An experiment showed that people often lie about the result of a secret die roll if it benefits them. 

The takeaway for board game designers, according to BoardGameNews:

“If you want someone to be honest, then do not allow him to roll a die in secret.”  

http://boardgamegeek.com/blogpost/9382/links-flash-mob-game-reviews-the-hasty-cheater-ye

RELATED:

Preventing cheating: Is the honor system sufficient?

http://cardboardedison.tumblr.com/post/19570523236/preventing-cheating-is-the-honor-system