins against 2, and 2 wins against 0. The idea is just that it should be the same situation as with nontransitive dices: you can chose the right dice, but overall no dice is the best, no dice is the worst either. (when n=2 it's rock-paper-scissor.)

I hope you understand what I mean, because i think I'm not so good at explaining my ideas.

Now we would need a list of nontransitive bits from 1 to n, for example from 1 to 100. This represents the wallet.

Here's the idea for sending money:

- Your wallet is what you think is "state of the art" information, you assume that this wallet is the best to win battles (send money).
- In a battle there is at first nobody who is to send, or who is to receive money. At first it's all balanced and equal from the game's perspective.
- The winner is the one who "knew" more (explanation below)

One of the battlers starts with list item 1. He sends to the other battler the bit. One of the bits win. Then the second battler does the same for list item 2. It's repeated for a certain number of rounds.

The important point of all this:
If both battlers have not previously leaked any information and still one of them wins by a statistically significant margin, then there is only one conclusion:
The "winning" information must have come from other battlers, that is, from battlers that the defeated battler had a battle with (they had a money transaction). The idea is that then one of the battlers should be able to improve (update) the other battlers information in regards to the rest of the world.

Another point is: The wallet would age, I assume.

Some improvement of the sending process:
- When Alice sends Bob money (nontransitive bits, NB), Alice is the one who should tend to leak information, and Bob should tend to control the process.
- So when Alice wants to send Bob 1000 NB, Bob is allowed to send Alice a list of (random) indices that she has to answer. Alice will reply with the corresponding NB list, e.g.
745=0,324=2 etc. Bob can then check if a significant number of NB win and determine the worth of it to him (like if Alice would go to the pawnshop owned by Bob).

What do you think about this?