Prediction market based on LMSR: Sell, or buy other side?

Question

Consider a prediction market with two outcomes (Yes and No) and a scoring rule based on Hansons’s LMSR, i.e. ln(e^a+e^b), where a and b are the number of Yes resp. No shares sold.

Assume that I have previously bought 10 Yes shares, but now I changed my mind and want to bet on the other side. I have the option to either sell my 10 yes shares, or buy 10 no shares.

When should I choose one or the other option? Is it always the same, or does it depend on, say, the current market?

Answer 1

For the market it does not matter, the prices/chances change exactly the same: e^a-10/(e^a-10+e^b) = e^a/(e^a+e^b+10).

For you as the trader, selling 10 yes shares is preferable. It means you get your money out and can invest it elsewhere.