Logarithmic Versus Linear Pricing in Prediction Markets

Summary

The document asks whether a binary prediction market can quote trades with a linear cost rule instead of Hanson's logarithmic market scoring rule (LMSR). It describes a coin toss with heads and tails payouts and proposes a cost formula based on the proposed bet size and the existing quantities on each side. The author suggests that a linear rule may be computationally more efficient and asks what disadvantages it would have compared with a logarithmic rule.

No answer, derivation, comparison, or empirical evidence is provided. In particular, the document does not establish whether the proposed rule produces coherent prices, guarantees market liquidity, or limits the market maker's loss. It is useful as a prompt about prediction market design, but traders or researchers would need additional analysis to assess the formula or compare it with LMSR.

Key ideas

• The document contrasts logarithmic market scoring with a proposed linear cost rule for a binary outcome.
• The proposed rule uses bet size and existing quantities on each outcome to determine a trade cost.
• The author raises computational efficiency as a possible advantage of linear pricing.
• The document does not answer how the two approaches compare in market behavior or risk.

Tags

# Why are prediction markets based on logarithms when a linear solution can suffice?


# Why are prediction markets based on logarithms when a linear solution can suffice?












For example, take a binary outcome; A coin toss, heads or tails.

If heads, then those that picked heads receive \$1 and tails receive \$0. To quote the prices for each bet Hanson's LMSR uses logarithms.

Isn't it simple enough to quote the price using a linear model?

For example, in a linear model, the cost for placing a bet on heads is: `x * (q_heads + x) / (q_heads + x + q_tails)`

Where `x` is the amount of bets to place, `q_heads` is the amount of existing bets placed on heads and `q_tails` is the amount of existing bets placed on tails.

Computationaly this is far more efficient. What are the disadvatages to using a linear market scoring algorithm vs a logarithmic scoring algo?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.