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Logarithmic Market Scoring Rule is a type of scoring rule that can be used to extract good probability estimates from individuals or groups in a betting market. This scoring rule is logarithmic and maintains the probability of an event and the conditional probability of another event. In addition, estimates can be obtained for all combinations of basic events at no additional cost. The purpose of these market scoring rules is to effectively aggregate modular combinatorial information. The problem with betting markets is that it is a zero-sum game of "my gain is your loss." In the latter case, rational people would not bet on them.
Normal speculative markets like the stock market are excellent at aggregating relevant opinions and information and reflecting them in market prices, which represent estimates of collective probabilities.
However, when markets become thin, such as in the case of a market for rotten mushrooms that few people trade in, liquidity problems arise. That is, the market price does not represent important collective probability estimates because there are too few people trading.
Scoring rules are very effective in eliciting individual evaluations of probabilities related to events. Scoring rules are based on the principle of mercenaries: the better I predict future events, the higher my score and the greater the monetary reward I receive for it. It also means how to define the outcome that end users are looking for in prediction markets. The existence of market makers turns the market into a positive-sum game and provides incentives for rational traders to participate. In addition, participants can trade with market makers at any time if they find the current price attractive, overcoming the obstacle of thin trading.