I feel like you could probably 'fix' it by the following protocol: 1. Ask your participant to write down a random number. 2. After they've written that number

I feel like you could probably 'fix' it by the following protocol: 1. Ask your participant to write down a random number. 2. After they've written that number down, inform them you will guess at their number, and give them a dollar if you guess wrong. 3. Ask if they'd like to change their random number. 4. Allow them to write down their new number. The before/after would probably change the distribution, and pretty much demonstrate that people can be more random when motivated.