Representation Of State¶

Introduction¶

PredictionSwap changes how economic state is recorded on-chain.¶

Traditional prediction markets record token balances first, and the conditional value of an account under each outcome is derived from those balances.

PredictionSwap records the account value conditional on outcomes directly.

The Traditional Representation¶

An account’s state is defined by asset balances:¶

Cash balance
YES tokens
NO tokens

State is a collection of token quantities.

The same conditional account value can arise from different collections of tokens.

The Conditional Account Value Vector Representation¶

An account state is defined by a single object:¶

\[ e = (e_1, e_2, \dots, e_n) \]

Where:

$ e_k $ represents the account’s value if outcome $ k $ occurs.

This vector is the account’s complete economic state.

What is a Conditional Account Value Vector?¶

A payoff function defined over outcome space.¶

For an event with outcomes:

\[ \Omega = \{ \omega_1, \omega_2, \dots, \omega_n \} \]

a Conditional Account Value Vector

\[ e = (e_1, e_2, \dots, e_n) \]

specifies the value of an account in each possible outcome.

Each component $ e_k $ is the account’s value if outcome $ \omega_k $ occurs.

The Conditional Account Value Vector fully describes the economic state of the account.

An Example¶

Consider a mutually exclusive outcome space:

\[ \Omega = \{R, G, B\} \]

Exactly one of these outcomes will occur.

We consider how we represent a position for Alice within this market under the traditional representation and under a PredictionSwap representation.

Traditional Representation¶

Tokens as the Primitive¶

YES–R pays $1 if $ R $ occurs, otherwise $0
YES–G pays $1 if $ G $ occurs, otherwise $0
NO–G pays $1 if $ G $ does not occur (i.e. if $ R $ or $ B $ occurs)

Alice holds:¶

3 YES–R
6 NO–G
1 YES–G
$10 cash

Payoffs by Outcome¶

If $ R $ occurs:¶

$10
+3 from YES–R
+6 from NO–G

Total: $19¶

If $ G $ occurs:¶

$10
+1 from YES–G

Total: $11¶

If $ B $ occurs:¶

$10
+6 from NO–G

Total: $16¶

Economic State¶

Alice’s economic state is therefore:¶

\[ e = (19, 11, 16) \]

This vector completely describes her economic position.

Conditional Account Value Representation¶

PredictionSwap stores:¶