Making something illegal is sure to help stop people from doing something. In this case, criminalizing the denial of the holocaust would stop some people from doing so. The less people denying the holocaust, the more the argument against the holocaust being a real event is muffled. While there will always be people risking legal action or a bad reputation, the law against it will surely help.
There's reason to criminalize thought and speech. Why throw people in jail for simply stating their opinion? Actually performing a holocaust is still illegal in almost all countries besides for ISIS and Australia. The lady doth protest too much methinks. Dealing with distasteful comments is part of living in a free country. And as we all know freedom isn't free, it actually costs a buck o' five.
It will silence some deniers but the truth will prevail. Throughout history many great lies have been exposed. Nowadays most people think everything they are taught or they hear is true. But, I can see countries criminalize this issue a it's not surprising because especially lies as big as holocaust need to be exposed to everybody.
I see no lawsuit against people who deny the apollo landing or the people who thinks santa is real.
I see no reason as to why many countries would go so far as to criminalize the denial of holocaust if they truly believe that holocaust happened?
Criminilization will not stop the truth from coming out.
I don't think that criminalization does not help muffle holocaust deniers, in fact it probably would make it worse. I think if this were actually enforced it was cause a lot of commotion and protest. This would cause a divide between different political and religious associations. Criminalization of the denial of the holocaust would be way too extreme.