Representation Of State¶

Introduction¶

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

Traditional prediction markets record token balances first and economic exposure is then derived from those balances.

PredictionSwap records economic exposure 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 economic exposure can arrise from different collections of tokens.

The Exposure 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 an Exposure Vector?¶

A payoff function defined over outcome space.¶

For an event with outcomes:

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

an exposure 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 exposure vectorfully describes economic state.

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 positon 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.

Exposure Representation¶

PredictionSwap stores:¶