Proposal: Implement Multiple choice with binary contracts for each answer

The UI can be very similar to current multiple choice
- All grouped on the market page, with Yes/No buttons for each answer
Costs M$50 per answer you add (used as initial liquidity for each binary market)

Pros

Uses the same binary mechanism, so less technical debt
Automatically get support for limit orders, liquidity subsidization, daily changed, etc
Supports the use case of resolving multiple answers to Yes, in addition to resolving only one to Yes
- E.g. Which products will Apple launch at WWDC? Can resolve Yes to both ipad and iPhone. Best you could do with current multiple choice is resolve each to 50%.
Can extend to Numeric
- In create page, choosing Numeric type lets you set up a series of numeric thresholds, each of which is a binary market
- This is really what traders want: simpler to bet on thresholds, and gain more leverage for higher returns than current pseudo-numeric
  - Rather than betting on specific buckets, they want to bet: will quantity be less or greater than threshold?
- Can deprecate Pseudo-numeric
- [A] Unsure - there are multiple use cases for pseudo-numeric, I think

Cons

Requires a bit more liquidity to get started?
- Not really true: multiple choice with many answers also requires more liquidity
Have to arbitrage to sum percentage to 100%
- But this is not so bad, because often you want to bet on each answer separately.
  - E.g. Jack asked how to bet the first answer to 40% and the second to 20%. With CPMM multiple choice, you have to make a series of bets to try and get them to both align. With binary, you just bet each one separately.
- [A] Think this one is pretty key — it’s kind of a bad experience to make users think about bidding down on all the others
  - [i] I think it’s not that big of a deal
  - [S] The point of AMMs is to handle the mechanical adjusting for you, to not have big arbitrage activities after you bet
  - [J] After thinking about it, it is a bit of a disadvantage. There is a way for us to still do it though:
  - [J] If we know from the contract creator that exactly one answer will be chosen, we can implement this arbitrage for you when you bet, so you don’t lose out.
    - After your YES bet brings total above 100%, buy equal shares of NO in each answer s.t. total prob equals 100.
    - Since all markets except one get resolved NO, you can immediately convert those shares to (n-1) * shares dollars. This is a new kind of redemption.
    - For the opposite case of someone buying NO bringing the total below 100%, buy equal YES shares in all answer s.t. prob equals 100. Then redeem those YES shares for equal M$, since one of the answers will be chosen.

Next steps

Deprecate new Multiple choice
1. Set new multiple choice to be created with old mechanism
2. Swap out World cup markets to old multiple choice
3. Resolve all new multiple choice to N/A
4. Delete all new multiple choice markets
  1. Script that also removes subcollections, and removes from group-contracts

See Discord discussion:

https://discord.com/channels/915138780216823849/918236290439335936/1044508272360706068

Alternative